Thermal Expansion Calculator
Calculate linear or volumetric thermal expansion from material type and temperature change.
Covers steel, aluminum, copper, glass, concrete, and wood.
Thermal expansion describes how materials change in size when heated or cooled. Virtually all solids expand when heated and contract when cooled. Engineers must account for this in bridges, railways, pipelines, buildings, and any structure subject to temperature variation.
Linear thermal expansion formula: ΔL = α × L₀ × ΔT
Where:
- ΔL = change in length (meters or inches)
- α = coefficient of linear thermal expansion (per °C or per °F) — a material property
- L₀ = original length at reference temperature
- ΔT = temperature change (final temperature − initial temperature)
Final length: L = L₀ × (1 + α × ΔT)
Area thermal expansion: ΔA = 2α × A₀ × ΔT (approximate, for small expansions)
Volumetric thermal expansion: ΔV = β × V₀ × ΔT, where β ≈ 3α for isotropic materials
Coefficients of linear thermal expansion (α) for common materials:
- Aluminum: 23.1 × 10⁻⁶ /°C
- Steel (structural): 11.0–13.0 × 10⁻⁶ /°C
- Concrete: 10.0–12.0 × 10⁻⁶ /°C
- Copper: 16.5 × 10⁻⁶ /°C
- Glass (borosilicate): 3.3 × 10⁻⁶ /°C
- PVC plastic: 52 × 10⁻⁶ /°C
- Wood (along grain): 3–5 × 10⁻⁶ /°C
Worked example: A steel railroad rail is 100 meters long at −10°C. It’s exposed to summer heat of 40°C. α for steel = 12 × 10⁻⁶ /°C.
- ΔT = 40 − (−10) = 50°C
- ΔL = 12 × 10⁻⁶ × 100 m × 50 = 0.06 meters = 6 cm
This 6 cm expansion per 100 m section is why railway tracks have expansion gaps between sections. Without gaps, the compressive force from thermal expansion is enormous — enough to buckle the track and cause derailments.