Heat Transfer Calculator
Calculate heat transfer four ways: the conduction rate through a material with Fourier law, convection from a surface to a fluid, radiation by the Stefan-Boltzmann law, and the heat energy to change a temperature with Q = mcΔT. Switch between metric and imperial units, see the worked steps, and add an optional running-cost estimate for steady heat loss.
Formula
Worked example
A 10 m² wall of fiberglass insulation (k = 0.04), 0.1 m thick, with a 20 K difference across it: Q/t = (0.04 × 10 × 20) / 0.1 = 8 / 0.1 = 80 W. At 0.17 per kWh that is about 9.8 kWh and 1.66 over a 24-hour day.
The three modes of heat transfer
Heat moves in three ways and this calculator handles all of them plus a total-energy mode. Conduction is heat passing through a solid material without the material itself moving, governed by Fourier law. Convection is heat carried away from a surface by a moving fluid such as air or water, described by Newton law of cooling. Radiation is heat emitted as electromagnetic waves from any surface above absolute zero, set by the Stefan-Boltzmann law. The first three return a rate in watts (joules per second); the fourth, Q = mcΔT, returns the total energy in joules to change a substance temperature. Pick the mode that matches your problem and the inputs adjust automatically.
Conduction: Fourier law and thermal resistance
Fourier law states that the conduction rate Q/t equals the thermal conductivity k times the cross-sectional area A times the temperature difference ΔT, all divided by the thickness d. The rate climbs when the material conducts well, when the area is large, or when the two faces differ sharply in temperature, and it drops as the material gets thicker. The inverse view is thermal resistance R = d/k, the resistance of one unit of area; a thicker layer or a lower conductivity both raise R and cut the heat flow, which is the principle behind the R-values quoted for building insulation. This calculator reports R and the heat flux alongside the rate so you can compare assemblies directly.
Convection and radiation
Convection uses Q = h·A·ΔT, where h is the convection coefficient, a number that captures how vigorously the fluid carries heat away. Still air gives a small h (around 5 to 25 W/m²·K), forced air a larger one, and moving water or boiling steam a very large one, which is why a fan or a pump cools a surface so much faster than still air. Radiation uses Q = σ·ε·A·(T₂⁴ - T₁⁴), with σ the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²·K⁴) and ε the emissivity between 0 and 1. Because the temperatures are raised to the fourth power, radiation grows steeply as a surface gets hotter, and it must be computed in absolute kelvin, so enter Celsius or Fahrenheit and the calculator converts for you.
Total energy and the optional running cost
The Q = mcΔT mode answers a different question: how much total energy does it take to change a substance temperature? Here Q equals mass m times specific heat capacity c times the temperature change ΔT. Specific heat is the energy to raise one kilogram by one kelvin; water is famously high at 4186 J/kg·K, which is why it heats and cools slowly. This mode ignores phase changes, melting or boiling carry extra latent heat the formula does not include. For the three rate modes you can switch on a running-cost estimate: it turns the steady wattage into kilowatt-hours over a chosen number of hours and multiplies by your energy price, a quick way to see what a heat loss is costing you.
Thermal conductivity of common materials
| Material | k (W/m·K) | Conducts heat |
|---|---|---|
| Copper | 401 | Very fast |
| Aluminum | 237 | Very fast |
| Steel | 50 | Fast |
| Concrete | 1.7 | Moderate |
| Glass | 0.8 | Slow |
| Wood | 0.12 | Slow |
| Fiberglass insulation | 0.04 | Very slow |
| Still air | 0.026 | Very slow |
Approximate values near room temperature, in watts per meter-kelvin. Higher means heat passes more easily.
Frequently asked questions
What is the formula for heat transfer by conduction?
Fourier law gives the rate as Q/t = k·A·ΔT / d, where k is thermal conductivity in W/m·K, A is the cross-sectional area in m², ΔT is the temperature difference across the material in kelvin (or °C, since the size of a degree is the same), and d is the thickness in meters. The result is in watts, the heat energy crossing the material each second.
How do I calculate convection and radiation heat transfer?
Convection uses Q = h·A·ΔT, where h is the convection coefficient in W/m²·K, A is the surface area, and ΔT is the surface-to-fluid temperature difference. Radiation uses the Stefan-Boltzmann law Q = σ·ε·A·(T₂⁴ - T₁⁴), with σ = 5.67 x 10⁻⁸ W/m²·K⁴, ε the emissivity from 0 to 1, and both temperatures in kelvin. This calculator switches between conduction, convection, radiation, and Q = mcΔT modes.
Why must radiation temperatures be in kelvin?
The Stefan-Boltzmann law raises temperature to the fourth power, and that only works on an absolute scale where zero means zero thermal energy. Using Celsius or Fahrenheit would give wrong (even negative) results. Enter your temperatures in any scale here and the calculator converts them to kelvin before applying the formula.
What is the difference between heat transfer rate and heat energy?
The conduction, convection, and radiation modes give a rate in watts, energy per second flowing at a steady temperature difference. The Q = mcΔT mode gives a total energy in joules needed to change a substance temperature. Multiply a steady rate by time to get energy, which is exactly what the optional running-cost estimate does to turn watts into kilowatt-hours and money.