Linear Thermal Expansion Calculator
Enter original length, expansion coefficient and temperature change to compute length change, final length and strain.
Input Data
Results
At a glance:Linear thermal expansion: a solid's length changes by ΔL = α·L₀·ΔT, where α is the coefficient of linear expansion (1/K), L₀ the reference length and ΔT the temperature change. The fractional change ΔL/L₀ = α·ΔT is the thermal strain ε (no stress if free to expand). The final length is L = L₀(1+α·ΔT). If expansion is constrained, the strain produces thermal stress σ = E·α·ΔT (E = Young's modulus). This tool returns ΔL, L and ε. For area use 2α, for volume 3α (small-α limit).
Formula
ΔL = α·L₀·ΔT
L = L₀(1+α·ΔT)
Strain: ε = α·ΔT
$$\Delta L = \alpha L_0 \Delta T, \quad \varepsilon = \frac{\Delta L}{L_0} = \alpha \Delta T$$How to Use
- Enter the original length L₀ (m).
- Enter the coefficient α (1/K) and temperature change ΔT (K).
- The calculator returns ΔL, L and strain ε.
Case Studies
Constrained beam
L₀=2 m, α=1.2e-5/K, ΔT=50 K, E=200 GPa.
ε = 1.2e-5×50 = 6e-4, ΔL = 1.2 mm.
If fixed: σ = 200e9×6e-4 = 120 MPa (significant).
FAQ
What is the difference between strain and length change?
ΔL is the absolute length change (m); strain ε = ΔL/L₀ = α·ΔT is the dimensionless fractional change. Both describe the same expansion.
Why does constrained expansion cause stress?
If the part cannot expand, the would-be strain α·ΔT is converted to stress σ = E·α·ΔT (Hooke's law). This is why pipes need expansion loops.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.