Thermal expansion calculator
Pick linear, area or volume expansion and a material, enter the starting size and the two temperatures. The calculator gives the change and the new size in the same unit, the percentage change and the coefficient it used. Cooling gives a negative change.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose length, area or volume.
- Pick a material, or “Own coefficient” and type it in units of 10⁻⁶ per kelvin (12 means 12 × 10⁻⁶/K).
- Enter the starting size with its unit (areas and volumes are in that unit squared or cubed) and the two temperatures.
- Length: ΔL = α × L₀ × ΔT.
- Area: ΔA = 2α × A₀ × ΔT. Volume: ΔV = 3α × V₀ × ΔT, or β × V₀ × ΔT.
- New size: L = L₀ + ΔL. A difference of 1 °C equals 1 K; 1 °F equals 5/9 K.
Worked example
A 100 m steel rail goes from 0 °C to 30 °C: ΔL = 12 × 10⁻⁶ × 100 × 30 = 0.036 m (36 mm), so it becomes 100.036 m long, a change of 0.036 %.
A 1000 cm³ copper block heated from 20 °C to 100 °C: ΔV = 3 × 17 × 10⁻⁶ × 1000 × 80 = 4.08 cm³.
Tips
- Holes grow too. A hole in a plate expands as if it were made of the plate’s material.
- Restrained parts that cannot expand build up stress instead; the stress–strain calculator helps there.
- The approximations 2α and 3α assume ΔT is small, which is true for everyday temperature ranges.
Frequently asked questions
What is the formula for thermal expansion?
For a length, ΔL = α × L₀ × ΔT, where α is the linear expansion coefficient. For an area, ΔA ≈ 2α × A₀ × ΔT, and for a volume, ΔV ≈ β × V₀ × ΔT with β ≈ 3α for solids.
How much does a steel rail expand?
With α ≈ 12 × 10⁻⁶ per kelvin, a 100 m rail warmed by 30 °C grows by 12 × 10⁻⁶ × 100 × 30 = 0.036 m, or 36 mm. That is why rails, bridges and pipelines have expansion joints.
Are the material values exact?
No. They are typical rounded values near room temperature; real coefficients depend on the alloy or mix and change with temperature. For precise work, choose "Own coefficient" and enter the value from a datasheet.
How do I use a volume coefficient for a liquid?
Choose Volume, then "Own coefficient", set "Coefficient entered" to Volume β and type β in units of 10⁻⁶ per kelvin. The calculator then uses ΔV = β × V₀ × ΔT directly.