How to use this calculator
- Choose the material. Select a material preset or choose a custom expansion coefficient.
- Enter original length. Use the length before heating or cooling.
- Enter temperature change. Use positive ΔT for heating and negative ΔT for cooling.
- Read expansion. Read length change, final length and thermal strain.
How it works
Linear thermal expansion is:
ΔL = α · L₀ · ΔT
where α is the coefficient of linear expansion, L₀ is the
original length and ΔT is temperature change. The coefficient is entered
in µm/(m·°C), equivalent to parts per million per degree C.
Worked example
Verified against the live calculator
A 1 m carbon-steel bar heated by 50°C expands by
12 × 1 m × 50 = 600 µm, or 0.60 mm. The final length is
1.0006 m. A 6061 aluminum bar of the same length and temperature rise
expands about 1.18 mm.
Frequently asked questions
What is the thermal expansion formula?
Linear thermal expansion is ΔL = α·L·ΔT, where α is the coefficient of linear thermal expansion, L is the original length and ΔT is the temperature change.
What units should I use for alpha?
This calculator uses µm/(m·°C), which is the same as ppm/°C. A value of 12 means the material grows 12 micrometres per metre for each 1°C temperature rise.
Is a °F temperature change the same as °C?
No. Convert a Fahrenheit temperature difference before entering it: Δ°C = Δ°F × 5/9. A 90°F rise is a 50°C rise.
Why do steel and aluminum expand differently?
Their coefficients of thermal expansion are different. Aluminum is roughly 23 µm/m·°C, about twice carbon steel at roughly 12 µm/m·°C.
Method & assumptions
- Uses linear expansion only; large parts, high gradients and constrained assemblies need stress/warping checks.
- Material coefficients are typical room-temperature values and vary with alloy, temper and temperature range.
- Use a negative temperature change for cooling and shrink fits.