What is the volume thermal expansion formula?

ΔV = β × ΔT × V₀, where β is the volumetric thermal expansion coefficient, ΔT is the temperature change, and V₀ is the initial volume. The final volume is V = V₀ + ΔV.

How does β relate to the linear expansion coefficient α?

For isotropic solids, β ≈ 3α. Each of the three linear dimensions expands by α·ΔT; combining them gives (1 + α·ΔT)³ ≈ 1 + 3α·ΔT for small ΔT, so β = 3α. Liquids have their own measured β values.

What units does β use?

β is expressed per degree Celsius or per Kelvin (numerically equal). For solids, typical values run from ~3×10⁻⁶ /°C (Invar) to ~75×10⁻⁶ /°C (PVC). For liquids, water is ~207×10⁻⁶ /°C at 20°C and ethanol is ~1120×10⁻⁶ /°C.

Why is water unusual for thermal expansion?

Water contracts from 0°C to 4°C (negative ΔV) before expanding above 4°C. The coefficient used here (~207×10⁻⁶ /°C) is a room-temperature approximation and is not accurate near 0°C or near boiling.

Does this formula work for gases?

No. Gases expand according to the ideal gas law (PV = nRT), not the small-ΔT approximation. Use a separate gas law calculator for gaseous systems.

Volume Thermal Expansion Calculator

Calculate how much a material's volume changes when its temperature changes using the volumetric thermal expansion coefficient.

Inputs

Material

Initial Volume (V₀)

Temperature Input

T₁ (initial)

T₂ (final)

Unit

Formula

ΔV = β × ΔT × V₀

β = volumetric expansion coefficient | V₀ = initial volume

For isotropic solids: β ≈ 3α (three times the linear coefficient)

Fill in the inputs and click Calculate

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Summary

Volume thermal expansion describes how a material's volume grows or shrinks as temperature changes. For solids, the volumetric coefficient β ≈ 3α (three times the linear coefficient); liquids have their own distinct β values. This tool computes the final volume, volume change, and percentage change for any material from a built-in list or a custom coefficient.

How it works

Select a material from the list or choose "Custom" to enter your own volumetric expansion coefficient (β).
Enter the initial volume of the object in your chosen unit (m³, cm³, L, or ft³).
Enter the initial and final temperatures, or switch to direct ΔT mode.
The calculator applies ΔV = β × ΔT × V₀ and shows the volume change and new total volume.
Use the copy button to grab any result for further calculations.

Use cases

Estimate how much fuel expands in a storage tank between seasons.
Calculate the change in volume of a metal component when heated during manufacturing.
Determine expansion of a liquid coolant in an automotive cooling system.
Check overflow margins when filling tanks with temperature-sensitive liquids.
Teach or verify volumetric expansion formulas in physics and engineering courses.
Design expansion joints for pipelines carrying heated fluids.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu