Thermal Expansion Calculator
How much a length or volume grows or shrinks with temperature: ΔL = α L ΔT and ΔV = β V ΔT, with a few material coefficients or your own.
Result…
How it's calculated
ΔL = α × L × ΔT ΔV = β × V × ΔT, with β ≈ 3α for isotropic solids ΔT in K = ΔT in °C = ΔT in °F × 5 ÷ 9
Most materials grow when heated because their atoms vibrate further apart. Over a moderate range the change is proportional to the original size and the temperature change; the constant is the coefficient of linear expansion α, or of volume expansion β. For a solid that expands equally in all directions, (1 + α ΔT)³ ≈ 1 + 3α ΔT, so β ≈ 3α. Material presets are single linear values from Engineering ToolBox near 25 °C (77 °F); enter your own for other grades, other temperatures or liquids. A coefficient per °F is 5 ÷ 9 of the same coefficient per K.
Your numbers, step by step
About the Thermal Expansion calculator
This thermal expansion calculator shows how much a length or a volume changes when the temperature changes. Linear expansion uses ΔL = α × L × ΔT, and volume expansion uses ΔV = β × V × ΔT, where β is about 3α for a solid that expands the same in every direction. Choose a material from a short list of coefficients taken from Engineering ToolBox, or enter your own α or β, which is the way to go for liquids, alloys and unusual temperatures. Temperatures can be in °C, K or °F, lengths in mm, cm, m, inches or feet, and volumes in cm³, litres, m³, in³, ft³ or US gallons. It helps when leaving gaps for pipes, rails and decking, fitting parts by heating or cooling, or doing physics homework. A negative answer means the part shrinks.
How to use it
- Choose “Expansion”: linear for a length or volume for a volume.
- Pick a “Material”, or choose your own and enter the “Coefficient” in millionths per degree.
- Enter the “Original length” or “Original volume” and its unit.
- Enter the “Starting temperature” and “Final temperature” and pick the “Temperature unit”.
- Read the change, the final size and the change in percent.
Worked example
A 6000 mm stainless steel 304 pipe (α = 17.3 × 10⁻⁶ per K) warms from 15 °C to 85 °C, a rise of 70 K. It grows by 17.3 × 10⁻⁶ × 6000 × 70 ≈ 7.27 mm (about 0.29 in), to 6007.27 mm. That is a change of about 0.12%.
Updated
Questions people ask
How do I calculate thermal expansion of a length?
Multiply the coefficient of linear expansion by the original length and by the temperature change: ΔL = α L ΔT. With α per K and ΔT in K or °C, ΔL comes out in the same unit as L.
Why is volume expansion about three times linear expansion?
A cube that grows by a fraction αΔT along each edge has volume (1 + αΔT)³, which is very close to 1 + 3αΔT when the change is small. That only holds for isotropic solids; wood, composites and crystals expand by different amounts in different directions.
Do I convert °F to °C before using the formula?
Only the temperature change matters, and a change of 1 °F equals 5 ÷ 9 of a kelvin. A common mistake is to add 32 when converting a difference. The calculator handles it; for converting single temperatures, use the temperature converter.
What expansion coefficient should I use for water or another liquid?
Liquids have a volume coefficient β only, and for water it changes strongly with temperature. Pick your own coefficient, choose volume β, and enter a value for your liquid near your temperatures.
How accurate is the thermal expansion result?
It uses one constant coefficient, which suits moderate temperature ranges. Over very wide ranges, near phase changes or for parts held so they cannot move, real behaviour differs. Expansion joints in buildings, pipework or bridges should follow the relevant code and an engineer's design.