About the Heat Transfer Calculator
This heat transfer calculator uses Fourier's law of conduction to find how fast heat flows through a flat layer of material — a wall, window, slab of insulation, cooking pan base or metal rod. Choose a material (or enter its thermal conductivity), give the area, thickness and the temperatures on each side, and it returns the heat flow in watts and BTU per hour, the heat flux per square metre, and the energy that passes through over a chosen number of hours.
It also reports the thermal resistance, the R-value in both SI (m²·K/W) and US (ft²·°F·h/BTU) units, and the U-value, so you can compare insulation products or check building-science homework. A chart shows how the heat flow falls as the layer gets thicker.
The calculation assumes steady-state, one-dimensional conduction through a uniform layer with fixed surface temperatures. It ignores convection and radiation at the surfaces (the air films that add resistance in real walls and windows), thermal bridging and moisture. The listed conductivities are typical room-temperature values — real products vary, so use the manufacturer’s figure when you have it.
With the default inputs, the heat flow rate (q) is 100 W. Change any value above to recalculate instantly.
How to use the heat transfer calculator
- 1Choose the material or enter a custom thermal conductivity.
- 2Enter the area and thickness of the layer.
- 3Enter the temperature on the warm and cold sides.
- 4Set a time period to see the total energy transferred.
- 5Read the heat flow, R-value and U-value; use the chart to test thicker layers.
Formula and method
Fourier's law states that the rate of heat conduction through a flat layer is proportional to the thermal conductivity k, the area A and the temperature difference ΔT across it, and inversely proportional to the thickness L. Heat always flows from the warmer side to the colder side. The temperature difference is the same in kelvin and degrees Celsius; Fahrenheit differences are converted with ×5/9.
The R-value (thermal resistance per unit area) is L/k in m²·K/W; multiply by 5.678 to get the US R-value in ft²·°F·h/BTU. The U-value is its reciprocal. Thermal resistance of the whole layer is L/(kA) in K/W. Layers in series add their R-values, so for a multi-layer wall add the R of each layer and use Q = A·ΔT / ΣR. Energy over a time period is Q × hours ÷ 1,000 in kWh.
- Q
- Heat flow rate (W)
- k
- Thermal conductivity (W/m·K)
- A
- Area perpendicular to the heat flow (m²)
- ΔT
- Temperature difference across the layer (K or °C)
- L
- Thickness of the layer (m)
- R, U
- R-value (m²·K/W) and U-value (W/m²·K)
Worked examples
100 mm of fibreglass insulation, 10 m², 20 °C inside and −5 °C outside
Q = 0.04 × 10 × 25 / 0.1 = 100 W. The layer has an R-value of 0.1/0.04 = 2.5 m²·K/W (about R-14 in US units), and over a day it lets through 2.4 kWh.
Copper rod 1 cm² × 50 cm between 100 °C and 0 °C
Q = 401 × 0.0001 × 100 / 0.5 = 8.02 W. The rod’s thermal resistance is 0.5 / (401 × 0.0001) = 12.47 K/W.
Uninsulated 200 mm concrete wall, 12 m², 21 °C to 0 °C
Q = 1.4 × 12 × 21 / 0.2 = 1,764 W through the concrete alone, about 42 kWh a day. Real walls lose less because of surface air films and finishes, but this shows why bare masonry needs insulation.
Frequently asked questions
What is Fourier's law of heat conduction?+
Fourier's law says the conductive heat flow through a material is Q = kAΔT/L: proportional to thermal conductivity, area and temperature difference, and inversely proportional to thickness.
What is thermal conductivity?+
Thermal conductivity k (W/m·K) measures how easily heat passes through a material. Metals such as copper (about 400) conduct heat thousands of times better than insulation such as fibreglass or foam (about 0.02–0.04).
How do I convert R-value between SI and US units?+
Multiply an SI R-value (m²·K/W) by 5.678 to get the US R-value (ft²·°F·h/BTU). For example, R-2.5 SI is about R-14 US, and R-19 US is about 3.35 m²·K/W.
What is the difference between R-value and U-value?+
R-value is resistance to heat flow per unit area; higher is better insulation. U-value is its reciprocal, the heat flow per square metre per degree of temperature difference; lower is better.
Does this include convection and radiation?+
No. It models conduction through the solid layer only. Real walls and windows also have surface air films that add resistance, and hot surfaces lose heat by radiation, so total heat loss can differ.