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Thermal Expansion (Linear) Calculator

Work out thermal expansion (linear) instantly with clear inputs, formula shown and shareable results.

About Thermal Expansion (Linear) Calculator

Linear expansion is dL = L.alpha.dT. A 12 m steel beam with alpha = 12e-6 per kelvin grows 5.04 mm over a 35 K rise - which is why bridges need expansion joints and rails were traditionally laid with gaps. Restraining that growth instead generates thermal stress of E.alpha.dT, about 84 MPa for steel over 35 K.

Formulas

Linear expansion

dL = L x alpha x dT

Thermal strain

strain = alpha x dT

Worked example

With the default values below, Thermal Expansion (Linear) Calculator returns Change In Length of 5.0400. Change any input above and every figure here is recalculated in your browser.

Inputs used

Original lengthminimum 0 m
12 m
Linear expansion coefficientminimum 0 1/K
0.000012 1/K
Temperature change
35 K

Results

Change In Length
5.0400 mm
Same Change In Metres
5.0400 × 10⁻³
New Length
12.00504 m
Thermal Strain
4.2000 × 10⁻⁴

Step by step

  1. 1Values used
  2. 2Linear expansion
  3. 3Thermal strain
  4. 4Change In Length= 5.0400 mm
  5. 5Same Change In Metres= 0.0050
  6. 6New Length= 12.00504 m
  7. 7Thermal Strain= 0.0004

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What happens if expansion is prevented?

The material develops thermal stress equal to E.alpha.dT. For steel that is about 2.4 MPa per kelvin, so even modest heating can buckle a restrained member.

Which materials expand least?

Invar at about 1.2e-6 per kelvin and fused silica at 0.5e-6, which is why they are used in precision instruments.

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