U-Value Calculator (Thermal Transmittance)
Calculate U-value and thermal resistance for building envelope layers including walls, roofs, and windows
Category: Hvac
U-Value Calculator (Thermal Transmittance) Calculator Inputs
U-Value Calculator (Thermal Transmittance) Calculator Formula
Equation
U = 1 / R_total where R_total = Σ(thickness/conductivity) + R_surface
Excel Formula
=U=1/R_totalwhereR_total=Σ(thickness/conductivity)+R_surface
Variables
- Layer 1 Thickness (Interior) (mm) — Thickness of innermost layer in millimeters
- Layer 1 Thermal Conductivity (W/(m·K)) — Thermal conductivity of layer 1 (gypsum ≈ 0.21, wood ≈ 0.13)
- Layer 2 Thickness (mm) — Thickness of layer 2 (structural layer)
- Layer 2 Thermal Conductivity (W/(m·K)) — Thermal conductivity (concrete ≈ 1.6, brick ≈ 0.7)
- Layer 3 Thickness (Insulation) (mm) — Thickness of insulation layer
- Layer 3 Thermal Conductivity (W/(m·K)) — Conductivity (mineral wool ≈ 0.035, polyurethane ≈ 0.025)
- Layer 4 Thickness (Exterior) (mm) — Thickness of exterior finish
- Layer 4 Thermal Conductivity (W/(m·K)) — Conductivity of exterior (stucco ≈ 0.7, siding ≈ 0.15)
How the U-Value Calculator (Thermal Transmittance) Calculator Works
The U-value (thermal transmittance) quantifies how effective a building element is at preventing heat flow. Lower U-values indicate better insulation performance. U-value calculations are essential for energy code compliance, heating/cooling load calculations, and building envelope optimization. The calculation involves summing thermal resistances of all layers including surface resistances.
The core relationship is U = 1 / R_total where R_total = Σ(thickness/conductivity) + R_surface. Typical inputs include Layer 1 Thickness (Interior), Layer 1 Thermal Conductivity, Layer 2 Thickness, Layer 2 Thermal Conductivity.
Enter your values in the u-value calculator (thermal transmittance) calculator above, review the step-by-step solution, and compare against the worked examples below so you can see how each input changes the result. This free online hvac tool is built for homework, design checks, and professional verification.
U-Value Calculator (Thermal Transmittance) Calculator Theory & Explanation
Fundamental Relationships
Thermal resistance (R-value) and thermal transmittance (U-value) are reciprocals:
U = (1)/(R_total) \quad \text[W/(m²·K)]
**Total Thermal Resistance**:
R_total = R_si + R_1 + R_2 + ... + R_n + R_se
where: - R_si = internal surface resistance (m²·K/W) - R_n = resistance of layer n - R_se = external surface resistance (m²·K/W)
**Layer Resistance**:
R = (d)/(\lambda)
where: - d = thickness (m) - \lambda = thermal conductivity (W/(m·K))
**Standard Surface Resistances** (ISO 6946): - Internal (vertical): R_si = 0.13 m²·K/W - External (vertical): R_se = 0.04 m²·K/W - Horizontal upward heat flow: R_si = 0.10 m²·K/W - Horizontal downward heat flow: R_si = 0.17 m²·K/W
Heat Transfer Mechanisms
Heat transfer through building envelopes involves three mechanisms:
**1. Conduction** through solid materials:
q = \lambda · A · (Δ T)/(d)
**2. Convection** at surfaces:
q = h_c · A · Δ T
where h_c is convection coefficient, typically: - Internal surfaces: 7.7 W/(m²·K) - External surfaces: 25 W/(m²·K)
**3. Radiation** between surfaces:
q = \varepsilon · \sigma · A · (T_1^4 - T_2^4)
Convection and radiation at surfaces are combined into surface resistance:
R_s = (1)/(h_c + h_r)
For typical building applications, standard values suffice.
Material Properties
Common thermal conductivities (λ) for building materials:
**Insulation Materials**: - Polyurethane foam: 0.022-0.028 W/(m·K) - Polystyrene (XPS): 0.029-0.038 W/(m·K) - Mineral wool: 0.035-0.045 W/(m·K) - Fiberglass: 0.035-0.040 W/(m·K) - Cellulose: 0.037-0.042 W/(m·K)
**Structural Materials**: - Concrete (normal): 1.40-2.00 W/(m·K) - Concrete block (hollow): 0.50-1.00 W/(m·K) - Brick (solid): 0.60-0.90 W/(m·K) - Wood (softwood): 0.12-0.14 W/(m·K) - Wood (hardwood): 0.16-0.23 W/(m·K) - Gypsum board: 0.17-0.21 W/(m·K)
**Finish Materials**: - Plaster/Stucco: 0.70-0.80 W/(m·K) - Tile (ceramic): 1.00-1.30 W/(m·K) - Air gap (20-50mm): 0.18 equivalent resistance
Actual values vary with density, moisture, and temperature.
Windows and Glazing
Window U-values are more complex due to:
**Center-of-Glass U-value**:
U_g = (1)/(R_si) + R_glazing + R_se
For multiple panes with air gap:
R_glazing = Σ \fracd_glass\lambda_glass + Σ R_gap
Air gap resistance depends on: - Gap width (optimal: 12-16mm) - Orientation and heat flow direction - Gas fill (air, argon, krypton)
**Typical Window U-values**: - Single glazing: 5.0-5.8 W/(m²·K) - Double glazing (air): 2.7-3.0 W/(m²·K) - Double glazing (argon, low-e): 1.4-1.8 W/(m²·K) - Triple glazing (argon, low-e): 0.8-1.2 W/(m²·K)
**Whole Window U-value** considers frame:
U_w = (A_g · U_g + A_f · U_f + L_p · \psi_p)/(A_g + A_f)
where subscript g = glazing, f = frame, p = perimeter (linear thermal bridge).
U-Value Calculator (Thermal Transmittance) Calculator Worked Examples
Worked Example
Inputs
- layer1Thickness: 15
- layer1Conductivity: 0.21
- layer2Thickness: 200
- layer2Conductivity: 1.6
- layer3Thickness: 100
- layer3Conductivity: 0.035
- layer4Thickness: 20
- layer4Conductivity: 0.7
- surfaceTypeInternal: wall
- surfaceTypeExternal: wall
Result: U-Value: 0.304 W/(m²·K) | R-Total: 3.29 m²·K/W | Heat Loss: 304 W per m² per 10°C difference
Explanation
For a wall assembly with gypsum board, concrete block, insulation, and stucco:
**Layer 1** (Interior): Gypsum Board - Thickness: 15mm = 0.015m - Conductivity: 0.21 W/(m·K) - Resistance: R₁ = 0.015 / 0.21 = 0.071 m²·K/W
**Layer 2**: Concrete Block - Thickness: 200mm = 0.200m - Conductivity: 1.6 W/(m·K) - Resistance: R₂ = 0.200 / 1.6 = 0.125 m²·K/W
**Layer 3**: Mineral Wool Insulation - Thickness: 100mm = 0.100m - Conductivity: 0.035 W/(m·K) - Resistance: R₃ = 0.100 / 0.035 = 2.857 m²·K/W ← Main insulating layer
**Layer 4** (Exterior): Stucco - Thickness: 20mm = 0.020m - Conductivity: 0.7 W/(m·K) - Resistance: R₄ = 0.020 / 0.7 = 0.029 m²·K/W
**Surface Resistances** (Vertical Wall): - Internal: Rsi = 0.13 m²·K/W - External: Rse = 0.04 m²·K/W
**Total Resistance**: R_total = 0.13 + 0.071 + 0.125 + 2.857 + 0.029 + 0.04 = 3.252 m²·K/W
**U-Value**: U = 1 / R_total = 1 / 3.252 = 0.307 W/(m²·K)
**Heat Transfer Rate**: For ΔT = 10°C: q = U × A × ΔT = 0.307 × 1m² × 10K = 3.07 W per m²
This wall meets energy codes in moderate climates (typical requirement: U < 0.35 W/m²·K).
Second Scenario
Inputs
- layer1Thickness: 19.75
- layer1Conductivity: 0.21
- layer2Thickness: 200
- layer2Conductivity: 1.6
- layer3Thickness: 100
- layer3Conductivity: 0.035
- layer4Thickness: 20
- layer4Conductivity: 0.7
- surfaceTypeInternal: wall
- surfaceTypeExternal: wall
Result: U-Value: 0.304 W/(m²·K) | R-Total: 3.29 m²·K/W | Heat Loss: 304 W per m² per 10°C difference
Explanation
This scenario uses different inputs (layer1Thickness = 19.75, layer1Conductivity = 0.21, layer2Thickness = 200, layer2Conductivity = 1.6, layer3Thickness = 100, layer3Conductivity = 0.035, layer4Thickness = 20, layer4Conductivity = 0.7, surfaceTypeInternal = wall, surfaceTypeExternal = wall) to show how changing one variable affects the u-value calculator (thermal transmittance) result. Run the calculator above with these values to get the exact updated output with step-by-step work.
Common U-Value Calculator (Thermal Transmittance) Calculator Use Cases
- HVAC load and equipment sizing
- Comfort and indoor air quality analysis
- Energy audit support
- Roofs
- And windows
U-Value Calculator (Thermal Transmittance) Calculator FAQs
What is the difference between U-value and R-value?
U-value and R-value are reciprocals measuring thermal performance inversely. R-value (thermal resistance) measures how well a material resists heat flow - higher R-values mean better insulation (R = thickness/conductivity). U-value (thermal transmittance) measures how easily heat passes through - lower U-values mean better insulation (U = 1/R_total). In the US, R-values are common (ft²·°F·h/Btu), while U-values dominate in Europe and energy codes (W/m²·K). Example: R-20 insulation = U-0.28 W/m²·K. Always convert properly: U[W/m²·K] = 1/R[m²·K/W] or U = 5.678/R when R is in US units.
How do I account for thermal bridging?
Thermal bridges are localized areas of higher heat transfer (studs, joists, concrete columns) that reduce overall insulation effectiveness. Methods to account for thermal bridging: 1) Parallel Path Method: Calculate area-weighted average of clear wall and framed sections. 2) Isothermal Planes Method: More accurate, uses temperature planes. 3) Linear Thermal Bridges: Add ψ-value (psi-value) term for edges and junctions. Effective U-value increases 10-40% due to framing. Example: R-20 cavity insulation with wood studs 16" o.c. effectively performs like R-16. Use software (THERM, HEAT3) for complex geometries or apply framing factors from building codes.
Why do surface resistances matter?
Surface resistances account for convection and radiation at interior and exterior surfaces. Though small (Rsi = 0.13, Rse = 0.04 m²·K/W for walls), they: 1) Represent 5-10% of total R-value for insulated assemblies. 2) Vary with orientation: horizontal surfaces have different values than vertical. 3) Change with wind speed (external) and air movement (internal). 4) Affect condensation risk - surface temperature depends on surface resistance. 5) Required for standardized U-value calculations per ISO 6946 and ASHRAE. Always include standard surface resistances for code compliance calculations. For high-performance buildings (passive house), accurate surface coefficients are critical for heating/cooling load precision.
What does the U-Value Calculator (Thermal Transmittance) calculate?
It applies the formula on this page to your inputs and returns the primary result plus any supporting values shown in the output panel.
How many decimal places should I trust?
Match precision to your input accuracy. Extra digits from the tool are not evidence of higher measurement quality.