Thermal Expansion Calculator
Length change with temperature, and the stress if the part cannot move.
How it works
ΔL = α L ΔT — nothing more than that for the length. Area expands at roughly 2α and volume at 3α, because the same fractional change happens along each axis independently.
The number that surprises people is the restrained stress, and it does not depend on length at all: σ = E α ΔT.
A steel member held rigidly and warmed by 60 °C develops about 151 MPa — comfortably past half the yield strength of mild steel — whether it is 100 mm long or 100 metres. Length changes how much it wants to move, not how hard it pushes when it cannot. That single fact is why bridges have expansion joints, why pipework has bellows and loops, why rails are welded under controlled tension and why long runs of plastic conduit buckle in the sun.
Mismatch matters as much as the absolute value. Aluminium moves about twice as far as steel, so an aluminium part bolted to a steel frame builds up stress every time the temperature changes and eventually elongates its own holes. Glass-to-metal seals exist as an engineering discipline precisely because getting two coefficients to agree is difficult.
The extremes are useful to know. Invar barely moves at all — that is what it was invented for, and why precision instruments and measuring standards are made of it. HDPE moves nearly seventeen times as much as steel, which is why a long plastic pipe run needs deliberate slack.
Common questions
Why doesn't the stress depend on length?
Because strain is a ratio. A long bar wants to grow more, but it also has more length to distribute the compression over, and the two cancel exactly. Stress from restrained expansion is a material property times a temperature change, full stop.
How much clearance should I leave?
Take the worst-case temperature swing the part will ever see, not the working range. A steel rail outdoors can go from −20 °C to +50 °C, so 70 K, not the 20 K it experiences on a given day.
Do the coefficients stay constant?
Approximately, over normal engineering ranges. They creep upward with temperature and change markedly near a phase transition, so the values here are fine from roughly −50 °C to 300 °C for metals and over a much narrower band for plastics.
What about a shrink fit?
Same arithmetic, used deliberately. Heat the outer part or chill the inner one until the interference clears, assemble, and let it equalise. Aluminium on steel is the easy case; steel on steel usually needs liquid nitrogen or an oven at 200 °C.