Enter the original length, the length after a change in temperature, the original temperature, and the final temperature to determine the coefficiency of thermal expansion.

## CTE Formula

The following formula is used to calculate the coefficiency of thermal expansion.

a = (L2-L1)/(T2-T1)

• Where a is the coefficient of thermal expansion (CTE)
• L2 is the final length of the object after a temperature change
• L1 is the initial length of the object before temperature change
• T2 is the final temperature
• T1 is the initial temperature

It’s important to note that this formula solves for a linear coefficient of thermal expansion. This means it can only be applied to the object in linear terms.

## CTE Definition

What is a coefficient of thermal expansion?

A coefficient of thermal expansion is a measure of how much change in size occurs in a material or object when subjected to a change in temperature. The greater the change in size the greater the coefficient of expansion.

## Example Problem

How to calculate a coefficient of thermal expansion (CTE)?

The following example problem outlines the steps necessary to calculate the linear coefficient of thermal expansion.

First, measure the original length of the material and take the initial temperature. For this example, the original length is 10 inches and the initial temperature is 40 degrees Fahrenheit.

Next, subject the material to a temperature change and measure the final length of the object after it fully reaches the final temperature. For this example problem, the final length is measured to be 12 inches and the final temperature is 80 F.

Finally, calculate the coefficient of thermal expansion using the formula above:

a = (L2-L1)/(T2-T1)

a = (12-10)/(80-40)

a = .05 inches per degrees F