Heat Transfer Calculator

The Heat Transfer Calculator finds the rate at which heat moves through a system by conduction, convection, or radiation. Enter the material or surface properties, the area, and the hot and cold temperatures, and the tool returns the heat transfer rate in watts, the heat flux, thermal resistance, and the total energy moved over time — together with an animated heat-flow diagram and a step-by-step formula breakdown. It is built for students, engineers, builders, and anyone curious about how fast heat travels.

The Three Modes of Heat Transfer

Heat always flows from a hotter region to a colder one, but it gets there in three distinct ways. This calculator handles each with its own physical law.

Heat Transfer Formulas

Where:

• \(Q\) — heat transfer rate, in watts (W)
• \(k\) — thermal conductivity of the material, in W/m·K
• \(h\) — convection heat-transfer coefficient, in W/m²·K
• \(\varepsilon\) — surface emissivity (0 to 1, dimensionless)
• \(\sigma\) — Stefan–Boltzmann constant, \(5.67\times10^{-8}\) W/m²·K⁴
• \(A\) — surface area, in m²
• \(\Delta T\) — temperature difference between the two sides
• \(d\) — material thickness, in metres
• \(T_h, T_c\) — hot and cold absolute temperatures, in kelvin

Typical Thermal Conductivity Values (k)

Typical Convection Coefficients (h) and Emissivity (ε)

Emissivity ranges from about 0.05 for polished metals up to 0.90–0.98 for paint, brick, water, skin, and other matte surfaces, with an ideal black body at exactly 1.0.

What is Heat Flux, Thermal Resistance and R-value?

Heat flux is the heat transfer rate per unit area (\(Q/A\)), measured in W/m². It tells you how concentrated the heat flow is, independent of how large the surface is. Thermal resistance is the opposition to heat flow (in K/W); a higher resistance means less heat moves for the same temperature difference. For building materials this is expressed as an R-value — the higher the R-value, the better the insulation. The calculator reports both the SI R-value (RSI, in m²·K/W) and the US R-value used on insulation packaging.

Why Radiation Uses Absolute Temperature

Conduction and convection depend only on the difference in temperature, and a 10° difference is the same whether you measure it in Celsius or kelvin. Radiation is different: it depends on the absolute temperature raised to the fourth power, so it must be calculated in kelvin, which begins at absolute zero (−273.15 °C). This fourth-power relationship is why a surface that is twice as hot in absolute terms radiates sixteen times as much heat, and why radiation dominates at high temperatures like flames and furnaces.

How to Use This Calculator

1. Choose the heat transfer mode: Select Conduction, Convection, or Radiation using the tabs at the top of the form.
2. Enter the material and geometry: Pick a material, condition, or surface from the built-in library (or choose "Custom value" to type your own), then enter the surface area — and the thickness for conduction.
3. Enter the temperatures: Type the hot side and cold side temperatures and select °C, °F, or K. Add an optional duration in hours to see the total energy transferred.
4. Click Calculate: Review the heat transfer rate in watts, the heat flux, thermal resistance, energy over time, the animated heat-flow diagram, and the full step-by-step working.

Frequently Asked Questions

What are the three modes of heat transfer?

Heat moves in three ways. Conduction is heat flowing through a solid material by direct contact, such as warmth passing through a wall. Convection is heat carried away by a moving fluid like air or water, for example a fan cooling a hot surface. Radiation is heat emitted as infrared electromagnetic waves, such as the warmth you feel from a fire or the sun, and it needs no medium at all.

How do you calculate heat transfer by conduction?

Conduction uses Fourier's law: Q = k × A × ΔT / d, where k is the material's thermal conductivity in watts per metre-kelvin, A is the area in square metres, ΔT is the temperature difference, and d is the thickness in metres. The result Q is the heat transfer rate in watts.

How do you calculate heat transfer by convection?

Convection uses Newton's law of cooling: Q = h × A × ΔT, where h is the convection heat-transfer coefficient in watts per square metre-kelvin, A is the surface area, and ΔT is the difference between the surface temperature and the fluid temperature. Larger h values mean faster-moving fluids that carry heat away more quickly.

How do you calculate heat transfer by radiation?

Radiation uses the Stefan–Boltzmann law: Q = ε × σ × A × (Th⁴ − Tc⁴), where ε is the emissivity between 0 and 1, σ is 5.67 × 10⁻⁸ watts per square metre-kelvin to the fourth power, A is the area, and Th and Tc are the absolute temperatures in kelvin. Because temperature is raised to the fourth power, radiation grows very quickly as objects get hotter.

What units does the heat transfer rate use?

The heat transfer rate Q is a power, measured in watts (joules per second). One watt means one joule of heat moves every second. The calculator also shows the heat flux in watts per square metre and the total energy transferred over a chosen time in kilowatt-hours and joules.

Why must temperatures be converted to Kelvin for radiation?

The Stefan–Boltzmann law depends on absolute temperature raised to the fourth power, so it only works with kelvin, which starts at absolute zero. For conduction and convection, only the temperature difference matters, and a difference in degrees Celsius equals the same difference in kelvin, so those modes are unaffected by the choice between Celsius and Kelvin.

Additional Resources

• Heat Transfer - Wikipedia
• Thermal Conduction - Wikipedia
• Stefan–Boltzmann Law - Wikipedia