Thermal Expansion Calculator — ΔL = αL₀ΔT
Solids grow when heated and shrink when cooled. The change in length is ΔL = αL₀ΔT, where α is the material’s coefficient of linear expansion. Pick a material from the list (or type your own α) and the calculator finds the expansion and the final length.
The effect is small per metre but impossible to ignore in long structures — it is why bridges have expansion joints, railway tracks have gaps, and power lines sag more on hot days.
Use the calculator
Pick a material (or enter α), the original length and the temperature change.
The formula
ΔL = αL₀ΔT, and final length L = L₀ + ΔL. A negative ΔT gives a contraction (ΔL negative). Typical α values: steel 12 × 10⁻⁶, copper 17 × 10⁻⁶, aluminium 23 × 10⁻⁶ per °C.
Worked example
Worked example: A 10 m steel beam warms by 30 °C. ΔL = 12 × 10⁻⁶ × 10 × 30 = 0.0036 m = 3.6 mm, so its final length is 10.0036 m. Scale that to a 300 m bridge deck and the movement is over 10 cm — hence the joints.
Frequently asked questions
Why do bridges have expansion joints?
A long deck expands and contracts by centimetres across the seasons. Joints give the structure room to move; without them the thermal stress would crack the deck or buckle the supports.
Does thermal expansion depend on the original length?
Yes — ΔL is directly proportional to L₀. Doubling the length doubles the expansion for the same temperature change, which is why the effect matters most in long structures.
What happens when a material is cooled?
It contracts: ΔT is negative, so ΔL is negative and the final length is shorter than L₀. The same formula handles both cases with signs.