Linear Thermal Expansion Calculator
Estimate how much a straight dimension changes when its temperature changes. Enter the initial length, material’s linear coefficient of thermal expansion, and temperature difference. A negative temperature difference represents cooling. Choose metric or US customary units; temperature inputs are differences, not absolute temperatures.
Interactive calculator
Enter values and select Calculate.
Linear expansion formula
For a constant expansion coefficient over the temperature interval, ΔL = α × L0 × ΔT. Here, ΔL is the change in length, α is the linear expansion coefficient per degree, L0 is the initial length, and ΔT is the temperature change. The estimated final length is L0 + ΔL.
Worked example
For a 1,000 mm steel length, an illustrative coefficient of 12 µm/(m·°C), and a 50°C temperature rise, change is 1,000 × 12 × 10⁻⁶ × 50 = 0.6 mm. The estimated final length is 1,000.6 mm. For a 50°C drop, the same model estimates −0.6 mm change and a final length of 999.4 mm.
The coefficient depends on the material and temperature range. NIST describes the coefficient through the relationship between length change, original length, and temperature change in its metrology reference on thermal effects. Look up a coefficient that matches the exact alloy and relevant temperature range; the 12 µm/(m·°C) example is illustrative.
Limits of the estimate
This is a one-dimensional, unconstrained estimate with a constant coefficient. It does not model temperature gradients, anisotropic materials, contact conditions, thermal stress, expansion joints, fasteners, or a constrained assembly. Large temperature ranges may require integrating a temperature-dependent coefficient. A part constrained by other parts can develop stress rather than freely changing length.
Use the result to understand the scale of a change, then verify the material data and boundary conditions for design or inspection decisions. If a feature chain also depends on dimensional tolerances, use the tolerance stack-up calculator.
