Thermal Expansion Calculator

Estimate the dimensional change of an unconstrained solid over a temperature interval. Choose length, area or volume and supply a linear expansion coefficient appropriate to the material. The same calculation supports metres, centimetres, millimetres, feet and inches, while temperature can be entered in Celsius, Fahrenheit or kelvin.

How to use this tool

1. Choose whether the starting measure is a length, area or volume.
2. Enter that measure in the selected dimensional unit.
3. Enter the linear coefficient in millionths per kelvin.
4. Enter initial and final temperatures in one scale, then read the change and final measure.

Formula

ΔL = L0αΔT; ΔA ≈ A0(2α)ΔT; ΔV ≈ V0(3α)ΔT

For an isotropic solid, the first-order area and volume coefficients are approximately two and three times the linear coefficient. The input 12 means 12 × 10⁻⁶ per kelvin. A Fahrenheit temperature difference is multiplied by 5/9; Celsius and kelvin differences have the same size.

Example

A 2 m member with α = 12 × 10⁻⁶/K warming from 20°C to 120°C changes length by 2 × 12 × 10⁻⁶ × 100 = 0.0024 m, or 2.4 mm. Its predicted final length is 2.0024 m. These numbers use the supplied coefficient rather than identifying a particular alloy.