Most materials grow when heated and shrink when cooled. The formula for thermal expansion tells you how much, which matters for pipes, rails, bridges, and any long run that sees a temperature swing.

The formula for thermal expansion

The linear expansion formula multiplies the original length by the expansion coefficient and the temperature change:

ΔL = α × L × ΔT

L is the original length, α is the coefficient of linear expansion (the fractional growth per degree), and ΔT is the temperature change. The thermal expansion calculator applies this for steel, aluminum, and other materials.

Worked example

A 10 m steel bar heated by 50°C, with α = 0.000012 per °C: ΔL = 0.000012 × 10 × 50 = 0.006 m, or 6 mm. Small, but across a long pipe run it is enough to buckle a fixed joint, which is why expansion loops and gaps exist.

Coefficients for common materials

The coefficient of linear expansion sets how far a material moves. Typical values per °C: steel and concrete about 0.000012, copper 0.000017, aluminum 0.000023, glass 0.000009. Aluminum grows nearly twice as much as steel for the same heating, which is why mixed metal assemblies loosen or bind as they cycle. The heat that drives the change follows the heat transfer formula, Q = m × c × ΔT.

Area and volume expansion

The linear formula covers one dimension. Area grows at roughly twice the coefficient and volume at about three times, since expansion happens along every axis. For most engineering the linear form is what you need.

Blocked expansion becomes stress

When a part cannot expand freely, the growth does not vanish; it turns into large internal stress instead. That is why pipework uses sliding supports and bellows. The heat that drives the temperature rise is handled by the heat transfer calculator.

Common mistakes

• Wrong coefficient. Each material has its own α; steel and aluminum are not the same.
• Confusing linear with area or volume. The linear formula covers length only.
• Ignoring cooling. A negative temperature change gives a shrink of the same size.

Quick reference

Thermal expansion: ΔL = α × L × ΔT. Steel α ≈ 0.000012 per °C. Try your own values in a free online calculator from CalculateGuide.