TAHA Engineering Toolsby TAHA Knowledge Lab

HVAC & Building Services

U-Value & Heat Loss Calculator

U-value of a wall, roof or floor from its layers, and the heat loss or gain Q = U × A × ΔT.

Inputs

Calculate from
Section through a wall with three layers: a thin board on the inside, thick insulation in the middle and brick on the outside. Warm inside air on the left, cold outside air on the right. A heat-flow arrow Q crosses the wall, and a temperature line falls a little at each surface and most steeply across the insulation.temperatureheat flow Qinside (warm)tᵢ, Rsioutside (cold)tₒ, Rseλ₂λ₃λ₁d₂insulationbrickboard
Heat flows from the warm side to the cold side through the surface films (Rsi, Rse) and each layer (R = d ÷ λ). The temperature falls most across the layer with the largest resistance — usually the insulation. Diagram not to scale.

Sets the inside and outside surface resistances. In summer a roof or ceiling has downward heat flow; in winter heating, upward.

Enter each solid layer with its thickness and λ (the order does not change the U-value). Leave unused layers empty.

For an air cavity, or a product known only by its R-value: enter its R from ISO 6946 tables or the data sheet. Leave empty if none.

Area of the wall, roof, floor or window through which heat flows (use the net area: subtract windows and doors from a wall).

The size of the difference, entered as a positive number for heat loss and heat gain, e.g. inside 20 °C and outside 0 °C → ΔT = 20 K.

Result

U-value
0.310559
Total thermal resistance (with surfaces)
3.22
Resistance of the layers only
3.05
Heat flow through the area
62.1118
Heat flow per square metre
6.21118
Working
Layer 1: R = d ÷ λ = 0.11 m ÷ 0.77 W/(m·K) = 0.1429 m²·K/W Layer 2: R = d ÷ λ = 0.1 m ÷ 0.035 W/(m·K) = 2.857 m²·K/W Layer 3: R = d ÷ λ = 0.0125 m ÷ 0.25 W/(m·K) = 0.05 m²·K/W Rt = Rsi + ΣR + Rse = 0.13 + 3.05 + 0.04 = 3.22 m²·K/W U = 1 ÷ Rt = 0.3106 W/(m²·K) Q = U × A × ΔT = 0.3106 × 10 m² × 20 K = 62.11 W

The element has a U-value of about 0.310559 W/(m²·K). About 62.1118 W of heat flows through this area for the given temperature difference.

  • This U-value is for the plain layers only. Thermal bridges (studs, wall ties, frames, mortar joints), air leaks and wet insulation make the real heat flow higher.

Educational estimate — check the assumptions below.

About this calculator

The U-value (thermal transmittance) tells you how much heat passes through 1 m² of a wall, roof, floor or window for each 1 K of temperature difference between the air on the two sides. A lower U-value means better insulation. It is the main number used to compare building elements and to estimate heat loss in winter and conduction heat gain in summer.

Three different quantities are involved and are often confused:

  • Thermal conductivity λ (or k), in W/(m·K), is a property of a material. It does not depend on thickness.
  • Thermal resistance R, in m²·K/W, belongs to a layer of a given thickness: R = d ÷ λ. Resistances of layers in series add up.
  • U-value, in W/(m²·K), belongs to the whole element including the air films on both surfaces: U = 1 ÷ Rtotal.

Formula

U from layers

Rlayer = d ÷ λ    Rt = Rsi + R1 + R2 + … + Rse    U = 1 ÷ Rt

Q = U × A × ΔT

d = layer thickness (m), λ = thermal conductivity (W/(m·K)), Rsi and Rse = inside and outside surface resistances (m²·K/W), A = area (m²), ΔT = air temperature difference (K), Q = heat flow (W).

Surface resistances used for the standard choices (plane surfaces in still indoor air and outdoor air, ISO 6946): Rsi = 0.13 for horizontal heat flow, 0.10 for upward and 0.17 for downward heat flow; Rse = 0.04.

Inch-pound: R-values in h·ft²·°F/Btu add the same way, and U (Btu/(h·ft²·°F)) = 1 ÷ R. 1 W/(m²·K) = 0.1761 Btu/(h·ft²·°F).

Heat flow from a known U

Q = U × A × ΔT    R = 1 ÷ U

The steady heat flow through an element of known U-value and area for a given air temperature difference.

Worked example

An example wall (the default values): 110 mm brick (λ = 0.77 W/(m·K)), 100 mm mineral wool (λ = 0.035) and 12.5 mm plasterboard (λ = 0.25), with horizontal heat flow.

  • Rbrick = 0.110 ÷ 0.77 = 0.1429; Rwool = 0.100 ÷ 0.035 = 2.8571; Rboard = 0.0125 ÷ 0.25 = 0.0500 m²·K/W.
  • Rt = 0.13 + 0.1429 + 2.8571 + 0.0500 + 0.04 = 3.2200 m²·K/W → U = 1 ÷ 3.22 = 0.311 W/(m²·K) (0.0547 Btu/(h·ft²·°F); R-value 18.3 h·ft²·°F/Btu).
  • For 10 m² and ΔT = 20 K: Q = 0.311 × 10 × 20 = 62.1 W.
  • Notice that the insulation gives almost 90% of the total resistance.

The λ values above are only an example. Use the manufacturer’s declared value or a recognized table (for example ISO 10456 or CIBSE Guide A) for your materials.

Assumptions and limitations

  • One-dimensional steady heat flow through flat, uniform layers in series.
  • Thermal bridges are not included: studs, joists, wall ties, window frames and mortar joints carry extra heat, so the real U-value is higher. ISO 6946 gives corrections for these.
  • Moisture is not included. Wet insulation and wet masonry conduct much more heat than their dry λ values.
  • Air gaps: do not enter an air cavity as a thickness with λ of air. Heat crosses a cavity by convection and radiation as well, so enter the cavity’s R from a recognized table (ISO 6946) in the “Additional thermal resistance” box.
  • The standard surface resistances are for still indoor air and normal outdoor exposure. Strong wind, sheltered or reflective surfaces need different values; choose “Enter my own surface resistances”.
  • Solar heating of sunlit walls and roofs is not included in Q = U × A × ΔT. For cooling loads use an equivalent temperature difference (see the AC Cooling Load Estimator).
  • Ground floors and basement walls lose heat to the ground in a different way (ISO 13370); this calculator does not cover that.
  • Enter ΔT as a positive size of the difference. The same Q applies to heat loss in winter and conduction heat gain in summer; heat flows from the warm side to the cold side.

References

  • ISO 6946 — Building components and building elements: thermal resistance and thermal transmittance, calculation methods (surface resistances, layers in series).
  • ISO 10456 — Building materials and products: hygrothermal properties, tabulated design values (λ).
  • ASHRAE Handbook — Fundamentals, chapters on heat transfer and thermal and moisture control in insulated assemblies.