Calculate linear, area, or volume expansion of materials due to temperature change using expansion coefficients, with presets for steel, aluminium, glass, and more.
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Expansion / change
1.2000e-3 m
Final dimension
1.001200 m
Strain (ΔL/L₀)
1.2000e-3
ΔT (°C)
100.00
Mode
linear
Also in Physics
Science — Physics
Materials expand when heated and contract when cooled. The change in length, area, or volume is proportional to the original dimension, the coefficient of thermal expansion, and the temperature change. Engineers account for thermal expansion in bridge joints, pipeline loops, rail track gaps, and precision instruments.
Linear expansion: ΔL = α × L₀ × ΔT, where α is the linear expansion coefficient (per °C or per K). Area expansion: ΔA = 2α × A₀ × ΔT. Volume expansion for solids: ΔV = 3α × V₀ × ΔT (using the same linear α). For liquids, a separate volumetric expansion coefficient β is measured directly. Common coefficients: steel 12 × 10⁻⁶/°C, aluminium 23.1 × 10⁻⁶/°C, glass 9 × 10⁻⁶/°C, PVC 52 × 10⁻⁶/°C.
A 100 m steel rail at 0 °C expands by 0.12 m (12 cm) when heated to 100 °C — this is why rail joints and expansion gaps are essential. The calculator solves for any unknown: given the expansion, original length, and coefficient, it finds the temperature change; or given expected temperatures and a material, it finds the expansion to allow for in a joint or fitting.
Frequently asked questions
A square of side L expands to (L + ΔL)² ≈ L² + 2L·ΔL for small expansions, so ΔA ≈ 2α·A₀·ΔT. The factor of 2 comes from the two dimensions each expanding by α·L·ΔT independently.
Most materials expand on heating. A notable exception is water between 0 °C and 4 °C, which contracts as it warms (maximum density at 4 °C). Some specialty materials like Invar (FeNi alloy) have near-zero thermal expansion by design, used in precision instruments and telescope mirrors.
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