# Thermal Expansion Calculator

Created by Luis Hoyos
Last updated: Dec 16, 2022

Welcome to our thermal expansion calculator, where you'll be able to calculate the thermal expansion of steel, aluminum, and other common materials.

From the thermal expansion equation, you'll note that to calculate the thermal expansion, you only need to know:

• The thermal expansion coefficient (aka CTE).
• The initial dimension (length for linear expansion and volume for volumetric expansion).
• The temperature change.

Additionally, you can use this tool to calculate the CTE as long as you know the initial dimension and the temperature and dimensional changes.

## What is thermal expansion?

1. When we increase the temperature of some material, we're supplying energy to its molecules (the amount of energy required depends on the specific heat of the material).
2. That energy supply causes an increase in the kinetic energy and speed of the molecules.
3. The more these molecules move, the further away they need to stay from each other.
4. This molecular separation is what causes the material to expand (and change its density slightly)

### Linear expansion

Linear expansion refers to one-dimensional expansion, and we typically observe it in objects whose length is much higher than the width, for example, resistors. Check the to learn more about resistance.

### Volumetric expansion

On the other hand, this is a three-dimensional expansion. A real-life example is opening a closed glass jar with a metal lid. It might be difficult, but it gives way more easily after pouring some hot water on the lid. It happens because the latter expands much faster than glass.

## Thermal expansion equation

• Linear thermal expansion equation: $\Delta L = aL_1\Delta T$, where:
• $\Delta L$ — Change in object's length;
• $L_1$ — Initial length;
• $a$ — Linear expansion coefficient;
• Volumetric thermal expansion equation: $\Delta V = bV_1\Delta T$, where:
• $\Delta V$ — Change in object's volume;
• $V_1$ — Initial volume; and
• $b$ — Volumetric expansion coefficient.

$\Delta T$ refers to the temperature change, and it's simply the difference between the final and the initial temperatures ($T_2$ and $T_1$, respectively):

$\Delta T = T_2 - T_1$

## Coefficient of thermal expansion equation

From the previous equations, we can solve for $a$ and $b$ and obtain the coefficient of thermal expansion equations:

• Linear coefficient of thermal expansion formula: $a = \frac{\Delta L/L_1}{\Delta T}$
• Volumetric coefficient of thermal expansion formula: $b = \frac{\Delta V/V_1}{\Delta T}$

## Coefficient of thermal expansion of various materials

You can use the following values of CTE to calculate the thermal expansion of steel and other solid materials:

Material

CTE (K-1 or (°C)-1)

Linear

Volumetric

Aluminum

2.4 × 10-5

7.2 × 10-5

Brass

2.0 × 10-5

6.0 × 10-5

Copper

1.7 × 10-5

5.1 × 10-5

Glass

0.4-0.9 × 10-5

1.2-2.7 × 10-5

Invar

0.09 × 10-5

0.27 × 10-5

Quartz (fuzed)

0.04 × 10-5

0.12 × 10-5

Steel

1.2 × 10-5

3.6 × 10-5

For liquids, only volumetric expansion has physical meaning:

• Ethanol: 75 × 10-5 K-1
• Carbon disulfide: 115 × 10-5 K-1
• Glycerin: 49 × 10-5 K-1
• Mercury: 18 × 10-5 K-1
Luis Hoyos
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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