Thermal Expansion Calculator
Calculate linear, area, and volumetric thermal expansion for 8+ materials. Includes constrained thermal stress (σ=EαΔT), expansion gap for bridges and rails, and 15+ material coefficients.
Length Change (mm)
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New Length (m) —
α Used (×10⁻⁶/°C) —
Extended More scenarios, charts & detailed breakdown ▾
ΔL (mm)
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New Length (m) —
Professional Full parameters & maximum detail ▾
Expansion & Gap
ΔL (mm) —
Required Expansion Gap (mm) —
Constrained Thermal Stress
Thermal Stress σ (MPa) if constrained —
Material Reference (α ×10⁻⁶/°C)
Material α Reference —
How to Use This Calculator
- Enter Original Length (m), Temperature Change ΔT (°C), and select the Material.
- See length change in mm and new length immediately.
- Use the Volumetric tab for 3D volume expansion (β=3α).
- Use the Area tab for 2D surface expansion (2α).
- The Professional tab adds constrained thermal stress, expansion gap for bridges, and a material reference table.
Formula
Linear: ΔL = α·L₀·ΔT | Area: ΔA = 2α·A₀·ΔT | Volumetric: ΔV = 3α·V₀·ΔT
Thermal Stress: σ = E·α·ΔT
Example
10 m steel rail, ΔT=50°C → ΔL = 11.7×10⁻⁶×10×50 = 5.85 mm. If constrained: σ = 200×10⁹×11.7×10⁻⁶×50 = 117 MPa.
Frequently Asked Questions
- ΔL = α × L₀ × ΔT, where α is the coefficient of linear thermal expansion (in 1/°C), L₀ is original length, and ΔT is temperature change. The new length is L = L₀ + ΔL.
- ΔV = β × V₀ × ΔT, where β ≈ 3α for isotropic materials. For a 1 m³ steel block heated 100°C: ΔV = 3×11.7×10⁻⁶×1×100 ≈ 0.00351 m³ = 3510 cm³.
- When a material is constrained (cannot expand), heating creates compressive stress: σ = E × α × ΔT, where E is Young's modulus. For steel: E=200 GPa, α=11.7×10⁻⁶, ΔT=50°C → σ = 117 MPa.
- A 50 m steel bridge heated 40°C expands by α×L×ΔT = 11.7×10⁻⁶×50×40 = 23.4 mm. Without expansion joints, this would cause buckling or cracking. Joints provide the necessary gap.
- Invar (Fe-Ni alloy) has α≈1.2×10⁻⁶/°C, among the lowest of any metal. Used in precision instruments and standards. Pure fused silica glass has α≈0.55×10⁻⁶/°C.