Thermal Expansion Calculator

Calculate the dimensional change a temperature swing produces in a material.

About Thermal Expansion Calculator

Free expansion is proportional to length, coefficient and temperature change. If expansion is prevented, the same strain appears as stress instead — and for steel that reaches 96 MPa for only 40 K, which is why expansion joints exist. Restrained thermal stress is independent of length, so even a short fully fixed member develops the same high stress as a long one.

Formula

Thermal Expansion

ΔL = L α ΔT; restrained stress σ = E α ΔT

α: Linear expansion coefficient per kelvin
restrained stress: Stress that develops when expansion is prevented

Worked example

With the default values below, Thermal Expansion Calculator returns Change in Length of 0.004800. Change any input above and every figure here is recalculated in your browser.

Inputs used

Original lengthminimum 0 m: 10 m
Linear expansion coefficientminimum 0 1/K: 0.000012 1/K
Temperature changeminimum -500 K: 40 K
Elastic modulusminimum 0.01 GPa: 200 GPa

Results

Change in Length: 0.004800 m
Change in Length: 4.800 mm
Final Length: 10.00480 m
Thermal Strain: 0.00048000
Stress if Fully Restrained: 96.000 MPa

Step by step

1Values used
2Thermal Expansion
3Change in Length= 0.004800 m
4Change in Length= 4.800 mm
5Final Length= 10.00480 m
6Thermal Strain= 0.00048000
7Stress if Fully Restrained= 96.000 MPa

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Thermal Expansion calculated?

ΔL = L α ΔT; restrained stress σ = E α ΔT Free expansion is proportional to length, coefficient and temperature change. If expansion is prevented, the same strain appears as stress instead — and for steel that reaches 96 MPa for only 40 K, which is why expansion joints exist.

Why does Thermal Expansion matter?

Restrained thermal stress is independent of length, so even a short fully fixed member develops the same high stress as a long one.

What values do I need to enter?

This calculator takes 4 inputs: Original length, Linear expansion coefficient, Temperature change, Elastic modulus. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.