Thermal Expansion Calculator
Calculate how much a part grows with temperature, and the stress if it cannot.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Thermal Expansion Calculator does
Materials expand roughly in proportion to temperature change and original length. If the movement is allowed, you get displacement; if it is prevented, you get stress instead — and that stress is independent of length, which surprises people the first time they meet it.
Formula
ΔL = α L ΔTArea change ≈ 2 α ΔTVolume change ≈ 3 α ΔTRestrained stress σ = E α ΔT
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Material | one of 13 options | Yes | — |
| Original length | number | Yes | — |
| Original length unit | one of 9 options | Yes | — |
| Temperature change | number | Yes | — |
| Temperature change unit | one of 3 options | Yes | — |
| Expansion in | one of 3 options | Yes | — |
| Custom expansion coefficient | µm/m·K | Optional | Overrides the material if set. Accepts 0 or more. |
How to use it
- Choose Material and Original length unit.
- Enter Original length and Temperature change.
- Optionally add Custom expansion coefficient.
- Select Calculate.
Worked example
A 10 m steel beam warmed by 40 °C.
- Material
- Structural steel
- Length
- 10 m
- ΔT
- 40
ΔL = 12 × 10⁻⁶ × 10 × 40 = 4.8 mm. If fully restrained instead, the stress would be 200 GPa × 12 × 10⁻⁶ × 40 = 96 MPa — 38% of yield.
Frequently asked questions
Why does restrained thermal stress not depend on length?
Because strain is what generates stress, and thermal strain is αΔT regardless of length. A long bar wants to move more, but it also has more length over which to distribute the same proportional strain.
How big should an expansion gap be?
At least αLΔT using the full temperature swing the structure will see, plus an allowance for installation tolerance.
Method and sources
Method. Linear thermal expansion, ΔL = α × L₀ × ΔT, using representative coefficients for common materials, with area and volume treated as approximately 2α and 3α.
Assumptions
- The expansion coefficient is constant across the temperature range entered, and the material is free to expand without restraint.
- The material is isotropic, so it expands equally in every direction.
Limitations
- Coefficients are representative values for a material class, not certified figures for a specific alloy, temper or grade — those come from the supplier.
- The linear model degrades over wide temperature ranges and near phase changes, where the coefficient itself varies with temperature.
- Restrained expansion generates stress rather than movement. This calculates the movement; the resulting force is a separate and more consequential calculation.
Sources
- Published coefficient of thermal expansion tables for engineering materials — Materials reference handbooks; supplier datasheets for a specific grade. The representative expansion coefficients offered per material.