# Thermal Conductivity Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

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's 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 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. Check out our heat transfer coefficient calculator to understand heat transfer through the wall.

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. Heat energy transferred every second per unit area is called the heat flux. According to Fourier's law, heat flux is defined as:

$q = -λ \frac{\Delta T}{\Delta x}$

where:

• λ is the thermal conductivity of the material;
• ΔT is the temperature difference across the object;
• Δx is the distance of heat transfer (the thickness of the object); and
• q is 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

1. Enter the value of temperature difference across the object. We can assume a difference of 20 K.
2. Determine the thickness of the object - for example, 35 cm.
3. Enter the thermal conductivity of the material if 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).
4. Calculate the heat flux according to Fourier's law: q = -λΔT/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.
5. You can also use the thermal conductivity calculator to find the λ coefficient.

## Thermal conductivity units

The units of thermal conductivity are watts per meter per Kelvin. You can convert them to SI units like this:

W/(m·K) = (kg·m²/s³) / (m·K) = kg·m / (s³·K)

Make sure to check out the thermal expansion calculator, and thermal stress calculator as well.

Bogna Szyk
q = -λΔT/Δx
Thermal conductivity constant (λ)
BTU/(h·ft·°F)
Temperature difference (ΔT)
°F
Distance (Δx)
ft
Heat flux (q)
W/m²
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