About the Thermal Expansion Calculator
This thermal expansion calculator tells you how much a part, pipe, rail, beam or volume of liquid will grow when it warms up — or shrink when it cools. Pick a material (or enter your own coefficient), enter the starting size and the initial and final temperatures, and it returns the change in size, the final size and the percentage change. Switch between linear expansion for lengths and volumetric expansion for volumes.
It is useful for physics and engineering students, for engineers and installers sizing expansion gaps in bridges, pipework, railings, decking and cladding, for machinists dealing with shrink fits, and for anyone checking how much a tank of water expands when heated. The size can be in any unit — the change comes back in the same unit.
The calculation assumes the coefficient is constant over the temperature range, which is a good approximation for solids over everyday ranges. Coefficients are typical room-temperature values; alloys and grades differ, and liquids such as water expand non-linearly (water is densest near 4 °C), so treat liquid results as estimates.
With the default inputs, the change in size is 0.03. Change any value above to recalculate instantly.
How to use the thermal expansion calculator
- 1Choose linear (length) or volumetric (volume) expansion.
- 2Pick the material, or enter a custom coefficient.
- 3Enter the initial size in any unit.
- 4Enter the starting and ending temperatures and their unit.
- 5Read the change and final size in the same unit as your input.
Formula and method
Most materials expand when heated because their atoms vibrate with larger amplitude and sit slightly further apart. For moderate temperature changes the change in length is proportional to the original length and to the temperature change: ΔL = α·L₀·ΔT, where α is the coefficient of linear thermal expansion (per kelvin, which is the same size as per °C). Temperatures in °F are converted with ΔT(K) = ΔT(°F) × 5/9.
Volumes follow ΔV = β·V₀·ΔT. For an isotropic solid, β is very close to 3α because the material grows in all three directions. Liquids are specified directly by β. The linear approximation is accurate when α·ΔT is small (well under 1%), which is true for almost all practical cases.
- ΔL, ΔV
- Change in length or volume
- L₀, V₀
- Initial length or volume
- α
- Linear expansion coefficient (1/K)
- β
- Volumetric expansion coefficient (1/K)
- ΔT
- Temperature change (K or °C)
Worked examples
50 m steel bridge span, −10 °C to 40 °C
ΔL = 12 × 10⁻⁶ × 50 m × 50 K = 0.030 m. A 50 m steel span grows by 30 mm between a cold winter night and a hot summer day, which is why bridges need expansion joints.
6 m aluminium rail heated from 20 °C to 100 °C
ΔL = 23.1 × 10⁻⁶ × 6 × 80 = 0.011088 m, about 11.1 mm — almost twice what a steel rail of the same length would grow.
1,000 L of water heated from 20 °C to 80 °C
Using β = 207 × 10⁻⁶/K, ΔV = 207 × 10⁻⁶ × 1000 × 60 = 12.4 L. Because water’s β rises with temperature the real figure is closer to 27 L (about 2.7%, from densities of 998.2 and 971.8 kg/m³), which is why heating systems need an expansion vessel.
Same steel span with temperatures in °F
14 °F to 104 °F is a 90 °F change, which equals 50 K, so the 50 m steel span again grows by 0.030 m.
Frequently asked questions
What is the formula for linear thermal expansion?+
ΔL = α × L₀ × ΔT, where α is the material’s coefficient of linear expansion, L₀ the original length and ΔT the temperature change. For steel (α ≈ 12 × 10⁻⁶/K), a 1 m bar grows 0.012 mm for every 1 °C.
How much does steel expand per degree?+
Carbon steel expands roughly 12 millionths of its length per °C — about 0.012 mm per metre per °C, or 1.2 mm per 100 m per °C. Stainless steel expands more, around 17 × 10⁻⁶/K.
What is the relationship between linear and volumetric expansion?+
For an isotropic solid the volumetric coefficient is approximately three times the linear coefficient, β ≈ 3α, because the material expands equally along all three dimensions.
Is the coefficient per °C or per K?+
Both are the same, because a change of 1 °C equals a change of 1 K. Coefficients per °F are 5/9 as large; this calculator converts °F temperature changes automatically.
Why does water behave differently?+
Water contracts as it warms from 0 °C to about 4 °C, then expands, and its expansion coefficient keeps rising with temperature. A single coefficient therefore gives only an estimate for water over wide ranges.