The thermal conductivity calculator is a tool that lets you calculate the thermal conductivity of any material or the heat flux through any object, according to Fourier's law. This article will provide you with a definition of thermal conductivity, explain how to use the formula for heat flux correctly, and analyze the thermal conductivity units in greater detail.
Thermal conductivity definition
Thermal conductivity is a measure of a material's ability to transfer heat. It does not depend on the external conditions or the object's mass — it is a property inherent to a given material. It is proportional to the heat energy transferred and to the distance of heat transfer, and inversely proportional to the temperature difference across the material.
For example, imagine an insulated wall. Its thermal conductivity is low if only a small amount of heat energy is transferred through it. The reciprocal of thermal conductivity is called the thermal resistivity.
Fourier's law and heat flux
It is necessary to know the thermal conductivity of a material if you want to calculate the heat energy transferred through it. The heat energy transferred every second per unit area is called the heat flux. According to Fourier's law, the heat flux is defined as:
q = −λ · (ΔT / Δx)
where:
- λ — the thermal conductivity of the material;
- ΔT — the temperature difference across the object;
- Δx — the distance of heat transfer (the thickness of the object); and
- q — the heat flux, measured in W/m².
The negative sign describes the direction of heat transfer. As heat always flows from a warm body to a cold body, the direction of heat transfer is always opposite to the temperature gradient.
How to use the thermal conductivity calculator: an example
- Enter the thermal conductivity of the material for which you want to find the heat flux through it. Let's assume a brick wall with a conductivity equal to 0.8 W/(m·K).
- Enter the value of the temperature difference across the object. We can assume a difference of 20 K.
- Determine the thickness of the object — for example, 35 cm (0.35 m).
- Calculate the heat flux according to Fourier's law: q = λ · ΔT / Δx = 0.8 × 20 / 0.35 = 45.71 W/m². This result means that every second, 45.71 joules of heat energy is transferred through every 1 m² of the wall.
You can also use the thermal conductivity calculator to find the λ coefficient, the temperature difference, or the required thickness — just choose the matching mode.
Thermal conductivity units
The units of thermal conductivity are watts per meter per kelvin. You can convert them to SI base units like this:
W/(m·K) = (kg·m²/s³) / (m·K) = kg·m / (s³·K)
This calculator supports both the metric (SI) system — λ in W/(m·K), ΔT in K, Δx in m, q in W/m² — and the American/Imperial system — λ in BTU/(h·ft·°F), ΔT in °F, Δx in ft, q in BTU/(h·ft²). Pick the measurement system that fits your data and the units update automatically.
Thermal conductivity of common materials
| Material | λ (W/(m·K)) | λ (BTU/(h·ft·°F)) |
|---|---|---|
| Copper | 401 | 231.7 |
| Aluminum | 237 | 137.0 |
| Carbon steel | 50 | 28.9 |
| Stainless steel | 15 | 8.67 |
| Ice | 2.2 | 1.271 |
| Concrete | 1.7 | 0.982 |
| Brick / Glass | 0.8 | 0.462 |
| Water | 0.6 | 0.347 |
| Wood (pine) | 0.12 | 0.0693 |
| Fiberglass insulation | 0.04 | 0.0231 |
| Polystyrene foam | 0.033 | 0.0191 |
| Air (still) | 0.026 | 0.0150 |
FAQs
What is thermal resistance?
Thermal resistance per unit area is R = Δx / λ, measured in m²·K/W (or ft²·h·°F/BTU). A thicker wall or a lower-conductivity material gives a higher thermal resistance — which is exactly what you want from insulation. This calculator reports the R-value of your layer alongside the heat flux.
Why is the heat flux negative in Fourier's law?
The minus sign is a direction convention: heat flows down the temperature gradient, from hot to cold. The magnitude of the heat flux is what tells you how much energy crosses each square meter every second.
Does thermal conductivity depend on the size of the object?
No. Thermal conductivity is an intrinsic material property, independent of mass or shape. The heat flux through an object, however, does depend on its thickness and the temperature difference across it.