Thermal Expansion Calculator

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.

Bimetallic strips, differential expansion in action. Bond two metals with different α values back-to-back and heat the strip. The metal with higher α stretches more, so the strip curves toward the lower-α side. This is how mechanical thermostats, automotive temperature gauges, and old-style circuit breakers work: temperature rises, the strip bends, and at a set point it makes or breaks an electrical contact. Brass + steel is the classic pairing.

Water’s anomalous behavior, the reason ice floats. Most materials shrink as they cool. Water does the same until about 4°C, then expands again as it cools further to 0°C. At freezing, the volume jumps by about 9%. Solid water (ice) is therefore less dense than liquid water at 4°C, so ice floats on lakes rather than sinking and accumulating at the bottom. If water behaved like most other liquids, lakes would freeze from the bottom up, killing all aquatic life every winter. The exception traces back to hydrogen bonding: ice’s crystal lattice holds water molecules slightly farther apart than they sit in the liquid.

Thermal stress, when expansion is blocked. If a material is mechanically constrained and cannot expand freely as it heats, internal stress builds up:

σ = α × E × ΔT

where E is the material’s elastic modulus (Young’s modulus). For a steel rail (E ≈ 200 GPa, α ≈ 12×10⁻⁶/°C) heated by 30°C, the constrained stress is 200×10⁹ × 12×10⁻⁶ × 30 ≈ 72 MPa, into the deformation zone for most steels. This is why constrained thermal expansion can crack concrete, warp metal parts, and fracture glass. Pyrex (borosilicate glass) has an unusually low α (≈ 3.3×10⁻⁶/°C) specifically to resist thermal shock in cooking and laboratory use. Invar, a 64% iron / 36% nickel alloy invented by Charles-Édouard Guillaume in 1896 (Switzerland), pushes the same idea further with α ≈ 1.2×10⁻⁶/°C, roughly a tenth that of ordinary steel. Invar is the standard choice for precision pendulum clocks, surveying tapes, and the structural shells of LNG tankers, where any temperature-driven dimensional change would be a problem.