Thermal Expansion Calculator
Calculate linear expansion of materials with temperature change.
Calculator
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Expansion ΔL: 48.0 mm (0.0480 m)
Formula
ΔL = α × L₀ × ΔT, where α is the coefficient of linear thermal expansion (1/°C), L₀ is original length (m), ΔT is temperature change (°C).
Example calculation
Steel pipe L₀ = 50 m, α = 12×10⁻⁶ /°C, ΔT = 80°C (from 20°C to 100°C): ΔL = 12×10⁻⁶ × 50 × 80 = 0.048 m = 48 mm.
Engineering notes
Thermal expansion coefficients: carbon steel 11–13 × 10⁻⁶/°C, stainless steel 17 × 10⁻⁶/°C, aluminium 23 × 10⁻⁶/°C, copper 17 × 10⁻⁶/°C, HDPE 130–200 × 10⁻⁶/°C. Always design pipe loops, expansion joints, or slide bearings to accommodate calculated expansion.
When to use this calculator
- Piping design — size expansion loops and bellows to accommodate thermal growth in hot process lines
- Structural steel — account for thermal expansion in long bridge girders and roof structures
- Rail track — calculate expansion gap between rail sections for summer temperature extremes
- Precision machining — compensate for workpiece dimensional change during hot cutting operations
- Tank and vessel design — calculate nozzle loads due to differential thermal expansion between shell and nozzle
Frequently asked questions
- Why is thermal expansion important in pipeline design?
- A 100 m carbon steel pipe heating from 20°C to 200°C expands by about 216 mm. If both ends are fixed (anchored), this generates enormous compressive stress — potentially millions of Newtons of force. Piping engineers design expansion loops (L-shaped or Z-shaped pipe runs), bellows expansion joints, or guided sliding supports to absorb this movement and prevent pipe failure or nozzle overload.
- What is the difference between linear and volumetric thermal expansion?
- Linear expansion (ΔL = α × L × ΔT) applies to one dimension — length of a rod or pipe. Volumetric expansion (ΔV = β × V × ΔT) applies to three dimensions, where the volumetric expansion coefficient β ≈ 3α for isotropic materials. For liquids, only volumetric expansion is meaningful. For process vessels, both shell expansion and liquid expansion must be considered when sizing expansion tanks or relief devices.
- How do I calculate the force generated by restrained thermal expansion?
- Thermal stress σ = E × α × ΔT (Pa), where E is the Young's modulus (Pa). Thermal force F = σ × A = E × α × ΔT × A, where A is cross-sectional area (m²). For carbon steel (E = 200 GPa, α = 12×10⁻⁶/°C) with ΔT = 100°C: σ = 200×10⁹ × 12×10⁻⁶ × 100 = 240 MPa — close to yield stress. This is why restraining thermal expansion is dangerous.