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 the 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?

The coefficient of thermal expansion is a numerical value that quantifies how much a material expands or contracts when its temperature changes.

It represents the fractional change in length, area, or volume of a material per unit change in temperature.

When a material is heated, its molecules gain kinetic energy and move more vigorously, causing them to spread apart. This expansion results in dimensional changes, which can significantly affect the performance and reliability of structures and components.

The coefficient of thermal expansion allows engineers and designers to predict and account for these changes, ensuring the proper functioning and durability of materials and assemblies.

In practical terms, a higher coefficient of thermal expansion means that a material will expand or contract more for a given change in temperature.

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