What is a typical linear expansion coefficient?

For steel, alpha is about 12 x 10^-6 per kelvin. Aluminium is about 23 x 10^-6 per kelvin. Invar (a nickel-iron alloy) has an exceptionally low alpha of about 1.2 x 10^-6 per kelvin, which is why it is used in precision instruments.

Why do bridge engineers leave expansion gaps?

Steel bridges can be hundreds of metres long. Using ΔL = alpha*L0*ΔT with a 40 C seasonal swing and alpha = 12e-6/K: a 200 m span expands by about 96 mm. Without expansion joints, this would buckle the structure.

Does this formula apply to two-dimensional or three-dimensional expansion?

This formula gives the change in one linear dimension. For area expansion, use ΔA ≈ 2*alpha*A0*ΔT; for volume expansion of a solid, use ΔV ≈ 3*alpha*V0*ΔT (the volumetric expansion coefficient is approximately three times the linear one).

Linear Thermal Expansion Calculator

Compute the change in length of a solid object due to temperature change using ΔL = α L₀ ΔT. Enter the coefficient of expansion, original length, and temperature change to get elongation.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

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How to use this tool

Enter coefficient of linear expansion (α), original length (l₀) and temperature change (δt) in the fields above.
Results update instantly as you type — or click Calculate.
Read your change in length (δl) and the full breakdown beneath it.

Formula

ΔL = α L₀ ΔT

How it works

Multiply the coefficient of linear expansion (1/K) by the original length (m) and the temperature change (K).

Worked example

Common mistakes to avoid

Using the final temperature instead of the temperature difference deltaT — the formula needs the change in temperature, not the absolute temperature.
Using the wrong expansion coefficient — alpha varies significantly between materials (e.g., steel ~12e-6/K, aluminium ~23e-6/K, concrete ~12e-6/K); using a generic value for the wrong material gives meaningless results.
Applying linear expansion to gases or liquids — this formula is for solids only; gases use the ideal gas law and liquids use volumetric expansion coefficients.

Key terms

Frequently asked questions

What is a typical linear expansion coefficient?: For steel, alpha is about 12 x 10^-6 per kelvin. Aluminium is about 23 x 10^-6 per kelvin. Invar (a nickel-iron alloy) has an exceptionally low alpha of about 1.2 x 10^-6 per kelvin, which is why it is used in precision instruments.
Why do bridge engineers leave expansion gaps?: Steel bridges can be hundreds of metres long. Using ΔL = alpha*L0*ΔT with a 40 C seasonal swing and alpha = 12e-6/K: a 200 m span expands by about 96 mm. Without expansion joints, this would buckle the structure.
Does this formula apply to two-dimensional or three-dimensional expansion?: This formula gives the change in one linear dimension. For area expansion, use ΔA ≈ 2*alpha*A0*ΔT; for volume expansion of a solid, use ΔV ≈ 3*alpha*V0*ΔT (the volumetric expansion coefficient is approximately three times the linear one).