Thermal Conductivity Heat Flow Calculator
Calculate heat flow rate through a material using thermal conductivity, thickness, area, and temperature difference.
Useful for insulation and building design.
Thermal Conductivity and Heat Flow
Thermal conductivity (k) measures how well a material conducts heat. A low k-value means the material is a good insulator. A high k-value means the material conducts heat readily.
Fourier’s Law of Heat Conduction
The rate of heat flow through a flat material is:
Q = k × A × ΔT ÷ d
Where:
- Q = Heat flow rate (Watts or BTU/hr)
- k = Thermal conductivity (W/m·K)
- A = Cross-sectional area (m²)
- ΔT = Temperature difference across the material (°C or K)
- d = Thickness of the material (m)
Thermal Conductivity of Common Materials
| Material | k (W/m·K) | Notes |
|---|---|---|
| Air (still) | 0.025 | Best natural insulator |
| Aerogel | 0.015 | Best solid insulator |
| Mineral wool | 0.030–0.045 | Common building insulation |
| EPS (Styrofoam) | 0.033–0.040 | Foam board insulation |
| Wood (pine) | 0.12 | Structural timber |
| Brick | 0.60–1.0 | Masonry walls |
| Concrete | 1.0–1.5 | Structural concrete |
| Glass | 0.96 | Windows |
| Steel | 50 | Structural steel |
| Aluminum | 205 | Heat sinks |
| Copper | 385 | Electrical wiring |
Relationship Between k, R-Value, and U-Value
R-value (m²·K/W) = d ÷ k
U-value (W/m²·K) = k ÷ d = 1 ÷ R-value
Higher R-value = better insulation. Lower U-value = better insulation.
Practical Example
A 100 mm (0.1 m) thick concrete wall (k = 1.0 W/m·K), area 10 m², with indoor 20°C and outdoor −5°C:
- ΔT = 25°C
- Q = 1.0 × 10 × 25 ÷ 0.1 = 2,500 Watts of heat loss
Compare to 100 mm of mineral wool (k = 0.035):
- Q = 0.035 × 10 × 25 ÷ 0.1 = 87.5 Watts — 28× less heat loss
A bit of history
This relationship is called Fourier’s law of heat conduction, published by Joseph Fourier in 1822 in his book Théorie analytique de la chaleur (The Analytical Theory of Heat). Fourier’s work on heat flow led directly to the Fourier series and Fourier transform, two of the most important mathematical tools in physics and engineering. His original problem was actually how heat spreads through the Earth’s interior, but the math turned out to apply to electromagnetic waves, signal processing, quantum mechanics, and much more. Most engineering students meet Fourier first through this thermal equation and again, a year or two later, through Fourier series in differential equations. The connection is direct: the heat equation requires Fourier series to solve.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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