Heat Transfer Calculator
Heat transfer by conduction describes how thermal energy moves through a solid material from a region of higher temperature to one of lower temperature. The governing formula, derived from Fourier's law, is Q = kAΔTt/d, where Q is the total heat transferred in joules, k is the thermal conductivity of the material in watts per metre-kelvin (W/(m·K)), A is the cross-sectional area in square metres, ΔT is the temperature difference across the material in kelvin (or degrees Celsius, since differences are equal), t is the elapsed time in seconds, and d is the thickness of the material in metres. Rearranging gives the heat flow rate P = Q/t = kAΔT/d in watts, which tells you the instantaneous power of heat transfer. This calculator lets you select a material from a list of common substances with pre-filled conductivity values drawn from NIST and engineering reference sources, or enter a custom k value. It returns total heat Q in joules and kilowatts-hours, and the flow rate P in watts, all formatted for easy reading. Understanding conduction is essential for building insulation, electronics cooling, industrial process design, and materials science.
Heat transferred: -- J, flow rate: -- W.
How heat conduction is calculated
Fourier's law states that the rate of heat transfer through a material is proportional to the area and temperature gradient, and inversely proportional to the thickness. Integrating over time gives the total heat transferred.
Q = (k × A × ΔT × t) / d
P = Q / t = (k × A × ΔT) / d
Where:
k = thermal conductivity (W/(m·K))
A = area (m²)
ΔT = temperature difference (K)
t = time (s)
d = thickness (m)
Worked example
A steel plate (k = 50 W/(m·K)), area 2 m², temperature difference 30 K, thickness 0.05 m, over 1 hour (3,600 s):
- P = (50 × 2 × 30) / 0.05 = 60,000 W (60 kW)
- Q = 60,000 × 3,600 = 216,000,000 J (216,000 kJ)
Thermal conductivity of common materials
| Material | k (W/(m·K)) | Notes |
|---|---|---|
| Copper | 401 | Excellent conductor; used in heatsinks and wiring |
| Aluminium | 237 | Common in heat exchangers and cookware |
| Steel (carbon) | 50 | Structural metal; moderate conductor |
| Concrete | 1.7 | Poor conductor; significant in building heat loss |
| Glass | 1.0 | Similar to concrete; window glazing matters |
| Wood (softwood) | 0.15 | Natural insulator; varies with moisture content |
| Air (still) | 0.026 | Very poor conductor; basis of most insulation |
Source: NIST and Engineering ToolBox. Values at approximately 20°C (293 K).
Heat transfer calculator: frequently asked questions
What is thermal conduction and how does Q = kAΔTt/d work?
Thermal conduction is the transfer of heat through a solid material without bulk movement of the material itself. The formula Q = kAΔTt/d gives the total heat energy transferred: k is thermal conductivity (W/(m·K)), A is the cross-sectional area (m²), ΔT is the temperature difference across the material (K or °C difference), t is time (s), and d is the thickness (m). A higher conductivity, larger area, greater temperature difference, or longer time all increase heat transfer.
What are typical thermal conductivity values for common materials?
Thermal conductivity varies enormously by material. Copper is among the highest at around 401 W/(m·K), aluminium at 237, steel at around 50, concrete at 1.7, glass at 1.0, wood at 0.15, and air at 0.026. These values come from NIST and engineering reference data. Metals conduct heat efficiently because free electrons carry thermal energy; gases and low-density materials like wood or foam conduct poorly because of limited molecular contact.
How does thermal conductivity relate to insulation R-value?
R-value (thermal resistance) is the inverse of conductance. For a slab of material, R = d / k, where d is thickness in metres and k is thermal conductivity. A high R-value means low conductivity or greater thickness, so less heat flows through. Building codes specify minimum R-values for walls, roofs and floors. Converting: R (SI, m²·K/W) = d / k. US R-values are in imperial units (ft²·°F·h/BTU) and are approximately 5.68 times the SI value.
What is heat flow rate and how does it differ from total heat transferred?
Heat flow rate P (in watts) is the power of heat transfer: P = Q / t = kAΔT / d. It tells you how many joules per second are passing through the material at any instant. Total heat Q (in joules) depends on how long that rate is sustained: Q = P × t. If you are sizing a heater or insulating a building, you typically work with P (watts) to match electrical or fuel power ratings. For cumulative energy calculations such as total energy lost overnight, you use Q (joules or kWh).
What are real-world applications of the heat conduction formula?
The conduction formula is used in building energy modelling to calculate heat loss through walls, windows and roofs; in electronics to size heatsinks and thermal interface materials; in manufacturing for mould cooling calculations; in geothermal engineering to estimate heat flow from the earth; and in cooking to predict how quickly food heats through. Any time heat moves through a solid from a hot side to a cold side, the Fourier law (of which Q = kAΔTt/d is the integrated form) applies.
Official sources
- NIST thermal conductivity: NIST Engineering Physics Division.
- Engineering ToolBox conductivity values: Thermal Conductivity of Materials.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.