Thermal Expansion of a Length
Linear thermal expansion ΔL = α·L·ΔT with your coefficient: new length, strain, area and volume change, restrained stress, or the ΔT for a wanted change.
The change in length and the new length, strain in ppm, approximate area and volume change, thermal stress from a Young’s modulus you give, or the temperature change for a target ΔL.
Example: A 12 m steel member (α 12 × 10⁻⁶/K) heated 40 K grows 5.76 mm (480 ppm); fully restrained with E = 200 GPa the thermal stress is 96 MPa. A 100 mm aluminium part (23 × 10⁻⁶) moves 0.05 mm for 21.7 K.
α times L
times ΔT.
The linear law, its area and volume cousins, and the stress of a part that cannot move.
Linear expansion
For modest temperature changes a length grows in proportion: ΔL = α·L₀·ΔT, where α is the coefficient of linear expansion from the material’s data sheet (per kelvin, or per °F in the imperial mode). The strain is α·ΔT; a reverse solve gives the ΔT that produces a wanted ΔL — for shrink fits and expansion gaps.
Area and volume
An isotropic solid expands the same in every direction, so area grows by about 2α·ΔT and volume by about 3α·ΔT for small strains (the page uses the exact (1 + ε)² − 1 and (1 + ε)³ − 1). Anisotropic materials — wood, composites, some crystals — need a coefficient per direction.
Restrained stress
If the part is held so it cannot expand, the prevented strain becomes stress: σ = E·α·ΔT with the Young’s modulus you enter. That is the fully restrained upper bound; partial restraint gives less, and whether the stress matters is a comparison with the material’s yield strength you make yourself. α varies with temperature over large ranges — use the mean value for the range. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- ΔL = α·L₀·ΔT; strain = α·ΔT; area ≈ 2α·ΔT, volume ≈ 3α·ΔT (isotropic, small strain); σ = E·α·ΔT fully restrained; α and E from the material data sheet — no table embedded
Last reviewed 21 September 2026. How results are checked: How we verify.