Thermal Expansion Calculator (Linear)
Thermal expansion calculator: change in length of a bar, pipe or rail from its expansion coefficient, length and temperature change.
ΔL = α · L₀ · ΔT
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
ΔL = α L₀ ΔT. Steel expands about 12 µm per meter per °C, so a 10 m steel beam grows about 4.8 mm when it warms by 40 °C.
Formula
ΔL = α · L₀ · ΔT
| Symbol | Quantity | Units |
|---|---|---|
| α | Expansion coefficient, 1/K | — |
| L₀ | Initial length | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| ΔT | Temperature change | K, °C, °F |
| ΔL | Change in length | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Constants used: α (1/K): steel 12e-6 · aluminum 23e-6 · copper 17e-6 · glass 9e-6 · concrete 12e-6
Worked example
Given: α = 1.2 × 10-5 · L₀ = 10 m · ΔT = 40 °C
ΔL = α L₀ ΔT
Result: ΔL = 4.8 mm
Change in length for different values of Expansion coefficient, 1/K
| α · Expansion coefficient, 1/K | ΔL · Change in length |
|---|---|
| 6 × 10-6 | 2.4 mm |
| 9 × 10-6 | 3.6 mm |
| 1.08 × 10-5 | 4.32 mm |
| 1.2 × 10-5 | 4.8 mm |
| 1.32 × 10-5 | 5.28 mm |
| 1.5 × 10-5 | 6 mm |
| 1.8 × 10-5 | 7.2 mm |
| 2.4 × 10-5 | 9.6 mm |
Other values as in the worked example.
Frequently asked questions
10 m of steel heated by 40 °C?
4.8 mm longer.
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