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Thermal Expansion Calculator

Calculate how much a material grows or shrinks with temperature. Enter an original length, a temperature change and the material — the calculator applies linear expansion, ΔL = α·L₀·ΔT, and returns the expansion amount and the final length. The expansion coefficients offered are standard reference values near room temperature, clearly labelled; they feed the calculation rather than replacing it, and you can enter your own coefficient for a specific alloy or grade. Real values vary with temperature and composition.

How to use this tool

  1. Enter the original length and choose its unit.
  2. Enter the temperature change in °C (positive for heating, negative for cooling).
  3. Choose the material, or pick “Custom coefficient” and enter your own α.
  4. Read the expansion amount and the final length.
  5. For long spans or big temperature swings, this is why expansion joints and gaps are designed in.

The formula

Most materials expand when heated. For a long thin member the change in length is proportional to the original length, the temperature change and the material’s linear expansion coefficient.

ΔL = α · L₀ · ΔT L_final = L₀ + ΔL
ΔL
Change in length
α
Linear expansion coefficient, per °C
L₀
Original length
ΔT
Temperature change, °C (= K for a difference)

A 1 °C step equals a 1 K step, so the coefficient is the same whether the temperature change is stated in Celsius or kelvin.

Worked examples

Steel bridge span

Given
10 m steel, ΔT 50 °C
Result
ΔL ≈ 6 mm

With α ≈ 12×10⁻⁶/°C, a 10 m steel member grows about 6 mm over a 50 °C rise — enough to need an expansion joint.

Aluminium part

Given
1 m aluminium, ΔT 100 °C
Result
ΔL ≈ 2.31 mm

Aluminium’s higher coefficient (23.1×10⁻⁶/°C) means about 2.3 mm growth per metre over 100 °C.

Cooling

Given
2 m copper, ΔT −40 °C
Result
ΔL ≈ −1.33 mm

A negative temperature change gives contraction: the copper shrinks by about 1.3 mm.

Frequently asked questions

It is how much a material’s length changes per unit length for each degree of temperature change, written α, typically a few parts per million per °C. Multiplying it by the original length and the temperature change gives the expansion. Different materials expand at very different rates.

No, as long as it is a temperature difference. A change of one degree Celsius is the same size as a change of one kelvin, so the coefficient and the result are identical whether you think in °C or K. Only the change matters, not the starting temperature.

Because long metal spans grow measurably when heated by the sun. A steel span can lengthen several millimetres per ten metres over a summer’s temperature swing; without expansion joints or gaps, that growth would build enormous forces and buckle the structure.

They are typical published values near room temperature and are good for estimation. Real coefficients vary with the specific alloy, grade and temperature range, and some materials expand differently along different directions. For critical work, use the value for your exact material — the tool lets you enter a custom coefficient.

This calculator does linear expansion, the change in a single length. Area expansion is about twice the linear coefficient and volume expansion about three times, for isotropic materials. For a length, gap or span, linear expansion is what you want.

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