Thermal Expansion Calculator

The thermal expansion calculator finds the change in length or volume of a material subject to extreme temperatures.

Change in length4.8 mm4.8 mm over 10 m for a 40 K change

New length10.0048 m

Linear coefficient1.2e-5 per KCarbon steel — 12 parts per million per kelvin

Strain0.000480.048%

Area coefficient2.4e-5 per Ktwice the linear value, to first order — the α² term is negligible

Volume coefficient3.6e-5 per Kthree times the linear value

Fractional volume change0.144%

Stress if expansion is fully prevented96 MPa96 MPa — E × α × ΔT, and note it does not depend on the length at all

Temperature change to reach 250 MPa104.17 Kroughly the yield stress of structural steel — which is why expansion joints exist

Force in a 100 mm² section9.6 kN

Over a 100 m span48 mmthe figure that matters for bridges, rails and pipework

The same span in Invar0.48 mm10× less movement — Invar exists precisely because some instruments cannot tolerate expansion

The formula

ΔL = αLΔT; area goes as 2α, volume as 3α

Stress does not depend on length

A solid expands in proportion to its length and to the temperature change. Over a short piece the movement is negligible; over 100 metres of steel a 40 K swing is nearly 50 mm, which is why bridges have expansion joints and railway track is either jointed or laid under controlled tension.

The result worth internalising is that if expansion is fully prevented, the stress is E × α × ΔT and contains no length term at all. A short restrained bar is stressed exactly as hard as a long one. For steel that works out around 2.4 MPa per kelvin, so a 100 K rise would approach the yield stress — restraint, not movement, is what breaks things.

Area and volume coefficients are two and three times the linear one. That is a first-order approximation, discarding α² and α³ terms, but since α is measured in parts per million those terms are utterly negligible at any ordinary temperature change.

The range across materials is wide: PVC moves about four times as much as steel, and Invar about a tenth as much. Invar was developed specifically so that precision instruments and standards would not change dimension with the weather.