Materials grow when heated. Linear thermal expansion is ΔL = α × L × ΔT, where α is the coefficient of expansion (parts per million per °C), L the original length, and ΔT the temperature change. This calculator returns the change in length, the final length and the thermal strain.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the linear-expansion relation, recomputed in code.
The formula
The coefficient α captures the material: aluminium (≈ 23) expands roughly twice as much as steel (≈ 12) for the same heating, while glass (≈ 9) and titanium (≈ 8.6) move least. Heating gives a positive ΔL; cooling a negative one (contraction). Thermal strain — the fractional change ΔL/L — equals α × ΔT and is independent of length.
Worked examples
10 m steel beam, +50 °C:
2 m aluminium bar, +80 °C:
100 m steel bridge span, +40 °C:
That 48 mm of movement on a 100 m span is exactly why bridges and pipelines use expansion joints. The thermal strain in the steel beam example is 12×10⁻⁶ × 50 = 6×10⁻⁴, or 0.06% — small per unit length, but it adds up over long runs.
Frequently Asked Questions
ΔL = α × L × ΔT. 10 m steel at +50 °C ≈ 6 mm.
Expansion per °C in ppm. Steel ≈ 12, aluminium ≈ 23, copper ≈ 17, glass ≈ 9.
≈ 6 mm per 10 m per 50 °C. A 100 m span moves ~48 mm over 40 °C.
ΔL/L = α × ΔT. Steel at 50 °C: 6×10⁻⁴ (0.06%).
Area ≈ 2α, volume ≈ 3α for the same ΔT. This page covers linear (length).