# Thermal Expansion Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Dec 22, 2021

The idea behind this thermal expansion calculator is simple: if you heat a material, it expands. If you cool it down, it shrinks. How much though? Well, it depends on the property of the material called the "thermal expansion coefficient". In this article, we explain this concept in more detail. If you want to learn the thermal expansion equation, just keep reading!

## What is thermal expansion?

Let's begin with the general idea of thermal expansion: why does it even take place? Every material is composed of molecules, stuffed together more or less densely. When we increase the temperature of the material, what we really do is supply energy (if you don't believe it, try the specific heat calculator). Obviously, energy cannot disappear; it just changes its form into kinetic energy. As molecules have higher kinetic energy, they begin to move around more. You can imagine that the more they move, the further away from each other they need to stay. As the separation between molecules increases, the material expands.

## Linear vs. volumetric expansion

Linear expansion is one-dimensional. We typically observe it in all objects, for which length is much higher than the width. Railroad tracks are a good example. Did you notice, that the tracks are not continuous, but rather made up of hundreds of pieces separated by small spaces (called control joints)? It is because of the thermal expansion. During extreme summers (40°C), a track can be .048% longer than by 0°C. It may not seem much, but if a track has a length of 1 km, the difference in length reaches 48 cm! Of course, it doesn't mean that the railroad tracks expand in one direction only; we neglect the increase in height and width, as they are multifold smaller.

Volumetric expansion, on the other hand, is three-dimensional. If a material is isotropic (has the same properties in all directions), it expands uniformly. Let's take a real-life example - opening a closed glass jar with a metal lid. You might find it difficult, but after pouring some hot water on the lid, it gives way more easily. It happens because the lid expanded much faster than glass.

There is also a third type of thermal expansion: two-dimensional area expansion. Can you give an example of this phenomenon?

## Thermal expansion equation

Our thermal expansion calculator uses a simple formula to find the thermal expansion of any object. The equations for linear and volumetric expansion are very similar.

Linear expansion: ΔL = aL₁(T₂ - T₁)

Volumetric expansion: ΔV = bV₁(T₂ - T₁)

where:

• T₁ is the initial temperature, and T₂ is the final temperature;
• ΔL is the change in object's length;
• L₁ is the initial length;
• a is the linear expansion coefficient;
• ΔV is the change in object's volume;
• V₁ is the initial volume; and
• b is the volumetric expansion coefficient.

Use the thermal expansion calculator to find the change in length or volume - simply type in other values and watch it do all work for you!

## Coefficient of linear expansion

The coefficients of linear and volumetric expansion are rates at which a material expands. For isotropic materials, these two coefficients are related: b = 3a.

You can find a list of the most common coefficients of linear expansion below.

• Aluminum: 22.2×10-6 1/K
• Concrete: 14.5×10-6 1/K
• Copper: 16.6×10-6 1/K
• Glass: 5.9×10-6 1/K
• Ice: 51×10-6 1/K
• Silver: 19.5×10-6 1/K
• Steel: 12.0×10-6 1/K
• Wood, parallel to grain: 3×10-6 1/K
• Wood, across (perpendicular) to grain: 30×10-6 1/K
Bogna Szyk
Initial temperature
°F
Final temperature
°F
Linear expansion
Linear expansion coefficient
1/K
Initial length
ft
Final length
ft
Change in length
ft
Volumetric expansion
Volumetric expansion coefficient
1/K
Initial volume
cu ft
Final volume
cu ft
Change in volume
cu ft
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