Passivhaus Compendium for Exam and Daily Use

Sources: Passivhaus Institut (PHI),
Passivhaus Dienstleistung GmbH (PHD)
v2.6m | page 1 | © André Harrmann | Not liable for any errors and omissions.
All references are made to PHPP Manual Version 8 (2013): [PHPP:page] www.15kwh10w.com
Annual Space
Heat Demand
Transmission
Heat Losses
Ventilation
Heat Losses
Utilization factor
for free heat gains
Solar
Gains
Internal
Heat Gains
QH = QT + QV – ƞ × ( QS + QI )
2,211 kWh/a 5,835 kWh/a 759 kWh/a 0.94 2,937 kWh/a 1,722 kWh/a
qH = qT + qV – ƞ × ( qS + qI )
14 kWh/m
2
a 37.4 kWh/m
2
a 4.9 kWh/m
2
a 0.94 18.8 kWh/m
2
a 11.0 kWh/m
2
a
QH = [PHPP:124] Amount of heat (fuel) required per year to keep building at 20˚C; Specific Annual Heat Demand qH = QH / ATFA ≤ 15kWh/m
2
a in a PH
QH,window = QT,window - QS = Window energy balance; QL = QT + QV = Total heat losses; QF = QI + QS = Free heat (heat gains); QG = QF x ƞG = useful heat gains
ƞ = Defined as the fraction of free heat that can be utilized for space heating. (Surplus heat, e.g. excess solar gains are not or only partially usable.)
ƞG = (1-(QF/QL)
5
) / (1-(QF/QL)
6
) = (1-(4,659/6,595)
5
)/(1-(4,659/6,595)
6
) = (1-0.175)/(1-0.124) = 0.94 (QF/QL=1  ƞ=0.8, QF/QL=2  ƞ=0.5) [PHPP:122,124]
Transmission
Heat Losses
Area of envelope /
building element
U-value
Temperature
correction factor
Heating
degree hours
QT = A × U × ft × Gt
2,075 kWh/a 184.3 m
2
0.138 W/m
2
K 1.0 81.9 kKh/a
QT = Calculated for each individual building element (exterior dimensions) [PHPP:115]. QT,window = Aw × U × Gt [PHPP:87]
QT,thermal bridge = l × Ψ × ft × Gt = 116.9m × -0.030W/mK × 1.0 × 81.9kKh/a = -285kWh/a  -285kWh/a / 156m
2
= -1.83kWh/m
2
a [PHPP:118]
Ψ (psi) = Linear thermal bridge heat loss coefficient, relative to the exterior dimensions, can be negative. l = length of thermal bridge
χ (chi) = Point thermal bridge loss coefficient. [PHPP:66,74,118]
ft = 1.0 if exposed to ambient air (worst case) [PHPP:55] ft < 1.0 if element is below ground or against unheated basement (reduction
for reduced temperature difference against ground is calculated [PHPP:76], typical 0.5-0.7) or adjoining other buffer zones [PHPP:55]
GT = Time integral of temperature differences between interior and outside air GT = ΔT × hours GT,Germany,PHPP-Default = 82 kKh/a
GT,monthly,5˚C = (20-5)K × (31d×24h)/1,000 = 11.16 kKh/month GT,Vancouver = 70, GT,Yellowknife = 213, GT,New York = 72, GT,San Francisco = 28 kKh/a
Ventilation &
Infiltration Losses
Ventilated
volume
Energetically effective
air exchange rate
Volumetric heat
capacity of air
Heating
degree hours
QV = VV × nV,Q × cp,air × Gt
759 kWh/a 390 m
3
0.072 h
-1
0.33 Wh/m
3
K 81.9 kKh/a
VV = TFA × average room height = Reference volume of the ventilation system = 156m
2
× 2.5m = 390m
3
(A standard residential room
height of 2.5m is used for calculation purposes – larger values would result in excessive exchanged air volume.) [PHPP:119]
nV,Q = Energetically effective air change rate (for Heat Demand calculation) = nequiv. equivalent air exchange = ventilation + leakage
nV,Q = nV,System × (1 - ϕHR) + nV,Rest,Q = 0.300h
-1
× (1 - 0.82) + 0.019h
-1
= 0.072h
-1
ϕHR = Overall heat recovery efficiency [PHPP:119,124]
nV,system = Average air exchange rate of the ventilation system = 0.4h
-1
default value for residences [PHPP:119] or calculated [PHPP:105]
nV,Rest,Q = Infiltration air change through envelope leakage = 0.6×0.07 = 0.042h
-1
default value at 0.6ACH [PHPP:103]
Solar
Gains
Reduction
factor
g-value
(= SHGC)
Gross window
area
Global solar
irradiation energy
QS = r × g × AW × G
2,489 kWh/a 0.44 0.5 30.4 m
2
370 kWh/m
2
a
g = SHGC = Total solar energy transmission coefficient for the glazing at a normal to the irradiated surface. From Windows worksheet.
AW = Rough opening of window; G = Total solar radiation energy (diffuse and direct) during heating period, averaged over all allocated
windows with the same orientation [PHPP:81,121]. Calculated on Windows sheet, based on deviation from cardinal points [PHPP:81].
r = Reduction / attenuation factor r = rShading × rDirt × rincidence-angle × rFrame [PHPP:90] rshading = rH × rR × rO × rother [PHPP:91-98]
rDirt = 0.95 Constant, rincidence-angle = 0.85 Constant for
reflection (non-perpendicular incident radiation),
rFrame = AGlass / AWindow = glazing fraction (0.6 …0.7 are
typical values; higher value = less frame)
rShading = 0.75 Default value or calculated on shading worksheet with these values:
rH = Continuous horizontal obstruction, rR = Vertical (reveal, vertical shading, lateral
wall), rO = Horizontal (overhang, balcony), rother = Additional shading.
(The larger the shading factor the less shaded the window is!)
Internal
Heat Gains
Length of
heating period
Spec. internal
heat gains
Treated Floor Area
(TFA)
QI = tHEAT × qi × ATFA
1,722 kWh/a 219 d/a x 0.024 kh/d 2.1 W/m
2
156.0 m
2
tHEAT = HT × 0.024 kh/a HT = Heating days per year [PHPP:120]
HT,Germany,PHPP-Default = 219d, HT,Vancouver = 208d, HT,Yellowknife = 243d, HT,New York = 181d, HT,San Francisco = 107d
Default average internal heat gains qi = 2.1 W/m
2
for residential project (PHPPv9: qi = 2.1 … 4.1W/m
2
depending on size of dwelling units)
qi = 4.1 W/m
2
for assisted living, qi = 3.5 W/m
2
for offices, qi = 2.8 W/m
2
for schools [PHPP:120], or calculated on IHG worksheet [PHPP:186]
Losses
QT Transmission Windows QT Transmission Opaque Elements QV Ventilation
& Infiltration
‘ƞ’
Energy
Balance
South ...other Roof Walls Ground
Gains
QS Solar Gains Windows South QS ...other QI Internal Heat Gains
QH Heating Demand
Free Heat (not usable heat gains are considered a loss  ‘ƞ’)
U-VALUE
VENTILATION
THERMAL BRIDGES
TFA
TFA

Space
Heating Load
Transmission
Heat Losses
Ventilation
Heat Losses
Solar
Gains
Internal
Heat Gains
PH = PT + PV – ( PS + PI )
1,558 W 2,188 W 264 W 645 W 250 W
pH = pT + pV - ( pS + pI )
9.99 W/m
2
14.03 W/m
2
1.69 W/m
2
4.13 W/m
2
1.60 W/m
2
PH = Size of heating system (maximum daily mean power) required to keep the building at 20˚C in 2 worst-case weather scenarios:
① cold, clear day (with higher heat losses and solar gains) or ② moderate, cloudy day (with lower heat losses and limited solar gains) [PHPP:132]
Specific Heating Load pH = PH / ATFA < 10W/m
2
in a PH = 1,558W / 156m
2
= 9.99W/m
2
PH,window = PT,window - PS = Window Energy Balance Pcandle ≈ 35W, Phuman ≈ 80W (55% of that is considered internal heat source as per PHPP)
Transmission
Heat Losses
Area of envelope or
building element
U-value
Temperature
correction factor
Temperature
difference
PT = A × U × ft × Δt1 or t2
774 W 184.3 m
2
0.138 W/m
2
K 1.0 30.6 K
PT = Calculated for each individual building element (exterior dimensions) [PHPP:129]. PT,window = Aw × U × Δt1 or t2
PT,thermal bridge = l × Ψ × ft × Δt = 116.9m × -0.030W/mK × 1.0 × 30.6K = -106W
Δt1 or t2 = Difference between 20˚C and outside temperature for worst case (of the two daily averages per PHPP climate data)
Ventilation &
Infiltration Losses
Ventilated
volume
air exchange rate
Volumetric heat
capacity of air
Temperature
difference
PV = VV × nV,P × cp,air × Δt1 or t2
264 W 390 m
3
0.068 h
-1
0.33 Wh/(m
3
K) 30.6 K
2
× 2.5m = 390m
3
PV = Heat losses via leakage through the envelope and through the HRV system.
nV,P = Energetically effective air change rate (for Heat Load design condition) [PHPP:129,132]
nV,P = nV,System × (1 - ϕHR1 or HR2) + nV,Rest,P = 0.300h
-1
× (1 - 0.93) + 0.047h
-1
= 0.068h
-1
nV,Rest,P = Infiltration air change through envelope leakage = 2.5 times the value of the average of the heating period
(worst case scenario) = 2.5 × nV,Rest,Q = 2.5 × 0.019h
-1
= 0.047h
-1
Solar
Gains
Reduction
factor
g-value
(= SHGC)
Gross window
area
Global solar
irradiation power
PS = r × g × AW × G1 or 2
605 W 0.44 0.5 30.4 m
2
90 W/m
2
g = SHGC = Total solar energy transmission coefficient for the glazing at a normal to the irradiated surface. From Windows sheet.
AW = Rough opening of window.
G = Daily mean global irradiation. Solar radiation power dependent on orientation for weather condition 1 & 2. [PHPP:130]
rFrame = AGlass / AWindow = glazing fraction(0.6 …0.7 are
Internal
Heat Gains
Internal
heat gains
Treated Floor Area
(TFA)
PI = qi,P × ATFA
250 W 1.6 W/m
2
156.0 m
2
qi,p = 1.6 W/m
2
default for residential projects (Reduced to simulate unoccupied building, cannot be
carried over from QH because annual heat demand calculates average for the entire heating period.) [PHPP:129]
(new with PHPPv9: qi,P = qi,Q - 0.5 = 2.1-0.5 = 1.6 W/m
2
)
Losses
PT Transmission Windows PT Transmission Opaque Elements PV Ventilation
& Infiltration
Energy
Balance
for two
scenarios
Gains
PS Solar Gains Windows South PS ...other PI Internal Heat Gains
PH Heating Load
Free Heat (PI is calculated with 0.5W/m
2
lower gains than QI)
HEATING via SUPPLY AIR
U-VALUE
THERMAL BRIDGES
TFA
VENTILATION
TFA
available at:
15kwh10w.com
full-sized set
PREVIEW

Space
Heating Load
Transmission
Heat Losses
Ventilation
Heat Losses
Solar
Gains
Internal
Heat Gains
PH = PT + PV – ( PS + PI )
1,558 W 2,188 W 264 W 645 W 250 W
pH = pT + pV - ( pS + pI )
9.99 W/m
2
14.03 W/m
2
1.69 W/m
2
4.13 W/m
2
1.60 W/m
2
PH = Size of heating system (maximum daily mean power) required to keep the building at 20˚C in 2 worst-case weather scenarios:
① cold, clear day (with higher heat losses and solar gains) or ② moderate, cloudy day (with lower heat losses and limited solar gains) [PHPP:132]
Specific Heating Load pH = PH / ATFA < 10W/m
2
in a PH = 1,558W / 156m
2
= 9.99W/m
2
PH,window = PT,window - PS = Window Energy Balance Pcandle ≈ 35W, Phuman ≈ 80W (55% of that is considered internal heat source as per PHPP)
Transmission
Heat Losses
Area of envelope or
building element
U-value
Temperature
correction factor
Temperature
difference
PT = A × U × ft × Δt1 or t2
774 W 184.3 m
2
0.138 W/m
2
K 1.0 30.6 K
PT = Calculated for each individual building element (exterior dimensions) [PHPP:129]. PT,window = Aw × U × Δt1 or t2
PT,thermal bridge = l × Ψ × ft × Δt = 116.9m × -0.030W/mK × 1.0 × 30.6K = -106W
Δt1 or t2 = Difference between 20˚C and outside temperature for worst case (of the two daily averages per PHPP climate data)
Ventilation &
Infiltration Losses
Ventilated
volume
air exchange rate
Volumetric heat
capacity of air
Temperature
difference
PV = VV × nV,P × cp,air × Δt1 or t2
264 W 390 m
3
0.068 h
-1
0.33 Wh/(m
3
K) 30.6 K
2
× 2.5m = 390m
3
PV = Heat losses via leakage through the envelope and through the HRV system.
nV,P = Energetically effective air change rate (for Heat Load design condition) [PHPP:129,132]
nV,P = nV,System × (1 - ϕHR1 or HR2) + nV,Rest,P = 0.300h
-1
× (1 - 0.93) + 0.047h
-1
= 0.068h
-1
nV,Rest,P = Infiltration air change through envelope leakage = 2.5 times the value of the average of the heating period
(worst case scenario) = 2.5 × nV,Rest,Q = 2.5 × 0.019h
-1
= 0.047h
-1
Solar
Gains
Reduction
factor
g-value
(= SHGC)
Gross window
area
Global solar
irradiation power
PS = r × g × AW × G1 or 2
605 W 0.44 0.5 30.4 m
2
90 W/m
2
g = SHGC = Total solar energy transmission coefficient for the glazing at a normal to the irradiated surface. From Windows sheet.
AW = Rough opening of window.
G = Daily mean global irradiation. Solar radiation power dependent on orientation for weather condition 1 & 2. [PHPP:130]
rFrame = AGlass / AWindow = glazing fraction(0.6 …0.7 are
Internal
Heat Gains
Internal
heat gains
Treated Floor Area
(TFA)
PI = qi,P × ATFA
250 W 1.6 W/m
2
156.0 m
2
qi,p = 1.6 W/m
2
default for residential projects (Reduced to simulate unoccupied building, cannot be
carried over from QH because annual heat demand calculates average for the entire heating period.) [PHPP:129]
(new with PHPPv9: qi,P = qi,Q - 0.5 = 2.1-0.5 = 1.6 W/m
2
)
Losses
PT Transmission Windows PT Transmission Opaque Elements PV Ventilation
& Infiltration
Energy
Balance
for two
scenarios
Gains
PS Solar Gains Windows South PS ...other PI Internal Heat Gains
PH Heating Load
Free Heat (PI is calculated with 0.5W/m
2
lower gains than QI)
HEATING via SUPPLY AIR
U-VALUE
THERMAL BRIDGES
TFA
VENTILATION
TFA
available in metric + imperial
15kwh10w.com

U-VALUE CALCULATION – OPAQUE ELEMENT [PHPP:45]
U =
1
RT
=
1
Rsi +
d1
λ1
+
d2
λ2
+
d3
λ3
+ Rse
Surface Film Thermal Resistances Rsi and Rse [m
2
K/W]:
* Considered horizontal if heat flow is up to ±30˚
from the horizontal
** Interior values might be used for ventilated
rainscreens (e.g. 0.13) and crawlspaces (e.g. 0.17)
and ventilated roofs (e.g. 0.10) [PHPP:48]
U=
1
0.13
m2K
W
+
0.30m
0.035
W
mK
+
0.24m
0.79
W
mK
+
0.015m
0.70
W
mK
+ 0.04
m2K
W
=
1
9.07
m2K
W
= 0.1103
W
m2K
Example above is: EIFS | Brick wall | interior plaster
U [W/m
2
K] = Heat transfer coefficient (heat flow in W through 1m
2
of a structure at ΔT = 1˚C)
U-value for composite building elements (e.g. framed wall) is calculated [PHPP:47-48]
RT [m
2
K/W] = Total thermal resistance Ri = di / λi = Thermal resistance of each layer [m
2
K/W]
λ [W/mK] = Thermal conductivity [PHPP:46] d [m] = thickness of each layer
Rsi [m
2
K/W] = Thermal resistance of the interior surface [PHPP:48]
Rse [m
2
K/W] = Thermal resistance of the exterior surface and below ground
Rsi and Rse are already included in Uglass and Uframe for windows.
Rsi is typically larger than Rse due to lower ΔT and less air movement on the interior surface
WINDOWS: U-Values and Surface Temperatures
Uwindow,installed =
(Aglass × Uglass) + (Aframe × Uframe) + (Lspacer × Ψspacer) + (Linstall × Ψinstall)
Awindow
Uwindow =
(1.224m2
× 0.6W/m2
K) + (0.596m2
× 1.6W/m2
K) + (4.45m × 0.08W/mK)
1.820m2 = 1.123W/m2
K
Uw,installed = Uwindow +
Linstall × Ψinstall
Awindow
= 1.123W/m2
K +
5.42m × 0.15W/mK
1.820m2 = 1.123W/m2
K + 0.447W/m2
K = 1.569W/m2
K
Awindow = wwindow × hwindow = Total window area (rough opening) = 1.23m × 1.48m = 1.820m
2
[PHPP:78,87]
Aglass = wglass × hglass = Glazing area = (1.23-0.117-0.117)m × (1.48-0.117-0.134)m = 0.996m × 1.229m = 1.224m
2
Aframe = Awindow - Aglass = Total window frame area = 1.820m
2
- 1.224m
2
= 0.596m
2
Lspacer = Lglass = 2 × wglass + 2 × hglass = Glazing perimeter (= spacer length) = (0.996+1.229)m × 2 = 4.45m
Linstall = Lframe = 2 × wwindow + 2 × hwindow = Window frame perimeter (install.) = (1.23+1.48)m × 2 = 5.42m
Ψspacer = Ψglazing edge = Average thermal bridge heat loss coefficient of the glazing edge seal, can be ~0.02 [PHPP:84]
Ψinstall = Average thermal bridge heat loss coefficient of the installation (~0.00 W/mK can be achieved with
window installed in insulation layer and 60mm ‘over-insulation’), PHPP default is 0.04W/mK, more precise values
may be obtained from window certification document, or calculated (e.g. THERM software) [PHPP:78,83-85]
Ψ for windows is not a material specific parameter, but depends on the type of installation and type of spacer Criteria for glazing:
Comfort: Ug ≤ 0.80 W/m
2
K
Energy: Ug - (S × g) < 0
S = radiation gain coefficient =
1.6W/m
2
K for Central Europe
Inside Surface Temperature of a Window (or Wall) Surface temperatures determine comfort level + risk of mould.
Tsi = Ti - (U × Rsi × ΔT) = 20˚C - (2.8W/m
2
K × 0.13m
2
K/W × 30˚C) = 9.08˚C
Tsi = Surface temperature inside Ti = Inside air temperature Te = Exterior air temperature
Rsi = Surface thermal resistance inside U = U-value of the component
ΔT = Temperature difference inside and outside ΔT = Ti - Te = 20˚C - (-10˚C) = 30˚C
H-VALUE [PHPP:59] THERMAL BRIDGES [PHPP:47,66,74,118]
H = Temperature specific
transmission heat losses
H = A × U
= 184.28m
2
× 0.138W/m
2
K
= 25.3W/K
HΨ = l × Ψ
= 116.85m × -0.03W/mK
= -3.5W/K
Hχ = χ = 0.77W/K
∑H = 22.57W/K
QT = ∑H × ft × Gt
= 22.57W/K × 1 × 81.9kKh/a
= 1,848kWh/a
PT = ∑H × ft × Δt1 or t2
= 22.57W/K × 1 × 30.6K
= 690W
The linear transmittance Ψ and point transmittance χ coefficients represent the increased heat flow at thermal bridges
compared to adjoining building components (using 2D modelling of the heat flow, based on exterior dimensions).
Compliance Definition ① (requires calculation of all thermal bridges): Thermal bridge free if there is no increase in the
building envelope’s average U-value due to ΔUTB ≤ 0W/m
2
K (actual transmission losses of all thermal bridges ≤ losses
of building elements alone, calculated using the external surfaces and regular U-values.)
HTB = ∑(l × Ψ) + ∑(χ) = -3.5W/K + 0.77W/K = -2.73W/K
ΔUTB = HTB / ATotal thermal envelope = -2.73W/K / 392.07m
2
≤ 0W/m
2
K  thermal bridge free
Compliance Definition ② (pragmatic approach): Thermal bridge free if for each linear thermal bridge Ψ < 0.01W/mK
(to avoid heat losses); and change in U-value for each point thermal bridge ΔUTB = χ/AElement < 0.01W/m
2
K (to be
considered for condensation), larger χ may be considered for transmission loss calculation [see example PHPP:88].
Thermal bridges for window openings are accounted for in the U-value calculation for windows Uw,installed.
Thermal Bridge Rules:
• Avoidance (do not penetrate insulation) • Geometry (avoid sharp angles, keep simple building form)
• Pierce-through (if disturbance of insulation layer is unavoidable, use materials with high thermal resistance)
• Connection (transfer insulation layers without gaps at connection details, connect the entire cross area)
Repeating thermal bridges in composite/inhomogeneous opaque building elements (e.g. timber stud walls) can be
approximated on the PHPP U-Values worksheet (recommended approach only if the calculation error resulting from
the variation of the λ values in the different wall sections is less than 10%). [PHPP:47]
hwindow=1.48m
wwindow = 1.23m
hglass=1.229m
wglass = 0.996m
Aglass
Aframe
0.117m
0.134m
0.117m
interior
exterior
below ground0.00
0.17 downward
0.00**
0.13 horizontal
0.04**
SEE ABOVE
available at:
15kwh10w.com

U-VALUE CALCULATION – OPAQUE ELEMENT [PHPP:45]
U =
1
RT
=
1
Rsi +
d1
λ1
+
d2
λ2
+
d3
λ3
+ Rse
Surface Film Thermal Resistances Rsi and Rse [m
2
K/W]:
* Considered horizontal if heat flow is up to ±30˚
from the horizontal
** Interior values might be used for ventilated
rainscreens (e.g. 0.13) and crawlspaces (e.g. 0.17)
and ventilated roofs (e.g. 0.10) [PHPP:48]
U=
1
0.13
m2K
W
+
0.30m
0.035
W
mK
+
0.24m
0.79
W
mK
+
0.015m
0.70
W
mK
+ 0.04
m2K
W
=
1
9.07
m2K
W
= 0.1103
W
m2K
Example above is: EIFS | Brick wall | interior plaster
U [W/m
2
K] = Heat transfer coefficient (heat flow in W through 1m
2
of a structure at ΔT = 1˚C)
U-value for composite building elements (e.g. framed wall) is calculated [PHPP:47-48]
RT [m
2
K/W] = Total thermal resistance Ri = di / λi = Thermal resistance of each layer [m
2
K/W]
λ [W/mK] = Thermal conductivity [PHPP:46] d [m] = thickness of each layer
Rsi [m
2
K/W] = Thermal resistance of the interior surface [PHPP:48]
Rse [m
2
K/W] = Thermal resistance of the exterior surface and below ground
Rsi and Rse are already included in Uglass and Uframe for windows.
Rsi is typically larger than Rse due to lower ΔT and less air movement on the interior surface
WINDOWS: U-Values and Surface Temperatures
Uwindow,installed =
(Aglass × Uglass) + (Aframe × Uframe) + (Lspacer × Ψspacer) + (Linstall × Ψinstall)
Awindow
Uwindow =
(1.224m2
× 0.6W/m2
K) + (0.596m2
× 1.6W/m2
K) + (4.45m × 0.08W/mK)
1.820m2 = 1.123W/m2
K
Uw,installed = Uwindow +
Linstall × Ψinstall
Awindow
= 1.123W/m2
K +
5.42m × 0.15W/mK
1.820m2 = 1.123W/m2
K + 0.447W/m2
K = 1.569W/m2
K
Awindow = wwindow × hwindow = Total window area (rough opening) = 1.23m × 1.48m = 1.820m
2
[PHPP:78,87]
Aglass = wglass × hglass = Glazing area = (1.23-0.117-0.117)m × (1.48-0.117-0.134)m = 0.996m × 1.229m = 1.224m
2
Aframe = Awindow - Aglass = Total window frame area = 1.820m
2
- 1.224m
2
= 0.596m
2
Lspacer = Lglass = 2 × wglass + 2 × hglass = Glazing perimeter (= spacer length) = (0.996+1.229)m × 2 = 4.45m
Linstall = Lframe = 2 × wwindow + 2 × hwindow = Window frame perimeter (install.) = (1.23+1.48)m × 2 = 5.42m
Ψspacer = Ψglazing edge = Average thermal bridge heat loss coefficient of the glazing edge seal, can be ~0.02 [PHPP:84]
Ψinstall = Average thermal bridge heat loss coefficient of the installation (~0.00 W/mK can be achieved with
window installed in insulation layer and 60mm ‘over-insulation’), PHPP default is 0.04W/mK, more precise values
may be obtained from window certification document, or calculated (e.g. THERM software) [PHPP:78,83-85]
Ψ for windows is not a material specific parameter, but depends on the type of installation and type of spacer Criteria for glazing:
Comfort: Ug ≤ 0.80 W/m
2
K
Energy: Ug - (S × g) < 0
S = radiation gain coefficient =
1.6W/m
2
K for Central Europe
Inside Surface Temperature of a Window (or Wall) Surface temperatures determine comfort level + risk of mould.
Tsi = Ti - (U × Rsi × ΔT) = 20˚C - (2.8W/m
2
K × 0.13m
2
K/W × 30˚C) = 9.08˚C
Tsi = Surface temperature inside Ti = Inside air temperature Te = Exterior air temperature
Rsi = Surface thermal resistance inside U = U-value of the component
ΔT = Temperature difference inside and outside ΔT = Ti - Te = 20˚C - (-10˚C) = 30˚C
H-VALUE [PHPP:59] THERMAL BRIDGES [PHPP:47,66,74,118]
H = Temperature specific
transmission heat losses
H = A × U
= 184.28m
2
× 0.138W/m
2
K
= 25.3W/K
HΨ = l × Ψ
= 116.85m × -0.03W/mK
= -3.5W/K
Hχ = χ = 0.77W/K
∑H = 22.57W/K
QT = ∑H × ft × Gt
= 22.57W/K × 1 × 81.9kKh/a
= 1,848kWh/a
PT = ∑H × ft × Δt1 or t2
= 22.57W/K × 1 × 30.6K
= 690W
The linear transmittance Ψ and point transmittance χ coefficients represent the increased heat flow at thermal bridges
compared to adjoining building components (using 2D modelling of the heat flow, based on exterior dimensions).
Compliance Definition ① (requires calculation of all thermal bridges): Thermal bridge free if there is no increase in the
building envelope’s average U-value due to ΔUTB ≤ 0W/m
2
K (actual transmission losses of all thermal bridges ≤ losses
of building elements alone, calculated using the external surfaces and regular U-values.)
HTB = ∑(l × Ψ) + ∑(χ) = -3.5W/K + 0.77W/K = -2.73W/K
ΔUTB = HTB / ATotal thermal envelope = -2.73W/K / 392.07m
2
≤ 0W/m
2
K  thermal bridge free
Compliance Definition ② (pragmatic approach): Thermal bridge free if for each linear thermal bridge Ψ < 0.01W/mK
(to avoid heat losses); and change in U-value for each point thermal bridge ΔUTB = χ/AElement < 0.01W/m
2
K (to be
considered for condensation), larger χ may be considered for transmission loss calculation [see example PHPP:88].
Thermal bridges for window openings are accounted for in the U-value calculation for windows Uw,installed.
Thermal Bridge Rules:
• Avoidance (do not penetrate insulation) • Geometry (avoid sharp angles, keep simple building form)
• Pierce-through (if disturbance of insulation layer is unavoidable, use materials with high thermal resistance)
• Connection (transfer insulation layers without gaps at connection details, connect the entire cross area)
Repeating thermal bridges in composite/inhomogeneous opaque building elements (e.g. timber stud walls) can be
approximated on the PHPP U-Values worksheet (recommended approach only if the calculation error resulting from
the variation of the λ values in the different wall sections is less than 10%). [PHPP:47]
hwindow=1.48m
wwindow = 1.23m
hglass=1.229m
wglass = 0.996m
Aglass
Aframe
0.117m
0.134m
0.117m
interior
exterior
below ground0.00
0.17 downward
0.00**
0.13 horizontal
0.04**
SEE ABOVE
15kwh10w.com

Fresh air [e.g. -10˚C]
ODA
Exhaust air
EHA
Extract air [20˚C]
Supply air
heat generator
cold
water (or...
DHW
hot water storage tank
HRAir-to-air plate
heat exchanger
combustionair
chimney
[≤ 52˚C]
post-heater
optional:
solar hot
water
system
Frost
protection
(cold water)
(or)
oil tank
[≥ 16.5˚C]
HEATING
Central Heating Boiler:
System Design
Supply Air ≤ 52˚C to avoid dust smoldering
Factors for thermal comfort:
• Air temperature
• Surface temperate
• Local temperature difference
• Draughts
• Relative air humidity
• Clothing and degree of activity
(Thermal comfort is achieved if losses from human body are equal to
heat production of body.)
Heat generation characteristics in PH (in addition to PH criteria)
Heat Demand for DHW = 12-35kWh/m
2
a (dominance over heating
demand in PH)
Typical distribution losses = 15kWh/m
2
a (not useful)
5kWh/m
2
a (useful)
It does not matter how and where heat is delivered
(could be through supply air).
VENTILATION [PHPP:29]
Dimensioning of Air Quantities nV,system and nV,Res [PHPP:105-108] (Too much ventilation leads to dry air - optimal 35-55% rel. humidity)
① Supply Air = 20 to 30m
3
/h per person = 4.5 person × 30m
3
/h/p = 134m
3
/h average airflow, distributed within the whole apartment
(The CO2 emissions of a person at average activity require 30m
3
/h for good air quality.)
Typical values used for energy modeling: dwellings & offices 30m
3
/h/p, schools 15-20m
3
/h/p, sport halls 60m
3
/h/p
② Extract Air = kitchen 60m
3
/h, bathroom 40m
3
/h, WC and storage 20m
3
/h
60m
3
/h + 40m
3
/h + 20m
3
/h + 20m
3
/h = 140m
3
/h (Not permanently required if larger than calculated supply air – follow ① more closely.)
③ Minimum air change = 0.30h
-1
x Vv 0.30h
-1
× 390m
3
= 117m
3
/h (average air flow)
 nV,system = Vaverage air flow / VV = 117m
3
h
-1
/390m
3
h
-1
= 0.30h
-1
m
3
/h ≈ cfm
20 12
30 18
40 24
50 29
60 35
100 59
150 88
200 118
Design Air Flow = max. of ① or ② or ③ [Vv × 0.3h
-1
× 1.3] 390m
3
× 0.30h
-1
× 1.3 = 152m
3
/h (at 100%) Normal flow rate = 152 × 77% = 117m
3
/h
Infiltration
nV,Res= n50 × e ×
Vn50
VV
≈ 10% of n50 = 0.22h-1
× 0.07 ×
480m3
390m3
= 0.019h-1 n50 =
V50
VAir
=
measured air flow
net interior air volume
=
106m3
/ℎ
480m3
= 0.22h-1
A50,Leakage ≈ 0.5cm
2
h/m
3
× V50
≈ 0.5 × 300m
3
/h = 150cm
2
nV,Rest = Infiltration air change through envelope n50 = Air change rate at pressure test e = exposure coefficient for screening class [PHPP:103]
Vn50 = VAir = Pressure test reference volume, net air volume “visible air” to underside of suspended ceiling. VV = Ventilated volume (see under QV)
V50 = Measured air flow rate at 50Pa measurements VP taken at a different pressure P can be approximately corrected to 50Pa by V50 ≈ (VP / P) × 50
Efficiency of Heat Recovery (HRV) [PHPP:78,100,110] ƞHR,eff  [PHPP:106] Maximum heating load transportable via the supply air [PHPP:130]
ηHR=
TETA- TEHA+
Pel
ṁ × cp
TETA- TODA
=
20˚C - 8.5˚C +
37W
120 m3 h⁄ × 0.33 Wh m3K⁄
20˚C - 4.0˚C
= 78%
Psupply,max = (Tsupply,max - Tsupply,min) × cp,air × VV,system
Psupply,max = (52˚C - 18˚C) × 0.33Wh/m
3
K × 117m
3
/h = 1,314W
PH ≤ Psupply,max 1,558W ≥ 1,314W  not suitable for supply air heating
Psupply,max = Maximum heating power which can be delivered in supply air
cp,air = Volumetric heat capacity of air = 0.33Wh/m
3
K constant
Tsupply,max = Max. supply air temp., ≤ 52˚C (downstream of post-heater)
Tsupply,min = Supply air temperature, ≥ 16.5˚C (upstream of post-heater)
Tsupply,min = TODA + ƞHR × (TETA - TODA) = -10˚C + 0.93 × (20˚C + 10˚C) = 18˚C
VV,system = Average air flow rate through the ventilation system
VV,system = VV × nV,system = 390m
3
× 0.30h
-1
= 117m
3
ƞHR = Efficiency of HRV (≥ 75% so that SUP ≥ 16.5˚C) ṁ × cp = Vflow × cp,air
ṁ = Mass flow [kg/s] cp = Specific heat capacity of air [Ws/kg]
cp,air = 0.33 Wh/m
3
K = Volumetric heat capacity of air at density 1.19 kg/m
3
Electricity Demand = Pel / Vflow = 37W / 120m
3
/h = 0.31Wh/m
3
(max. 0.45)
Pel = electrical power (fans+controls)
Vflow = Balanced air volume flow
ODA = Outdoor Air
EHA = Exhaust Air
ETA = Extract Air (20˚C)
SUP = Supply Air (≥ 16.5˚C)
10W/m
2
derivation:
pheating=
V
A
× ∆T × cp,air =
30m3
/(h × person)
30m2/person
× 30K × 0.33
Wh
m3K
≈ 10W/m2
Duct Diameter Openings for the transferred air
Duct diameter = 2×�
V
velocity × π × 3,600
= 2×�
150m3/h
2m/s × 3.14159 × 3,600
= 0.163m
To allow air travel from delivery to exhaust zone keep
pressure loss < 1Pa (~ 1m/s). Guidelines:
• Extract air rooms with 60m
3
/h  150cm
2
total opening
gross section
• Living rooms with 40m
3
/h  1.5-2cm gap under or
through door, or via lintel detail
V = Volumetric flow rate at standard rate (77%); Velocity = Speed of air flow in the duct,
ideally max. 2m/s (to avoid turbulences), but could be 1.5-2.5m/s
Typical: 100mm with ≤55m³/h, 150mm ≤120m³/h (at 2.0m/s) ≤160m³/h (at 2.5m/s)
Heating via Supply Air
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Fresh air [e.g. -10˚C]
ODA
Exhaust air
EHA
Extract air [20˚C]
Supply air
heat generator
cold
water (or...
DHW
hot water storage tank
HRAir-to-air plate
heat exchanger
combustionair
chimney
[≤ 52˚C]
post-heater
optional:
solar hot
water
system
Frost
protection
(cold water)
(or)
oil tank
[≥ 16.5˚C]
HEATING
Central Heating Boiler:
System Design
Supply Air ≤ 52˚C to avoid dust smoldering
Factors for thermal comfort:
• Air temperature
• Surface temperate
• Local temperature difference
• Draughts
• Relative air humidity
• Clothing and degree of activity
(Thermal comfort is achieved if losses from human body are equal to
heat production of body.)
Heat generation characteristics in PH (in addition to PH criteria)
Heat Demand for DHW = 12-35kWh/m
2
a (dominance over heating
demand in PH)
Typical distribution losses = 15kWh/m
2
a (not useful)
5kWh/m
2
a (useful)
It does not matter how and where heat is delivered
(could be through supply air).
VENTILATION [PHPP:29]
Dimensioning of Air Quantities nV,system and nV,Res [PHPP:105-108] (Too much ventilation leads to dry air - optimal 35-55% rel. humidity)
① Supply Air = 20 to 30m
3
/h per person = 4.5 person × 30m
3
/h/p = 134m
3
/h average airflow, distributed within the whole apartment
(The CO2 emissions of a person at average activity require 30m
3
/h for good air quality.)
Typical values used for energy modeling: dwellings & offices 30m
3
/h/p, schools 15-20m
3
/h/p, sport halls 60m
3
/h/p
② Extract Air = kitchen 60m
3
/h, bathroom 40m
3
/h, WC and storage 20m
3
/h
60m
3
/h + 40m
3
/h + 20m
3
/h + 20m
3
/h = 140m
3
/h (Not permanently required if larger than calculated supply air – follow ① more closely.)
③ Minimum air change = 0.30h
-1
x Vv 0.30h
-1
× 390m
3
= 117m
3
/h (average air flow)
 nV,system = Vaverage air flow / VV = 117m
3
h
-1
/390m
3
h
-1
= 0.30h
-1
m
3
/h ≈ cfm
20 12
30 18
40 24
50 29
60 35
100 59
150 88
200 118
Design Air Flow = max. of ① or ② or ③ [Vv × 0.3h
-1
× 1.3] 390m
3
× 0.30h
-1
× 1.3 = 152m
3
/h (at 100%) Normal flow rate = 152 × 77% = 117m
3
/h
Infiltration
nV,Res= n50 × e ×
Vn50
VV
≈ 10% of n50 = 0.22h-1
× 0.07 ×
480m3
390m3
= 0.019h-1 n50 =
V50
VAir
=
measured air flow
net interior air volume
=
106m3
/ℎ
480m3
= 0.22h-1
A50,Leakage ≈ 0.5cm
2
h/m
3
× V50
≈ 0.5 × 300m
3
/h = 150cm
2
nV,Rest = Infiltration air change through envelope n50 = Air change rate at pressure test e = exposure coefficient for screening class [PHPP:103]
Vn50 = VAir = Pressure test reference volume, net air volume “visible air” to underside of suspended ceiling. VV = Ventilated volume (see under QV)
V50 = Measured air flow rate at 50Pa measurements VP taken at a different pressure P can be approximately corrected to 50Pa by V50 ≈ (VP / P) × 50
Efficiency of Heat Recovery (HRV) [PHPP:78,100,110] ƞHR,eff  [PHPP:106] Maximum heating load transportable via the supply air [PHPP:130]
ηHR=
TETA- TEHA+
Pel
ṁ × cp
TETA- TODA
=
20˚C - 8.5˚C +
37W
120 m3 h⁄ × 0.33 Wh m3K⁄
20˚C - 4.0˚C
= 78%
Psupply,max = (Tsupply,max - Tsupply,min) × cp,air × VV,system
Psupply,max = (52˚C - 18˚C) × 0.33Wh/m
3
K × 117m
3
/h = 1,314W
PH ≤ Psupply,max 1,558W ≥ 1,314W  not suitable for supply air heating
Psupply,max = Maximum heating power which can be delivered in supply air
cp,air = Volumetric heat capacity of air = 0.33Wh/m
3
K constant
Tsupply,max = Max. supply air temp., ≤ 52˚C (downstream of post-heater)
Tsupply,min = Supply air temperature, ≥ 16.5˚C (upstream of post-heater)
Tsupply,min = TODA + ƞHR × (TETA - TODA) = -10˚C + 0.93 × (20˚C + 10˚C) = 18˚C
VV,system = Average air flow rate through the ventilation system
VV,system = VV × nV,system = 390m
3
× 0.30h
-1
= 117m
3
ƞHR = Efficiency of HRV (≥ 75% so that SUP ≥ 16.5˚C) ṁ × cp = Vflow × cp,air
ṁ = Mass flow [kg/s] cp = Specific heat capacity of air [Ws/kg]
cp,air = 0.33 Wh/m
3
K = Volumetric heat capacity of air at density 1.19 kg/m
3
Electricity Demand = Pel / Vflow = 37W / 120m
3
/h = 0.31Wh/m
3
(max. 0.45)
Pel = electrical power (fans+controls)
Vflow = Balanced air volume flow
ODA = Outdoor Air
EHA = Exhaust Air
ETA = Extract Air (20˚C)
SUP = Supply Air (≥ 16.5˚C)
10W/m
2
derivation:
pheating=
V
A
× ∆T × cp,air =
30m3
/(h × person)
30m2/person
× 30K × 0.33
Wh
m3K
≈ 10W/m2
Duct Diameter Openings for the transferred air
Duct diameter = 2×�
V
velocity × π × 3,600
= 2×�
150m3/h
2m/s × 3.14159 × 3,600
= 0.163m
To allow air travel from delivery to exhaust zone keep
pressure loss < 1Pa (~ 1m/s). Guidelines:
• Extract air rooms with 60m
3
/h  150cm
2
total opening
gross section
• Living rooms with 40m
3
/h  1.5-2cm gap under or
through door, or via lintel detail
V = Volumetric flow rate at standard rate (77%); Velocity = Speed of air flow in the duct,
ideally max. 2m/s (to avoid turbulences), but could be 1.5-2.5m/s
Typical: 100mm with ≤55m³/h, 150mm ≤120m³/h (at 2.0m/s) ≤160m³/h (at 2.5m/s)
Heating via Supply Air
15kwh10w.com

Evaluation Criteria for residential buildings [PHPP:19]
Space Heating Demand QH ≤ 15 kWh/m
2
a or alternatively
Peak Heating Load PH ≤ 10 W/m
2
(small building, large surface)
Useful Cooling Demand ≤ 15 kWh/m
2
a or alternatively
Peak Cooling Load ≤ 10 W/m
2
+ see [PHPP:19]
Primary Energy Demand PE ≤ 120 kWh/m
2
a + see [PHPP:19] (heating,
ventilation, cooling, DHW, aux electricity, household electricity)
Building Airtightness n50 ≤ 0.6h
-1
(0.649 is still OK)
EN 13829 Method A: Envelope in the same condition as it is when heating
or ventilation are being used. Difference between test results at positive
and negative pressure <10%.
Design temperature 20˚C (Can be different in justified cases.) [PHPP:32]
Excess temperature ≤ 10% of total yearly hours with indoor air >25˚C
Occupancy rate for Verification of residential buildings = 35 m
2
/person
(PHPPv9: Based on typical occupancy rates for specific dwelling unit sizes);
for Planning = 20-50 m
2
/p; entered manually for non-residential [PHPP:33]
New Evaluation Criteria 2015 with PHPPv9 (not yet mandatory in 2015)
All of the above, except alternative methodology for Primary Energy PE
and introduction of new classes to address renewable energy generation.
Primary Energy Renewable PER is the demand profile of the individual
energy application and locally available renewable primary power
production from PV and wind (and hydro power).
PER =
Edir +
EMS
ηMS
+
ESS
ηSS
+ EDL
Edir + EMS + ESS
PER Factor for each source and application [kWhPER/kWh]
Edir Electricity generated by RES used directly
EMS Electricity from short/medium term storage
ESS Electricity generated from energy in seasonal storage
EDL Distribution and other losses
ηMS and ηSS Efficiencies of storage processes (whole chain)
New Passive House Classes: Classic Plus Premium
Renewable PE Demand: ≤60 ≤45 ≤30 kWhPER/m
2
TFAa
Renewable Energy Generation: n/a ≥60 ≥120 kWhPER/m
2
grounda
Cross Ventilation:
Supply air zone  Transferred air zone  Extract air zone
Coanda-Effect:
Vacuum created by moving air from supply jet nozzle 5-20cm under ceiling
pulls secondary air towards the ceiling. The ceiling acts as a half-sided duct
and can move supply air up to 6m into room.
Ductwork – insulation thickness
ETA SUP SUP ODA
(~20˚C) (16-20˚C) (heated) / EHA
Outside thermal envelope: 100mm 100mm 150mm 0
Transfer/exhaust room inside: 0 0 20-30mm 50-100mm
Supplied room inside: 0 0 0 50-100mm
Insulation on cold ducts inside must be vapour impermeable. Use silencers.
Keep all ducts as short as possible – in particular cold ducts inside.
Treated Floor Area (TFA) The rules are based on German WoflV and DIN 277
and incentivise designing efficient plans with high-quality spaces within the
thermal envelope. Rules for residential buildings (WoflV) [PHPP:63]:
Included: Floor areas of rooms measured from clear width between building
elements, in particular: living and circulation areas, washrooms, auxiliary
rooms (storage, service, and utility rooms), stair heads and landings, floor to
ceiling window reveals which are ≥0.13m deep.
Included with 60%: Auxiliary rooms and circulation areas outside dwelling or
on floors of detached houses in which less than 50% of the floor area is
considered living space (e.g. in the basement).
Excluded: Stairs with more than 3 risers, walls and other elements >1.5m
high, shafts and chimneys and pillars >0.1m
2
, doorways, window reveals
(unless see above), areas outside thermal envelope.
Rule for all areas with reduced ceiling height: The TFA is reduced by 50% if
clear room height is 1-2m. Areas <1m high are excluded from TFA.
The necessity of an airtight building envelope:
(Infiltration and exfiltration are caused by wind and buoyancy, due to
leakages in envelope. Design one airtight layer all around the building.)
• Prevention of condensation in the construction (exfiltration most critical:
360g water/day can condense through 1mm x 1m leak, when outside 0˚C,
80%RH and inside 0˚C, 50%RH)
• Prevention of drafts
• Prevention of cold floors in the ground floor
• Preventing air pollution of the room air
• Securing the sound insulation of building components
• Securing the operation and effectiveness of the ventilation system
• Securing the insulation effect of the external building components
• Reduction of ventilation heat losses (infiltration)
• For HRV to work efficiently, airtightness is important
Passive House Components (Quality Criteria)
Heat protection:
U ≤ 0.15 W/m
2
K thermal envelope, opaque elements (typically 0.10-
0.15 W/m
2
K); thermal bridge free (to reduce heat loss and avoid cold
interior surfaces)
Heat Recovery Ventilation (HRV, MVHR):
ηHR ≥ 75% efficiency (to maintain min. 16.5˚C supply air temp. at -10˚C,
prefer 85-92%); Low velocity; Electricity demand max. 0.45 Wh/m
3
;
Max. 25dB(A) in habitable rooms, 30dB(A) in functional rooms, 35dB(A) in
room with ventilation unit;
Balanced (≤ 10% during operation between ODA and EHA) and Controlled
operation (basic / normal / purge: 54 / 77 / 100%, summer bypass);
Filters for outdoor air ≥ F7 exhaust air ≥ G4;
Frost protection to protect plate HE on exhaust side and post-heater if
extraction fan is broken (e.g. air subsoil, brine loop, electric);
Condensate drain in exhaust air, airtight and insulated.
Windows*:
Uwindow ≤ 0.80 W/m
2
K** and Uw,installed ≤ 0.85 W/m
2
K to keep radiant
temperature asymmetry <4.2K (comfort criterion***), typically <3K with
PH windows; Triple glazing Uglass ≤ 0.80 W/m
2
K, 0.60 W/m
2
K is typical;
g-value = SHGC = 50-55% typical for PH windows
* Values shown are for cool-temperate climate. (Transparent compo-
nent certification critera for other climate zones and efficiency
classes phA+, phA, phB and phC can be found on www.passiv.de)
** For PH certificate: Uw = 0.80 W/m
2
K verified with Uglass = 0.70 W/m
2
K
*** Other comfort criteria met by PH: Air speed < 0.08m/s; Room air
temperature stratification between head and ankles of seated
person < 2K; Felt temperature difference in a room from place to
place less than 0.8˚C
What happens if there is a problem (any problem) with the Passive House?
• Passive House Standard not met
• Level of comfort will decrease
• Heating demand increases
• Heating load increases
• Supplementary heating might be required
• No longer able to heat with supply air alone
• Risk of mould increases
• Exfiltration of internal air into structure leads to interstitial
condensation (n50)
Miscellaneous see [PHPP] for symbols & definitions
ϕ (phi), η (eta) = efficiency
λ (lambda) = thermal conductivity
ϑ (theta), T = temperature
ΔT = temperature difference
Ψ (psi) = linear thermal transmittance
χ (chi) = point thermal transmittance
Acircle = (π × d
2
) / 4 = π × r
2
≈ 0.7854 × d
2
Equilateral triangle = all sides and angles (60˚) equal
1 year = 365 days = 8,760 hours = 8.76 kh/a
1 hour = 3,600 seconds
Deviation from North
[PHPP:81]
North: 0°
Northeast: 45°
East: 90°
Southeast: 135°
South: 180°
Southwest: 225°
West: 270°
Northwest: 315°
THERMAL BRIDGES
available at:
15kwh10w.com

Evaluation Criteria for residential buildings [PHPP:19]
Space Heating Demand QH ≤ 15 kWh/m
2
a or alternatively
Peak Heating Load PH ≤ 10 W/m
2
(small building, large surface)
Useful Cooling Demand ≤ 15 kWh/m
2
a or alternatively
Peak Cooling Load ≤ 10 W/m
2
+ see [PHPP:19]
Primary Energy Demand PE ≤ 120 kWh/m
2
a + see [PHPP:19] (heating,
ventilation, cooling, DHW, aux electricity, household electricity)
Building Airtightness n50 ≤ 0.6h
-1
(0.649 is still OK)
EN 13829 Method A: Envelope in the same condition as it is when heating
or ventilation are being used. Difference between test results at positive
and negative pressure <10%.
Design temperature 20˚C (Can be different in justified cases.) [PHPP:32]
Excess temperature ≤ 10% of total yearly hours with indoor air >25˚C
Occupancy rate for Verification of residential buildings = 35 m
2
/person
(PHPPv9: Based on typical occupancy rates for specific dwelling unit sizes);
for Planning = 20-50 m
2
/p; entered manually for non-residential [PHPP:33]
New Evaluation Criteria 2015 with PHPPv9 (not yet mandatory in 2015)
All of the above, except alternative methodology for Primary Energy PE
and introduction of new classes to address renewable energy generation.
Primary Energy Renewable PER is the demand profile of the individual
energy application and locally available renewable primary power
production from PV and wind (and hydro power).
PER =
Edir +
EMS
ηMS
+
ESS
ηSS
+ EDL
Edir + EMS + ESS
PER Factor for each source and application [kWhPER/kWh]
Edir Electricity generated by RES used directly
EMS Electricity from short/medium term storage
ESS Electricity generated from energy in seasonal storage
EDL Distribution and other losses
ηMS and ηSS Efficiencies of storage processes (whole chain)
New Passive House Classes: Classic Plus Premium
Renewable PE Demand: ≤60 ≤45 ≤30 kWhPER/m
2
TFAa
Renewable Energy Generation: n/a ≥60 ≥120 kWhPER/m
2
grounda
Cross Ventilation:
Supply air zone  Transferred air zone  Extract air zone
Coanda-Effect:
Vacuum created by moving air from supply jet nozzle 5-20cm under ceiling
pulls secondary air towards the ceiling. The ceiling acts as a half-sided duct
and can move supply air up to 6m into room.
Ductwork – insulation thickness
ETA SUP SUP ODA
(~20˚C) (16-20˚C) (heated) / EHA
Outside thermal envelope: 100mm 100mm 150mm 0
Transfer/exhaust room inside: 0 0 20-30mm 50-100mm
Supplied room inside: 0 0 0 50-100mm
Insulation on cold ducts inside must be vapour impermeable. Use silencers.
Keep all ducts as short as possible – in particular cold ducts inside.
Treated Floor Area (TFA) The rules are based on German WoflV and DIN 277
and incentivise designing efficient plans with high-quality spaces within the
thermal envelope. Rules for residential buildings (WoflV) [PHPP:63]:
Included: Floor areas of rooms measured from clear width between building
elements, in particular: living and circulation areas, washrooms, auxiliary
rooms (storage, service, and utility rooms), stair heads and landings, floor to
ceiling window reveals which are ≥0.13m deep.
Included with 60%: Auxiliary rooms and circulation areas outside dwelling or
on floors of detached houses in which less than 50% of the floor area is
considered living space (e.g. in the basement).
Excluded: Stairs with more than 3 risers, walls and other elements >1.5m
high, shafts and chimneys and pillars >0.1m
2
, doorways, window reveals
(unless see above), areas outside thermal envelope.
Rule for all areas with reduced ceiling height: The TFA is reduced by 50% if
clear room height is 1-2m. Areas <1m high are excluded from TFA.
The necessity of an airtight building envelope:
(Infiltration and exfiltration are caused by wind and buoyancy, due to
leakages in envelope. Design one airtight layer all around the building.)
• Prevention of condensation in the construction (exfiltration most critical:
360g water/day can condense through 1mm x 1m leak, when outside 0˚C,
80%RH and inside 0˚C, 50%RH)
• Prevention of drafts
• Prevention of cold floors in the ground floor
• Preventing air pollution of the room air
• Securing the sound insulation of building components
• Securing the operation and effectiveness of the ventilation system
• Securing the insulation effect of the external building components
• Reduction of ventilation heat losses (infiltration)
• For HRV to work efficiently, airtightness is important
Passive House Components (Quality Criteria)
Heat protection:
U ≤ 0.15 W/m
2
K thermal envelope, opaque elements (typically 0.10-
0.15 W/m
2
K); thermal bridge free (to reduce heat loss and avoid cold
interior surfaces)
Heat Recovery Ventilation (HRV, MVHR):
ηHR ≥ 75% efficiency (to maintain min. 16.5˚C supply air temp. at -10˚C,
prefer 85-92%); Low velocity; Electricity demand max. 0.45 Wh/m
3
;
Max. 25dB(A) in habitable rooms, 30dB(A) in functional rooms, 35dB(A) in
room with ventilation unit;
Balanced (≤ 10% during operation between ODA and EHA) and Controlled
operation (basic / normal / purge: 54 / 77 / 100%, summer bypass);
Filters for outdoor air ≥ F7 exhaust air ≥ G4;
Frost protection to protect plate HE on exhaust side and post-heater if
extraction fan is broken (e.g. air subsoil, brine loop, electric);
Condensate drain in exhaust air, airtight and insulated.
Windows*:
Uwindow ≤ 0.80 W/m
2
K** and Uw,installed ≤ 0.85 W/m
2
K to keep radiant
temperature asymmetry <4.2K (comfort criterion***), typically <3K with
PH windows; Triple glazing Uglass ≤ 0.80 W/m
2
K, 0.60 W/m
2
K is typical;
g-value = SHGC = 50-55% typical for PH windows
* Values shown are for cool-temperate climate. (Transparent compo-
nent certification critera for other climate zones and efficiency
classes phA+, phA, phB and phC can be found on www.passiv.de)
** For PH certificate: Uw = 0.80 W/m
2
K verified with Uglass = 0.70 W/m
2
K
*** Other comfort criteria met by PH: Air speed < 0.08m/s; Room air
temperature stratification between head and ankles of seated
person < 2K; Felt temperature difference in a room from place to
place less than 0.8˚C
What happens if there is a problem (any problem) with the Passive House?
• Passive House Standard not met
• Level of comfort will decrease
• Heating demand increases
• Heating load increases
• Supplementary heating might be required
• No longer able to heat with supply air alone
• Risk of mould increases
• Exfiltration of internal air into structure leads to interstitial
condensation (n50)
Miscellaneous see [PHPP] for symbols & definitions
ϕ (phi), η (eta) = efficiency
λ (lambda) = thermal conductivity
ϑ (theta), T = temperature
ΔT = temperature difference
Ψ (psi) = linear thermal transmittance
χ (chi) = point thermal transmittance
Acircle = (π × d
2
) / 4 = π × r
2
≈ 0.7854 × d
2
Equilateral triangle = all sides and angles (60˚) equal
1 year = 365 days = 8,760 hours = 8.76 kh/a
1 hour = 3,600 seconds
Deviation from North
[PHPP:81]
North: 0°
Northeast: 45°
East: 90°
Southeast: 135°
South: 180°
Southwest: 225°
West: 270°
Northwest: 315°
THERMAL BRIDGES
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Material
Thermal
conductivity λ
W / mK
Umetric �
W
m2K
� =
5.678
Rimp. �
ft2
F h
Btu
�
U-value RSI U-value R-value
W /
m
2
K
m
2
K /
W
Btu /
ft
2
F h
ft
2
F h /
Btu
typicalvaluesforopaqueelements
0.055 18.18 0.010 103.24
0.060 16.67 0.011 94.64
0.065 15.38 0.011 87.36
0.070 14.29 0.012 81.12
0.075 13.33 0.013 75.71
0.080 12.50 0.014 70.98
0.085 11.76 0.015 66.80
0.090 11.11 0.016 63.09
0.095 10.53 0.017 59.77
0.100 10.00 0.018 56.78
0.105 9.52 0.018 54.08
0.110 9.09 0.019 51.62
0.115 8.70 0.020 49.38
0.120 8.33 0.021 47.32
0.125 8.00 0.022 45.43
0.130 7.69 0.023 43.68
0.135 7.41 0.024 42.06
0.140 7.14 0.025 40.56
0.145 6.90 0.026 39.16
0.150 6.67 0.026 37.86
0.20 5.00 0.035 28.39
0.25 4.00 0.044 22.71
0.30 3.33 0.053 18.93
0.35 2.86 0.062 16.22
0.40 2.50 0.070 14.20
0.45 2.22 0.079 12.62
0.50 2.00 0.088 11.36
0.55 1.82 0.097 10.32
typicalvaluesforwindows
0.60 1.67 0.106 9.46
0.61 1.64 0.107 9.31
0.62 1.61 0.109 9.16
0.63 1.59 0.111 9.01
0.64 1.56 0.113 8.87
0.65 1.54 0.114 8.74
0.66 1.52 0.116 8.60
0.67 1.49 0.118 8.48
0.68 1.47 0.120 8.35
0.69 1.45 0.122 8.23
0.70 1.43 0.123 8.11
0.71 1.41 0.125 8.00
0.72 1.39 0.127 7.89
0.73 1.37 0.129 7.78
0.74 1.35 0.130 7.67
0.75 1.33 0.132 7.57
0.76 1.32 0.134 7.47
0.77 1.30 0.136 7.37
0.78 1.28 0.137 7.28
0.79 1.27 0.139 7.19
0.80 1.25 0.141 7.10
0.81 1.23 0.143 7.01
0.82 1.22 0.144 6.92
0.83 1.20 0.146 6.84
0.84 1.19 0.148 6.76
0.85 1.18 0.150 6.68
0.86 1.16 0.151 6.60
0.87 1.15 0.153 6.53
0.88 1.14 0.155 6.45
0.89 1.12 0.157 6.38
0.90 1.11 0.158 6.31
0.95 1.05 0.167 5.98
1.00 1.00 0.176 5.68
1.05 0.95 0.185 5.41
1.10 0.91 0.194 5.16
1.15 0.87 0.203 4.94
1.20 0.83 0.211 4.73
1.25 0.80 0.220 4.54
1.30 0.77 0.229 4.37
1.35 0.74 0.238 4.21
1.40 0.71 0.247 4.06
1.45 0.69 0.255 3.92
1.50 0.67 0.264 3.79
Find converter tool app for mobile
devices on www.15kwh10w.com
Copper 3802
Aluminium 1601,2
- 2002
Mild Steel 402
- 501
- 802
λmetric �
W
mK
� =
0.1442
Rper inch �
ft2
F h
Btu inch
�
Stainless Steel 171
Concrete (Reinforced) 1.42
- 2.11
- 2.62
Cement Screed 1.41
Lightweight Concrete 0.151
- 0.31
Quinn Lite aerated concrete 0.1213
- 0.1913
Annual Energy Demand
Natural Stone 1.51
- 3.51
kWh /
m
2
a
kBtu /
ft
2
a
kWh /
ft
2
aSand-Lime Masonry 11
Solid Clay Brick Masonry 0.81
- 1.21
1 0.317 0.093
Vertically Perforated Lightweight Masonry 0.31
- 0.451
15* 4.755 1.394
Adobe 0.41
- 0.82
25* 7.925 2.323
Float Glass 11
30** 9.510 2.787
Solid Plastic (Typical) 0.171
- 0.31
45** 14.26 4.181
Rubber 0.171
60** 19.02 5.574
Linoleum 0.171
120** 38.04 11.15
Carpet 0.061 * Heating /cooling criteria for PH and
EnerPHit ** Primary Energy criteriaGypsum Plaster 0.181
- 0.561
Gypsum Plasterboard 0.251
For wood and wood products the thermal conductivity is to be multiplied by
a factor of 2.2 when the heat flow is parallel to the direction of the fibres.1
Heating Load
W /
m
2
Btu /
h.ft
2
Hardwood 0.181
Softwood 0.131
1 0.317
Chipboard 0.101
- 0.181
10* 3.171
Oriented Strand Board (OSB) 0.092
- 0.131 * Heating load criterion for PH
Plywood 0.082
- 0.112
Medium Density Fibreboard (MDF) 0.071
- 0.181
North American Softwood
Dimensional Lumber sizesWood Wool Lightweight Building Board 0.0651
- 0.0901
Fibre Insulating Material 0.0351
- 0.0501
nominal actual actual
Wooden Softboard 0.0401
- 0.0701
1" ¾" 19 mm
Agepan DWD Protect 0.0908
2" 1-½" 38 mm
Agepan THD Insulating Wood Fibre Board 0.0468
- 0.0508
3" 2-½" 64 mm
Agepan THD Static 0.0558
4" 3-½" 89 mm
Corkboard 0.0422
5" 4-½" 114 mm
Coconut Fibre 0.0404
- 0.0504
6" 5-½" 140 mm
Flax / hemp board 0.0406
7" 6-¼" 159 mm
Mineral wool (rock wool, fibreglass batts) 0.0351
- 0.0451
8" 7-¼" 184 mm
Roxul ComfortBoard CIS 0.0369
10" 9-¼" 235 mm
Fibreglass (blown fibres) 0.0383
- 0.0393
12" 11-¼" 286 mm
Expanded perlite (EPB) 0.0454
- 0.0704 Source: http://en.wikipedia.org/wiki/lumber
Sheep wool 0.0356
- 0.0452
1" = 25.4 mm 1' = 12" = 0.3048 m
Cellulose (blown fibres) 0.0392,3
- 0.0506
Strawbale 0.0602
- 0.0752 1 Passive House Planning Package PHPP; Version 8;
Darmstadt, 2013 [PHPP:46]
2 Building Science for Building Enclosures; Straube,
Burnett; Building Science Press; 2005
3 ASHRAE Handbook; Parsons; 2005
4 Dämmstoffe: Grundlagen, Materialien,
Anwendungen; DETAIL; Munich; 2007
5 Building Enclosure Design Guide; HPO; 2011
6 www.wecobis.de; July 2015
7 www.u-wert.de/daemmstoffe; July 2015
8 Agepan System Brochure; July 2015
9 www.roxul.com; July 2015
10 www.geocell-schaumglas.eu; July 2015
11 www.jackon-insulation.com; July 2015
12 www.building-int.foamglas.com; July 2015
13 www.quinn-lite.com; July 2015
14 www.kingspaninsulation.de; July 2015
15 Schaumglasschotter als Wärmedämmung;
Fraunhofer-IBP
Additional data is available in EN 12524 and national
standards. For modelling and project certification use
rated design values declared on technical data sheets.
Cellular Glass 0.0451
- 0.0601
Foamglas Perinsul loadbearing 0.05012
Foam glass gravel (dry) 0.08015
- 0.09515
Foam glass gravel (design value) 0.11015
- 0.14015
Geocell Foam Glass Gravel (design value) 0.11010
Expanded Rigid Polystyrene Foam (EPS) 0.0351
- 0.0401
Extruded Rigid Polystyrene Foam (XPS) 0.0301
- 0.0401
Jackodur Atlas (load bearing XPS) 0.03511
- 0.03811
Rigid Polyurethane Foam boards (PUR) 0.0236
- 0.0401
Low density open-cell spray foam (PUR) 0.0405
- 0.0385
High density closed-cell spray foam (PUR) 0.0285
- 0.0245
Rigid Polyisocyanurate 0.0202
- 0.0242
Rigid Phenolic foam (closed cell) 0.0172,3
- 0.0202
Kingspan Kooltherm phenolic foam board 0.02114
- 0.02214
Aerogel 0.0174
- 0.0214
Vacuum Insulated Panel (VIP) 0.0024
- 0.0084
Air space depending on thickness and heat flow  [PHPP:49]
available at:
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Material
Thermal
conductivity λ
W / mK
Umetric �
W
m2K
� =
5.678
Rimp. �
ft2
F h
Btu
�
U-value RSI U-value R-value
W /
m
2
K
m
2
K /
W
Btu /
ft
2
F h
ft
2
F h /
Btu
typicalvaluesforopaqueelements
0.055 18.18 0.010 103.24
0.060 16.67 0.011 94.64
0.065 15.38 0.011 87.36
0.070 14.29 0.012 81.12
0.075 13.33 0.013 75.71
0.080 12.50 0.014 70.98
0.085 11.76 0.015 66.80
0.090 11.11 0.016 63.09
0.095 10.53 0.017 59.77
0.100 10.00 0.018 56.78
0.105 9.52 0.018 54.08
0.110 9.09 0.019 51.62
0.115 8.70 0.020 49.38
0.120 8.33 0.021 47.32
0.125 8.00 0.022 45.43
0.130 7.69 0.023 43.68
0.135 7.41 0.024 42.06
0.140 7.14 0.025 40.56
0.145 6.90 0.026 39.16
0.150 6.67 0.026 37.86
0.20 5.00 0.035 28.39
0.25 4.00 0.044 22.71
0.30 3.33 0.053 18.93
0.35 2.86 0.062 16.22
0.40 2.50 0.070 14.20
0.45 2.22 0.079 12.62
0.50 2.00 0.088 11.36
0.55 1.82 0.097 10.32
typicalvaluesforwindows
0.60 1.67 0.106 9.46
0.61 1.64 0.107 9.31
0.62 1.61 0.109 9.16
0.63 1.59 0.111 9.01
0.64 1.56 0.113 8.87
0.65 1.54 0.114 8.74
0.66 1.52 0.116 8.60
0.67 1.49 0.118 8.48
0.68 1.47 0.120 8.35
0.69 1.45 0.122 8.23
0.70 1.43 0.123 8.11
0.71 1.41 0.125 8.00
0.72 1.39 0.127 7.89
0.73 1.37 0.129 7.78
0.74 1.35 0.130 7.67
0.75 1.33 0.132 7.57
0.76 1.32 0.134 7.47
0.77 1.30 0.136 7.37
0.78 1.28 0.137 7.28
0.79 1.27 0.139 7.19
0.80 1.25 0.141 7.10
0.81 1.23 0.143 7.01
0.82 1.22 0.144 6.92
0.83 1.20 0.146 6.84
0.84 1.19 0.148 6.76
0.85 1.18 0.150 6.68
0.86 1.16 0.151 6.60
0.87 1.15 0.153 6.53
0.88 1.14 0.155 6.45
0.89 1.12 0.157 6.38
0.90 1.11 0.158 6.31
0.95 1.05 0.167 5.98
1.00 1.00 0.176 5.68
1.05 0.95 0.185 5.41
1.10 0.91 0.194 5.16
1.15 0.87 0.203 4.94
1.20 0.83 0.211 4.73
1.25 0.80 0.220 4.54
1.30 0.77 0.229 4.37
1.35 0.74 0.238 4.21
1.40 0.71 0.247 4.06
1.45 0.69 0.255 3.92
1.50 0.67 0.264 3.79
Find converter tool app for mobile
devices on www.15kwh10w.com
Copper 3802
Aluminium 1601,2
- 2002
Mild Steel 402
- 501
- 802
λmetric �
W
mK
� =
0.1442
Rper inch �
ft2
F h
Btu inch
�
Stainless Steel 171
Concrete (Reinforced) 1.42
- 2.11
- 2.62
Cement Screed 1.41
Lightweight Concrete 0.151
- 0.31
Quinn Lite aerated concrete 0.1213
- 0.1913
Annual Energy Demand
Natural Stone 1.51
- 3.51
kWh /
m
2
a
kBtu /
ft
2
a
kWh /
ft
2
aSand-Lime Masonry 11
Solid Clay Brick Masonry 0.81
- 1.21
1 0.317 0.093
Vertically Perforated Lightweight Masonry 0.31
- 0.451
15* 4.755 1.394
Adobe 0.41
- 0.82
25* 7.925 2.323
Float Glass 11
30** 9.510 2.787
Solid Plastic (Typical) 0.171
- 0.31
45** 14.26 4.181
Rubber 0.171
60** 19.02 5.574
Linoleum 0.171
120** 38.04 11.15
Carpet 0.061 * Heating /cooling criteria for PH and
EnerPHit ** Primary Energy criteriaGypsum Plaster 0.181
- 0.561
Gypsum Plasterboard 0.251
For wood and wood products the thermal conductivity is to be multiplied by
a factor of 2.2 when the heat flow is parallel to the direction of the fibres.1
Heating Load
W /
m
2
Btu /
h.ft
2
Hardwood 0.181
Softwood 0.131
1 0.317
Chipboard 0.101
- 0.181
10* 3.171
Oriented Strand Board (OSB) 0.092
- 0.131 * Heating load criterion for PH
Plywood 0.082
- 0.112
Medium Density Fibreboard (MDF) 0.071
- 0.181
North American Softwood
Dimensional Lumber sizesWood Wool Lightweight Building Board 0.0651
- 0.0901
Fibre Insulating Material 0.0351
- 0.0501
nominal actual actual
Wooden Softboard 0.0401
- 0.0701
1" ¾" 19 mm
Agepan DWD Protect 0.0908
2" 1-½" 38 mm
Agepan THD Insulating Wood Fibre Board 0.0468
- 0.0508
3" 2-½" 64 mm
Agepan THD Static 0.0558
4" 3-½" 89 mm
Corkboard 0.0422
5" 4-½" 114 mm
Coconut Fibre 0.0404
- 0.0504
6" 5-½" 140 mm
Flax / hemp board 0.0406
7" 6-¼" 159 mm
Mineral wool (rock wool, fibreglass batts) 0.0351
- 0.0451
8" 7-¼" 184 mm
Roxul ComfortBoard CIS 0.0369
10" 9-¼" 235 mm
Fibreglass (blown fibres) 0.0383
- 0.0393
12" 11-¼" 286 mm
Expanded perlite (EPB) 0.0454
- 0.0704 Source: http://en.wikipedia.org/wiki/lumber
Sheep wool 0.0356
- 0.0452
1" = 25.4 mm 1' = 12" = 0.3048 m
Cellulose (blown fibres) 0.0392,3
- 0.0506
Strawbale 0.0602
- 0.0752 1 Passive House Planning Package PHPP; Version 8;
Darmstadt, 2013 [PHPP:46]
2 Building Science for Building Enclosures; Straube,
Burnett; Building Science Press; 2005
3 ASHRAE Handbook; Parsons; 2005
4 Dämmstoffe: Grundlagen, Materialien,
Anwendungen; DETAIL; Munich; 2007
5 Building Enclosure Design Guide; HPO; 2011
6 www.wecobis.de; July 2015
7 www.u-wert.de/daemmstoffe; July 2015
8 Agepan System Brochure; July 2015
9 www.roxul.com; July 2015
10 www.geocell-schaumglas.eu; July 2015
11 www.jackon-insulation.com; July 2015
12 www.building-int.foamglas.com; July 2015
13 www.quinn-lite.com; July 2015
14 www.kingspaninsulation.de; July 2015
15 Schaumglasschotter als Wärmedämmung;
Fraunhofer-IBP
Additional data is available in EN 12524 and national
standards. For modelling and project certification use
rated design values declared on technical data sheets.
Cellular Glass 0.0451
- 0.0601
Foamglas Perinsul loadbearing 0.05012
Foam glass gravel (dry) 0.08015
- 0.09515
Foam glass gravel (design value) 0.11015
- 0.14015
Geocell Foam Glass Gravel (design value) 0.11010
Expanded Rigid Polystyrene Foam (EPS) 0.0351
- 0.0401
Extruded Rigid Polystyrene Foam (XPS) 0.0301
- 0.0401
Jackodur Atlas (load bearing XPS) 0.03511
- 0.03811
Rigid Polyurethane Foam boards (PUR) 0.0236
- 0.0401
Low density open-cell spray foam (PUR) 0.0405
- 0.0385
High density closed-cell spray foam (PUR) 0.0285
- 0.0245
Rigid Polyisocyanurate 0.0202
- 0.0242
Rigid Phenolic foam (closed cell) 0.0172,3
- 0.0202
Kingspan Kooltherm phenolic foam board 0.02114
- 0.02214
Aerogel 0.0174
- 0.0214
Vacuum Insulated Panel (VIP) 0.0024
- 0.0084
Air space depending on thickness and heat flow  [PHPP:49]
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SEE NEXT PAGES
Which final value Kn does a current
capital K0 have at a future date t?
Which present value K0
does one future capital Kn have?
does a constant payment A have?
How high is the annuity A, that is
to be paid from a present value K0?
Kn = K0 × (1 + p)t
K0 = Kn × (1 + p)-t
K0 = A ×
1 - (1 + p)-n
p
A = K0 ×
p
1 - (1 + p)-n
Accumulation factor Discount factor:
equals the reciprocal value of the
accumulation factor = 1 / (1 + p)
t
Present value factor B:
equals the accumulated discount
factors of the considered time period
Annuity factor a = 1/B:
reciprocal value of the
present value factor
t = time index = interval from point of reference (t0 = starting date) n = useful life = number of periods = repayment period = length of mortgage
p = interest rate [decimal] (use real interest rate for investment considerations) initial repayment rate = a - p a = annuity factor
A = annuity = stream of payments (or income) with a fixed amount Ki B = present value factor
Kn = capital at a given time tn = future value / final value annuity A = present value K0 / present value factor B = K0 × annuity factor a
K0 = capital at a given time t0 = net present value NPV of annuity = current value of a stream of payments discounted by the interest rate
Net Present Value of an Annuity K0 = A ×
1 - (1 + p)-n
p
Capital to invest today for 3 years,
at an interest rate of 3.5%,
to be able to withdraw 500$ at the end of each year?
K0 = 500$ ×
1 - (1+0.035)-3
0.035
= 500$ × 2.802 = 1,401 $
What additional mortgage could be supported
by annual savings of 1,500$ on heating cost,
at an interest rate of 3% borrowed for 25 years?
K0 = 1,500$ ×
1 - (1+0.03)-25
0.03
= 1,500$ × 17.413 = 26,119 $
Annuity Calculation A = K0 ×
p
1 - (1 + p)-n
Which amount can be taken at the end of each year
for the next 4 years, from an initial capital of 3,000$
at an interest rate of 3.5%?
A = 3,000$ ×
0.035
1 - (1+0.035)-4 = 3,000$ × 0.272 = 816.75 $
A client borrows 250,000$ for construction, at an interest rate
of p = 4.5% for a repayment period n = 30a.
How high is monthly annuity (interest and repayment)?
What is the initial repayment rate?
A = 250,000$ ×
0.045
1 - (1+0.045)-30 = 250,000$ × 0.0614 = 15,347.89 $/a
monthly charge = 15,347$ / 12months = 1,278.99 $/month
initial repayment rate = annuity factor a – interest rate p = 0.0614 – 0.045 = 1.64%
Nominal and real interest rates:
pnominal = nominal interest rate (e.g. 7.5%)
i = inflation rate (e.g. 4%)
preal = real interest rate (inflation adjusted)
preal =
1 + pnominal
1 + i
- 1
At low inflation and interest rates
the result is approximately:
preal = pnominal - i
preal = (1+0.075) (1+0.04)⁄ - 1 = 0.034 = 3.4% preal = 0.075 - 0.04 = 0.035 = 3.5%
Profitability of energy saving measures calculated with  Pactual = 0.055 $/kWh:  Psaved = 0.0142 $/kWh:
Annual cost without
energy saving measures:
Aexist = P × Eexist
Aexist = 0.055$/kWh × [250m
2
× 1.03W/m
2
K × 1 × 84kKh/a / 0.90]
Aexist = 0.055$/kWh × 24,033kWh/a = 1,321 $/a
Aexist = 0.0142 × 24,033
= 341 $/a
Annual cost
with saving
measure:
Anew = P × Enew + aloan × (Iadd - R) + Z Anew = 0.055$/kWh × [250m
2
x 0.150W/m
2
K × 1 × 84kKh/a / 0.90]
+ 0.0672 × ($7,500$ - 3,170.79$) + 0$
Anew = 0.055$/kWh × 3,500 kWh/a + 291$ + 0$ = 483 $/a
Anew = 0.0142 × 3,500
+ 291 + 0
= 341 $/a
annual energy cost annuity of new
with saving measure investment
 Profitability if: Anew < Aexist 483 $ < 1,321 $  measure pays off  measure just pays off
Equivalent price of saved energy: aloan(20years,3%) = 0.0672 Iadd = 250m
2
× 1.50$/cm/m
2
× 20cm = 7,500 $
R = (1- a50years,3% x B20years,3%) × Iadd = (1- 0.0388 × 14.877) × 7,500$ = 3,170.79 $
Esaved = 250m
2
× (1.03-0.15)W/m
2
K × 1.0 × 84kKa/a / 0.90 = 250m
2
× 82.13kWh/a = 20,533 kWh/a
Psaved =
0.0672 × (7,500$ - 3,170.79$)+ 0$
20,533kWh/a
= 0.0142 $/kWh
Psaved =
aloan × (Iadd - Rcomponent) + Z
Esaved
Investment worthwhile if:
aloan × (Iadd - R) + Z ≤ (P × E)saved 0.0672 × (7,500$ - 3,170.79$) + 0$ ≤ 0.055$/kWh × 20,533kWh/a  291 $ ≤ 1,129 $  worthwhile
a = annuity factor B = present value factor
Iadd = additional cost of investment for saving measures
R = residual value of component R = (1 - alife expectancy × Binvestment) × Iadd
(A building component with an expected lifetime of 50 years has a
residual value of 39% after 20 years at preal = 3.5%.)
Z = possible additional cost for operational and maintenance cost
resulting from the saving measure (e.g. for mechanical systems,
not applicable for insulation)
P = price per energy unit
Psaved = equivalent price for saved energy
Example above:
new 20cm EIFS (1.50$/m
2
/cm) on existing 250m
2
wall,
resulting in improved U-value from 1.03W/m
2
K to 0.150W/m
2
K
lifetime of EIFS L = 50a ƞheating = 90%
time period under consideration n = 20a real interest rate i = 3%
Enew = annual energy consumption after taking energy saving measure
Eexist = annual energy consumption without taking measure
Esaved = Eexist - Enew = annual energy savings after taking measure
Esaved = Acomponent × q = Acomponent × Usaved × ft × Gt / ƞ Usaved = (Uexist – Unew)
ƞ = marginal annual efficiency of heating system
In a Passive House the investment becomes more important – and base prices for energy supply systems are significant. But energy costs
become almost insignificant because of the low consumption.
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Which final value Kn does a current
capital K0 have at a future date t?
does one future capital Kn have?
does a constant payment A have?
How high is the annuity A, that is
to be paid from a present value K0?
Kn = K0 × (1 + p)t
K0 = Kn × (1 + p)-t
K0 = A ×
1 - (1 + p)-n
p
A = K0 ×
p
1 - (1 + p)-n
Accumulation factor Discount factor:
equals the reciprocal value of the
accumulation factor = 1 / (1 + p)
t
Present value factor B:
equals the accumulated discount
factors of the considered time period
Annuity factor a = 1/B:
reciprocal value of the
present value factor
t = time index = interval from point of reference (t0 = starting date) n = useful life = number of periods = repayment period = length of mortgage
p = interest rate [decimal] (use real interest rate for investment considerations) initial repayment rate = a - p a = annuity factor
A = annuity = stream of payments (or income) with a fixed amount Ki B = present value factor
Kn = capital at a given time tn = future value / final value annuity A = present value K0 / present value factor B = K0 × annuity factor a
K0 = capital at a given time t0 = net present value NPV of annuity = current value of a stream of payments discounted by the interest rate
Net Present Value of an Annuity K0 = A ×
1 - (1 + p)-n
p
Capital to invest today for 3 years,
at an interest rate of 3.5%,
to be able to withdraw 500$ at the end of each year?
K0 = 500$ ×
1 - (1+0.035)-3
0.035
= 500$ × 2.802 = 1,401 $
What additional mortgage could be supported
by annual savings of 1,500$ on heating cost,
at an interest rate of 3% borrowed for 25 years?
K0 = 1,500$ ×
1 - (1+0.03)-25
0.03
= 1,500$ × 17.413 = 26,119 $
Annuity Calculation A = K0 ×
p
1 - (1 + p)-n
Which amount can be taken at the end of each year
for the next 4 years, from an initial capital of 3,000$
at an interest rate of 3.5%?
A = 3,000$ ×
0.035
1 - (1+0.035)-4 = 3,000$ × 0.272 = 816.75 $
A client borrows 250,000$ for construction, at an interest rate
of p = 4.5% for a repayment period n = 30a.
How high is monthly annuity (interest and repayment)?
What is the initial repayment rate?
A = 250,000$ ×
0.045
1 - (1+0.045)-30 = 250,000$ × 0.0614 = 15,347.89 $/a
monthly charge = 15,347$ / 12months = 1,278.99 $/month
initial repayment rate = annuity factor a – interest rate p = 0.0614 – 0.045 = 1.64%
Nominal and real interest rates:
pnominal = nominal interest rate (e.g. 7.5%)
i = inflation rate (e.g. 4%)
preal = real interest rate (inflation adjusted)
preal =
1 + pnominal
1 + i
- 1
At low inflation and interest rates
the result is approximately:
preal = pnominal - i
preal = (1+0.075) (1+0.04)⁄ - 1 = 0.034 = 3.4% preal = 0.075 - 0.04 = 0.035 = 3.5%
Profitability of energy saving measures calculated with  Pactual = 0.055 $/kWh:  Psaved = 0.0142 $/kWh:
Annual cost without
energy saving measures:
Aexist = P × Eexist
Aexist = 0.055$/kWh × [250m
2
× 1.03W/m
2
K × 1 × 84kKh/a / 0.90]
Aexist = 0.055$/kWh × 24,033kWh/a = 1,321 $/a
Aexist = 0.0142 × 24,033
= 341 $/a
Annual cost
with saving
measure:
Anew = P × Enew + aloan × (Iadd - R) + Z Anew = 0.055$/kWh × [250m
2
x 0.150W/m
2
K × 1 × 84kKh/a / 0.90]
+ 0.0672 × ($7,500$ - 3,170.79$) + 0$
Anew = 0.055$/kWh × 3,500 kWh/a + 291$ + 0$ = 483 $/a
Anew = 0.0142 × 3,500
+ 291 + 0
= 341 $/a
annual energy cost annuity of new
with saving measure investment
 Profitability if: Anew < Aexist 483 $ < 1,321 $  measure pays off  measure just pays off
Equivalent price of saved energy: aloan(20years,3%) = 0.0672 Iadd = 250m
2
× 1.50$/cm/m
2
× 20cm = 7,500 $
R = (1- a50years,3% x B20years,3%) × Iadd = (1- 0.0388 × 14.877) × 7,500$ = 3,170.79 $
Esaved = 250m
2
× (1.03-0.15)W/m
2
K × 1.0 × 84kKa/a / 0.90 = 250m
2
× 82.13kWh/a = 20,533 kWh/a
Psaved =
0.0672 × (7,500$ - 3,170.79$)+ 0$
20,533kWh/a
= 0.0142 $/kWh
Psaved =
aloan × (Iadd - Rcomponent) + Z
Esaved
Investment worthwhile if:
aloan × (Iadd - R) + Z ≤ (P × E)saved 0.0672 × (7,500$ - 3,170.79$) + 0$ ≤ 0.055$/kWh × 20,533kWh/a  291 $ ≤ 1,129 $  worthwhile
a = annuity factor B = present value factor
Iadd = additional cost of investment for saving measures
R = residual value of component R = (1 - alife expectancy × Binvestment) × Iadd
(A building component with an expected lifetime of 50 years has a
residual value of 39% after 20 years at preal = 3.5%.)
Z = possible additional cost for operational and maintenance cost
resulting from the saving measure (e.g. for mechanical systems,
not applicable for insulation)
P = price per energy unit
Psaved = equivalent price for saved energy
Example above:
new 20cm EIFS (1.50$/m
2
/cm) on existing 250m
2
wall,
resulting in improved U-value from 1.03W/m
2
K to 0.150W/m
2
K
lifetime of EIFS L = 50a ƞheating = 90%
time period under consideration n = 20a real interest rate i = 3%
Enew = annual energy consumption after taking energy saving measure
Eexist = annual energy consumption without taking measure
Esaved = Eexist - Enew = annual energy savings after taking measure
Esaved = Acomponent × q = Acomponent × Usaved × ft × Gt / ƞ Usaved = (Uexist – Unew)
ƞ = marginal annual efficiency of heating system
In a Passive House the investment becomes more important – and base prices for energy supply systems are significant. But energy costs
become almost insignificant because of the low consumption.
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Present Value Factor B =
1 - (1 + p)-n
p
n↓
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
←p
10.0%
0.9091
1.7355
2.4869
3.1699
3.7908
4.3553
4.8684
5.3349
5.7590
6.1446
6.4951
6.8137
7.1034
7.3667
7.6061
7.8237
8.0216
8.2014
8.3649
8.5136
8.6487
8.7715
8.8832
8.9847
9.0770
9.1609
9.2372
9.3066
9.3696
9.4269
9.4790
9.5264
9.5694
9.6086
9.6442
9.6765
9.7059
9.7327
9.7570
9.7791
9.7991
9.8174
9.8340
9.8491
9.8628
9.8753
9.8866
9.8969
9.9063
9.9148
10.0%
9.5%
0.9132
1.7473
2.5089
3.2045
3.8397
4.4198
4.9496
5.4334
5.8753
6.2788
6.6473
6.9838
7.2912
7.5719
7.8282
8.0623
8.2760
8.4713
8.6496
8.8124
8.9611
9.0969
9.2209
9.3341
9.4376
9.5320
9.6183
9.6971
9.7690
9.8347
9.8947
9.9495
9.9996
10.0453
10.0870
10.1251
10.1599
10.1917
10.2207
10.2472
10.2715
10.2936
10.3138
10.3322
10.3490
10.3644
10.3785
10.3913
10.4030
10.4137
9.5%
9.0%
0.9174
1.7591
2.5313
3.2397
3.8897
4.4859
5.0330
5.5348
5.9952
6.4177
6.8052
7.1607
7.4869
7.7862
8.0607
8.3126
8.5436
8.7556
8.9501
9.1285
9.2922
9.4424
9.5802
9.7066
9.8226
9.9290
10.0266
10.1161
10.1983
10.2737
10.3428
10.4062
10.4644
10.5178
10.5668
10.6118
10.6530
10.6908
10.7255
10.7574
10.7866
10.8134
10.8380
10.8605
10.8812
10.9002
10.9176
10.9336
10.9482
10.9617
9.0%
8.5%
0.9217
1.7711
2.5540
3.2756
3.9406
4.5536
5.1185
5.6392
6.1191
6.5613
6.9690
7.3447
7.6910
8.0101
8.3042
8.5753
8.8252
9.0555
9.2677
9.4633
9.6436
9.8098
9.9629
10.1041
10.2342
10.3541
10.4646
10.5665
10.6603
10.7468
10.8266
10.9001
10.9678
11.0302
11.0878
11.1408
11.1897
11.2347
11.2763
11.3145
11.3498
11.3823
11.4123
11.4399
11.4653
11.4888
11.5104
11.5303
11.5487
11.5656
8.5%
8.0%
0.9259
1.7833
2.5771
3.3121
3.9927
4.6229
5.2064
5.7466
6.2469
6.7101
7.1390
7.5361
7.9038
8.2442
8.5595
8.8514
9.1216
9.3719
9.6036
9.8181
10.0168
10.2007
10.3711
10.5288
10.6748
10.8100
10.9352
11.0511
11.1584
11.2578
11.3498
11.4350
11.5139
11.5869
11.6546
11.7172
11.7752
11.8289
11.8786
11.9246
11.9672
12.0067
12.0432
12.0771
12.1084
12.1374
12.1643
12.1891
12.2122
12.2335
8.0%
7.5%
0.9302
1.7956
2.6005
3.3493
4.0459
4.6938
5.2966
5.8573
6.3789
6.8641
7.3154
7.7353
8.1258
8.4892
8.8271
9.1415
9.4340
9.7060
9.9591
10.1945
10.4135
10.6172
10.8067
10.9830
11.1469
11.2995
11.4414
11.5734
11.6962
11.8104
11.9166
12.0155
12.1074
12.1929
12.2725
12.3465
12.4154
12.4794
12.5390
12.5944
12.6460
12.6939
12.7385
12.7800
12.8186
12.8545
12.8879
12.9190
12.9479
12.9748
7.5%
7.0%
0.9346
1.8080
2.6243
3.3872
4.1002
4.7665
5.3893
5.9713
6.5152
7.0236
7.4987
7.9427
8.3577
8.7455
9.1079
9.4466
9.7632
10.0591
10.3356
10.5940
10.8355
11.0612
11.2722
11.4693
11.6536
11.8258
11.9867
12.1371
12.2777
12.4090
12.5318
12.6466
12.7538
12.8540
12.9477
13.0352
13.1170
13.1935
13.2649
13.3317
13.3941
13.4524
13.5070
13.5579
13.6055
13.6500
13.6916
13.7305
13.7668
13.8007
7.0%
6.5%
0.9390
1.8206
2.6485
3.4258
4.1557
4.8410
5.4845
6.0888
6.6561
7.1888
7.6890
8.1587
8.5997
9.0138
9.4027
9.7678
10.1106
10.4325
10.7347
11.0185
11.2850
11.5352
11.7701
11.9907
12.1979
12.3924
12.5750
12.7465
12.9075
13.0587
13.2006
13.3339
13.4591
13.5766
13.6870
13.7906
13.8879
13.9792
14.0650
14.1455
14.2212
14.2922
14.3588
14.4214
14.4802
14.5354
14.5873
14.6359
14.6816
14.7245
6.5%
6.0%
0.9434
1.8334
2.6730
3.4651
4.2124
4.9173
5.5824
6.2098
6.8017
7.3601
7.8869
8.3838
8.8527
9.2950
9.7122
10.1059
10.4773
10.8276
11.1581
11.4699
11.7641
12.0416
12.3034
12.5504
12.7834
13.0032
13.2105
13.4062
13.5907
13.7648
13.9291
14.0840
14.2302
14.3681
14.4982
14.6210
14.7368
14.8460
14.9491
15.0463
15.1380
15.2245
15.3062
15.3832
15.4558
15.5244
15.5890
15.6500
15.7076
15.7619
6.0%
5.5%
0.9479
1.8463
2.6979
3.5052
4.2703
4.9955
5.6830
6.3346
6.9522
7.5376
8.0925
8.6185
9.1171
9.5896
10.0376
10.4622
10.8646
11.2461
11.6077
11.9504
12.2752
12.5832
12.8750
13.1517
13.4139
13.6625
13.8981
14.1214
14.3331
14.5337
14.7239
14.9042
15.0751
15.2370
15.3906
15.5361
15.6740
15.8047
15.9287
16.0461
16.1575
16.2630
16.3630
16.4579
16.5477
16.6329
16.7137
16.7902
16.8628
16.9315
5.5%
5.0%
0.9524
1.8594
2.7232
3.5460
4.3295
5.0757
5.7864
6.4632
7.1078
7.7217
8.3064
8.8633
9.3936
9.8986
10.3797
10.8378
11.2741
11.6896
12.0853
12.4622
12.8212
13.1630
13.4886
13.7986
14.0939
14.3752
14.6430
14.8981
15.1411
15.3725
15.5928
15.8027
16.0025
16.1929
16.3742
16.5469
16.7113
16.8679
17.0170
17.1591
17.2944
17.4232
17.5459
17.6628
17.7741
17.8801
17.9810
18.0772
18.1687
18.2559
5.0%
4.5%
0.9569
1.8727
2.7490
3.5875
4.3900
5.1579
5.8927
6.5959
7.2688
7.9127
8.5289
9.1186
9.6829
10.2228
10.7395
11.2340
11.7072
12.1600
12.5933
13.0079
13.4047
13.7844
14.1478
14.4955
14.8282
15.1466
15.4513
15.7429
16.0219
16.2889
16.5444
16.7889
17.0229
17.2468
17.4610
17.6660
17.8622
18.0500
18.2297
18.4016
18.5661
18.7235
18.8742
19.0184
19.1563
19.2884
19.4147
19.5356
19.6513
19.7620
4.5%
4.0%
0.9615
1.8861
2.7751
3.6299
4.4518
5.2421
6.0021
6.7327
7.4353
8.1109
8.7605
9.3851
9.9856
10.5631
11.1184
11.6523
12.1657
12.6593
13.1339
13.5903
14.0292
14.4511
14.8568
15.2470
15.6221
15.9828
16.3296
16.6631
16.9837
17.2920
17.5885
17.8736
18.1476
18.4112
18.6646
18.9083
19.1426
19.3679
19.5845
19.7928
19.9931
20.1856
20.3708
20.5488
20.7200
20.8847
21.0429
21.1951
21.3415
21.4822
4.0%
3.5%
0.9662
1.8997
2.8016
3.6731
4.5151
5.3286
6.1145
6.8740
7.6077
8.3166
9.0016
9.6633
10.3027
10.9205
11.5174
12.0941
12.6513
13.1897
13.7098
14.2124
14.6980
15.1671
15.6204
16.0584
16.4815
16.8904
17.2854
17.6670
18.0358
18.3920
18.7363
19.0689
19.3902
19.7007
20.0007
20.2905
20.5705
20.8411
21.1025
21.3551
21.5991
21.8349
22.0627
22.2828
22.4955
22.7009
22.8994
23.0912
23.2766
23.4556
3.5%
3.0%
0.9709
1.9135
2.8286
3.7171
4.5797
5.4172
6.2303
7.0197
7.7861
8.5302
9.2526
9.9540
10.6350
11.2961
11.9379
12.5611
13.1661
13.7535
14.3238
14.8775
15.4150
15.9369
16.4436
16.9355
17.4131
17.8768
18.3270
18.7641
19.1885
19.6004
20.0004
20.3888
20.7658
21.1318
21.4872
21.8323
22.1672
22.4925
22.8082
23.1148
23.4124
23.7014
23.9819
24.2543
24.5187
24.7754
25.0247
25.2667
25.5017
25.7298
3.0%
2.5%
0.9756
1.9274
2.8560
3.7620
4.6458
5.5081
6.3494
7.1701
7.9709
8.7521
9.5142
10.2578
10.9832
11.6909
12.3814
13.0550
13.7122
14.3534
14.9789
15.5892
16.1845
16.7654
17.3321
17.8850
18.4244
18.9506
19.4640
19.9649
20.4535
20.9303
21.3954
21.8492
22.2919
22.7238
23.1452
23.5563
23.9573
24.3486
24.7303
25.1028
25.4661
25.8206
26.1664
26.5038
26.8330
27.1542
27.4675
27.7732
28.0714
28.3623
2.5%
2.0%
0.9804
1.9416
2.8839
3.8077
4.7135
5.6014
6.4720
7.3255
8.1622
8.9826
9.7868
10.5753
11.3484
12.1062
12.8493
13.5777
14.2919
14.9920
15.6785
16.3514
17.0112
17.6580
18.2922
18.9139
19.5235
20.1210
20.7069
21.2813
21.8444
22.3965
22.9377
23.4683
23.9886
24.4986
24.9986
25.4888
25.9695
26.4406
26.9026
27.3555
27.7995
28.2348
28.6616
29.0800
29.4902
29.8923
30.2866
30.6731
31.0521
31.4236
2.0%
1.5%
0.9852
1.9559
2.9122
3.8544
4.7826
5.6972
6.5982
7.4859
8.3605
9.2222
10.0711
10.9075
11.7315
12.5434
13.3432
14.1313
14.9076
15.6726
16.4262
17.1686
17.9001
18.6208
19.3309
20.0304
20.7196
21.3986
22.0676
22.7267
23.3761
24.0158
24.6461
25.2671
25.8790
26.4817
27.0756
27.6607
28.2371
28.8051
29.3646
29.9158
30.4590
30.9941
31.5212
32.0406
32.5523
33.0565
33.5532
34.0426
34.5247
34.9997
1.5%
1.0%
0.9901
1.9704
2.9410
3.9020
4.8534
5.7955
6.7282
7.6517
8.5660
9.4713
10.3676
11.2551
12.1337
13.0037
13.8651
14.7179
15.5623
16.3983
17.2260
18.0456
18.8570
19.6604
20.4558
21.2434
22.0232
22.7952
23.5596
24.3164
25.0658
25.8077
26.5423
27.2696
27.9897
28.7027
29.4086
30.1075
30.7995
31.4847
32.1630
32.8347
33.4997
34.1581
34.8100
35.4555
36.0945
36.7272
37.3537
37.9740
38.5881
39.1961
1.0%
p→
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
↑n
available at:
15kwh10w.com

www.15kwh10w.com
Present Value Factor B =
1 - (1 + p)-n
p
n↓
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
←p
10.0%
0.9091
1.7355
2.4869
3.1699
3.7908
4.3553
4.8684
5.3349
5.7590
6.1446
6.4951
6.8137
7.1034
7.3667
7.6061
7.8237
8.0216
8.2014
8.3649
8.5136
8.6487
8.7715
8.8832
8.9847
9.0770
9.1609
9.2372
9.3066
9.3696
9.4269
9.4790
9.5264
9.5694
9.6086
9.6442
9.6765
9.7059
9.7327
9.7570
9.7791
9.7991
9.8174
9.8340
9.8491
9.8628
9.8753
9.8866
9.8969
9.9063
9.9148
10.0%
9.5%
0.9132
1.7473
2.5089
3.2045
3.8397
4.4198
4.9496
5.4334
5.8753
6.2788
6.6473
6.9838
7.2912
7.5719
7.8282
8.0623
8.2760
8.4713
8.6496
8.8124
8.9611
9.0969
9.2209
9.3341
9.4376
9.5320
9.6183
9.6971
9.7690
9.8347
9.8947
9.9495
9.9996
10.0453
10.0870
10.1251
10.1599
10.1917
10.2207
10.2472
10.2715
10.2936
10.3138
10.3322
10.3490
10.3644
10.3785
10.3913
10.4030
10.4137
9.5%
9.0%
0.9174
1.7591
2.5313
3.2397
3.8897
4.4859
5.0330
5.5348
5.9952
6.4177
6.8052
7.1607
7.4869
7.7862
8.0607
8.3126
8.5436
8.7556
8.9501
9.1285
9.2922
9.4424
9.5802
9.7066
9.8226
9.9290
10.0266
10.1161
10.1983
10.2737
10.3428
10.4062
10.4644
10.5178
10.5668
10.6118
10.6530
10.6908
10.7255
10.7574
10.7866
10.8134
10.8380
10.8605
10.8812
10.9002
10.9176
10.9336
10.9482
10.9617
9.0%
8.5%
0.9217
1.7711
2.5540
3.2756
3.9406
4.5536
5.1185
5.6392
6.1191
6.5613
6.9690
7.3447
7.6910
8.0101
8.3042
8.5753
8.8252
9.0555
9.2677
9.4633
9.6436
9.8098
9.9629
10.1041
10.2342
10.3541
10.4646
10.5665
10.6603
10.7468
10.8266
10.9001
10.9678
11.0302
11.0878
11.1408
11.1897
11.2347
11.2763
11.3145
11.3498
11.3823
11.4123
11.4399
11.4653
11.4888
11.5104
11.5303
11.5487
11.5656
8.5%
8.0%
0.9259
1.7833
2.5771
3.3121
3.9927
4.6229
5.2064
5.7466
6.2469
6.7101
7.1390
7.5361
7.9038
8.2442
8.5595
8.8514
9.1216
9.3719
9.6036
9.8181
10.0168
10.2007
10.3711
10.5288
10.6748
10.8100
10.9352
11.0511
11.1584
11.2578
11.3498
11.4350
11.5139
11.5869
11.6546
11.7172
11.7752
11.8289
11.8786
11.9246
11.9672
12.0067
12.0432
12.0771
12.1084
12.1374
12.1643
12.1891
12.2122
12.2335
8.0%
7.5%
0.9302
1.7956
2.6005
3.3493
4.0459
4.6938
5.2966
5.8573
6.3789
6.8641
7.3154
7.7353
8.1258
8.4892
8.8271
9.1415
9.4340
9.7060
9.9591
10.1945
10.4135
10.6172
10.8067
10.9830
11.1469
11.2995
11.4414
11.5734
11.6962
11.8104
11.9166
12.0155
12.1074
12.1929
12.2725
12.3465
12.4154
12.4794
12.5390
12.5944
12.6460
12.6939
12.7385
12.7800
12.8186
12.8545
12.8879
12.9190
12.9479
12.9748
7.5%
7.0%
0.9346
1.8080
2.6243
3.3872
4.1002
4.7665
5.3893
5.9713
6.5152
7.0236
7.4987
7.9427
8.3577
8.7455
9.1079
9.4466
9.7632
10.0591
10.3356
10.5940
10.8355
11.0612
11.2722
11.4693
11.6536
11.8258
11.9867
12.1371
12.2777
12.4090
12.5318
12.6466
12.7538
12.8540
12.9477
13.0352
13.1170
13.1935
13.2649
13.3317
13.3941
13.4524
13.5070
13.5579
13.6055
13.6500
13.6916
13.7305
13.7668
13.8007
7.0%
6.5%
0.9390
1.8206
2.6485
3.4258
4.1557
4.8410
5.4845
6.0888
6.6561
7.1888
7.6890
8.1587
8.5997
9.0138
9.4027
9.7678
10.1106
10.4325
10.7347
11.0185
11.2850
11.5352
11.7701
11.9907
12.1979
12.3924
12.5750
12.7465
12.9075
13.0587
13.2006
13.3339
13.4591
13.5766
13.6870
13.7906
13.8879
13.9792
14.0650
14.1455
14.2212
14.2922
14.3588
14.4214
14.4802
14.5354
14.5873
14.6359
14.6816
14.7245
6.5%
6.0%
0.9434
1.8334
2.6730
3.4651
4.2124
4.9173
5.5824
6.2098
6.8017
7.3601
7.8869
8.3838
8.8527
9.2950
9.7122
10.1059
10.4773
10.8276
11.1581
11.4699
11.7641
12.0416
12.3034
12.5504
12.7834
13.0032
13.2105
13.4062
13.5907
13.7648
13.9291
14.0840
14.2302
14.3681
14.4982
14.6210
14.7368
14.8460
14.9491
15.0463
15.1380
15.2245
15.3062
15.3832
15.4558
15.5244
15.5890
15.6500
15.7076
15.7619
6.0%
5.5%
0.9479
1.8463
2.6979
3.5052
4.2703
4.9955
5.6830
6.3346
6.9522
7.5376
8.0925
8.6185
9.1171
9.5896
10.0376
10.4622
10.8646
11.2461
11.6077
11.9504
12.2752
12.5832
12.8750
13.1517
13.4139
13.6625
13.8981
14.1214
14.3331
14.5337
14.7239
14.9042
15.0751
15.2370
15.3906
15.5361
15.6740
15.8047
15.9287
16.0461
16.1575
16.2630
16.3630
16.4579
16.5477
16.6329
16.7137
16.7902
16.8628
16.9315
5.5%
5.0%
0.9524
1.8594
2.7232
3.5460
4.3295
5.0757
5.7864
6.4632
7.1078
7.7217
8.3064
8.8633
9.3936
9.8986
10.3797
10.8378
11.2741
11.6896
12.0853
12.4622
12.8212
13.1630
13.4886
13.7986
14.0939
14.3752
14.6430
14.8981
15.1411
15.3725
15.5928
15.8027
16.0025
16.1929
16.3742
16.5469
16.7113
16.8679
17.0170
17.1591
17.2944
17.4232
17.5459
17.6628
17.7741
17.8801
17.9810
18.0772
18.1687
18.2559
5.0%
4.5%
0.9569
1.8727
2.7490
3.5875
4.3900
5.1579
5.8927
6.5959
7.2688
7.9127
8.5289
9.1186
9.6829
10.2228
10.7395
11.2340
11.7072
12.1600
12.5933
13.0079
13.4047
13.7844
14.1478
14.4955
14.8282
15.1466
15.4513
15.7429
16.0219
16.2889
16.5444
16.7889
17.0229
17.2468
17.4610
17.6660
17.8622
18.0500
18.2297
18.4016
18.5661
18.7235
18.8742
19.0184
19.1563
19.2884
19.4147
19.5356
19.6513
19.7620
4.5%
4.0%
0.9615
1.8861
2.7751
3.6299
4.4518
5.2421
6.0021
6.7327
7.4353
8.1109
8.7605
9.3851
9.9856
10.5631
11.1184
11.6523
12.1657
12.6593
13.1339
13.5903
14.0292
14.4511
14.8568
15.2470
15.6221
15.9828
16.3296
16.6631
16.9837
17.2920
17.5885
17.8736
18.1476
18.4112
18.6646
18.9083
19.1426
19.3679
19.5845
19.7928
19.9931
20.1856
20.3708
20.5488
20.7200
20.8847
21.0429
21.1951
21.3415
21.4822
4.0%
3.5%
0.9662
1.8997
2.8016
3.6731
4.5151
5.3286
6.1145
6.8740
7.6077
8.3166
9.0016
9.6633
10.3027
10.9205
11.5174
12.0941
12.6513
13.1897
13.7098
14.2124
14.6980
15.1671
15.6204
16.0584
16.4815
16.8904
17.2854
17.6670
18.0358
18.3920
18.7363
19.0689
19.3902
19.7007
20.0007
20.2905
20.5705
20.8411
21.1025
21.3551
21.5991
21.8349
22.0627
22.2828
22.4955
22.7009
22.8994
23.0912
23.2766
23.4556
3.5%
3.0%
0.9709
1.9135
2.8286
3.7171
4.5797
5.4172
6.2303
7.0197
7.7861
8.5302
9.2526
9.9540
10.6350
11.2961
11.9379
12.5611
13.1661
13.7535
14.3238
14.8775
15.4150
15.9369
16.4436
16.9355
17.4131
17.8768
18.3270
18.7641
19.1885
19.6004
20.0004
20.3888
20.7658
21.1318
21.4872
21.8323
22.1672
22.4925
22.8082
23.1148
23.4124
23.7014
23.9819
24.2543
24.5187
24.7754
25.0247
25.2667
25.5017
25.7298
3.0%
2.5%
0.9756
1.9274
2.8560
3.7620
4.6458
5.5081
6.3494
7.1701
7.9709
8.7521
9.5142
10.2578
10.9832
11.6909
12.3814
13.0550
13.7122
14.3534
14.9789
15.5892
16.1845
16.7654
17.3321
17.8850
18.4244
18.9506
19.4640
19.9649
20.4535
20.9303
21.3954
21.8492
22.2919
22.7238
23.1452
23.5563
23.9573
24.3486
24.7303
25.1028
25.4661
25.8206
26.1664
26.5038
26.8330
27.1542
27.4675
27.7732
28.0714
28.3623
2.5%
2.0%
0.9804
1.9416
2.8839
3.8077
4.7135
5.6014
6.4720
7.3255
8.1622
8.9826
9.7868
10.5753
11.3484
12.1062
12.8493
13.5777
14.2919
14.9920
15.6785
16.3514
17.0112
17.6580
18.2922
18.9139
19.5235
20.1210
20.7069
21.2813
21.8444
22.3965
22.9377
23.4683
23.9886
24.4986
24.9986
25.4888
25.9695
26.4406
26.9026
27.3555
27.7995
28.2348
28.6616
29.0800
29.4902
29.8923
30.2866
30.6731
31.0521
31.4236
2.0%
1.5%
0.9852
1.9559
2.9122
3.8544
4.7826
5.6972
6.5982
7.4859
8.3605
9.2222
10.0711
10.9075
11.7315
12.5434
13.3432
14.1313
14.9076
15.6726
16.4262
17.1686
17.9001
18.6208
19.3309
20.0304
20.7196
21.3986
22.0676
22.7267
23.3761
24.0158
24.6461
25.2671
25.8790
26.4817
27.0756
27.6607
28.2371
28.8051
29.3646
29.9158
30.4590
30.9941
31.5212
32.0406
32.5523
33.0565
33.5532
34.0426
34.5247
34.9997
1.5%
1.0%
0.9901
1.9704
2.9410
3.9020
4.8534
5.7955
6.7282
7.6517
8.5660
9.4713
10.3676
11.2551
12.1337
13.0037
13.8651
14.7179
15.5623
16.3983
17.2260
18.0456
18.8570
19.6604
20.4558
21.2434
22.0232
22.7952
23.5596
24.3164
25.0658
25.8077
26.5423
27.2696
27.9897
28.7027
29.4086
30.1075
30.7995
31.4847
32.1630
32.8347
33.4997
34.1581
34.8100
35.4555
36.0945
36.7272
37.3537
37.9740
38.5881
39.1961
1.0%
p→
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
↑n
15kwh10w.com

Passivhaus Compendium for Exam and Daily Use

Passivhaus Compendium for Exam and Daily Use

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Passivhaus Compendium for Exam and Daily Use