Mechanical
Thermal Expansion Calculator
When a solid is heated, it expands. Linear thermal expansion calculates the change in length for a given temperature change and coefficient of linear thermal expansion (α). You must supply α — no material property lookup is performed.
TypeInteractive calculator — separate from unit conversions
Calculator
Results
Length change (ΔL)0.006 m
Final length10.006 m
Thermal strain (ε)0.0006 —
Formulas
Length change
ΔL = α × L₀ × ΔT
Final length
L = L₀ + ΔL
Thermal strain
ε = α × ΔT
Diagram
Worked example
A steel pipe is 10 m long. α = 12 × 10⁻⁶ 1/K. Temperature increases by 50 K. What is the expansion?
- 01ΔL = α × L₀ × ΔT
- 02ΔL = 12 × 10⁻⁶ × 10 × 50
- 03ΔL = 0.006 m (6 mm)
- 04Final length = 10 + 0.006 = 10.006 m
- 05Strain = 12 × 10⁻⁶ × 50 = 6 × 10⁻⁴
Result
The pipe expands by 0.006 m (6 mm). Final length is 10.006 m. Thermal strain is 6 × 10⁻⁴.
FAQ
Does this look up material coefficients?
No. You must supply the coefficient of linear thermal expansion (α). No material property lookup is performed.
Can I use this for volumetric expansion?
This calculator handles linear expansion only. For isotropic materials, volumetric expansion is approximately 3α × ΔT, but this is not calculated here.
Is this valid for large temperature ranges?
Only if α is approximately constant. For large temperature ranges, α may vary and a more detailed model is needed.
Does this account for mechanical constraints?
No. This assumes free expansion. Thermal stress due to constraints is not calculated.