Method and variables
Formula: ΔL = L₀ × α × ΔT.
- ΔL — change in length
- L₀ — original unconstrained length
- α — linear thermal-expansion coefficient
- ΔT — temperature change, not the absolute temperature
Worked example
A 10 m aluminum member with α = 22 × 10⁻⁶/K heated by 40 °C changes length by 10 × 22 × 10⁻⁶ × 40 = 0.0088 m, or 8.8 mm.
When this estimate applies
This is a linear, free-expansion estimate. It is useful for early checks of rails, pipe runs, frames and long members where a temperature swing may matter.
Important limits
It does not calculate thermal stress in a restrained member, nonlinear behavior over wide temperature ranges, gradients through a part, phase changes or connection and joint movement. Use the relevant material data and applicable code for final design.
References
Related tools
Heat Energy Calculator · Heat Conduction Calculator · Engineering Calculators
Frequently asked questions
How is linear thermal expansion calculated?
The calculator uses ΔL = L₀ × α × ΔT. L₀ is the original length, α is the material's linear expansion coefficient, and ΔT is the temperature change.
Can I use Fahrenheit for a temperature change?
Yes. A temperature difference of 1 °F equals 5/9 K or °C, so the calculator converts a Fahrenheit difference before applying the formula.
Is this suitable for final engineering design?
It is a first-pass linear estimate. Final design needs the exact material grade, operating range, constraints, joints and the applicable engineering standard.