A metre of steel expands about 1 mm when heated ~85 °C.
α ≈ 12 µm/m·°C for carbon steel. Aluminium moves nearly twice as much — which is why mixed-metal assemblies need sliding joints.
Austenitic stainless moves about half again as much (17 µm/m·K against 12), so the same rule under-predicts it by 40%. And a restrained member does not grow at all — it builds stress instead, roughly 2.4 MPa per °C, which is how buried pipework buckles without anything moving.
At 85 °C the rule says 1 mm and the exact answer is 1.02 mm — 2% low. It stays inside 5% across the whole range shown.
Carbon steel expands 12 µm per metre per °C, so 1 mm actually arrives at 83 °C. The rule is 2% shy, and stainless moves half as much again.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
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