Volumetric Thermal Expansion Calculator
Calculate how much the volume of a liquid or solid changes with temperature, ΔV = β·V₀·ΔT, with coefficients for water, fuel, ethanol, mercury, steel, aluminium and copper.
How it works
ΔV = β · V₀ · ΔT · V = V₀(1 + β·ΔT) · for isotropic solids β ≈ 3α · density changes as ρ = ρ₀ / (1 + β·ΔT)
Most materials take up more space when they warm because their particles vibrate further apart. Over a moderate temperature range the fractional change in volume is proportional to the temperature change; the constant of proportionality is the volumetric (cubic) expansion coefficient β. Liquids expand far more than solids, which is why fuel tanks, radiators and hot-water systems need expansion space. Coefficients are typical values near room temperature from OpenStax College Physics (Table 13.2) and engineering handbooks; water is unusual, with β rising from almost zero at 4 °C to about 210 × 10⁻⁶ /°C at 20 °C.
Worked example
50 L of gasoline (β = 950 × 10⁻⁶ /°C) warms from 20 °C to 35 °C, so ΔT = +15 °C. ΔV = 0.000950 × 50 × 15 = +0.7125 L, giving a final volume of 50.7125 L — a 1.425% increase. The density falls by 1.405%, so the same mass of fuel occupies more litres when it is warm.
Sources: OpenStax College Physics 2e — Thermal Expansion of Solids and Liquids · The Engineering ToolBox — Volumetric (cubic) expansion coefficients of liquids
Frequently asked questions
What is the difference between linear and volumetric expansion?
Linear expansion (α) is the change in one length; volumetric expansion (β) is the change in volume. For a solid that expands equally in all directions β ≈ 3α. Liquids have no fixed shape, so only β is used.
Why does water behave strangely?
Water contracts as it warms from 0 °C to 4 °C and only then expands, so its β is near zero around 4 °C and grows with temperature. The value here (207 × 10⁻⁶ /°C) is for about 20 °C.
Why does a full fuel tank overflow on a hot day?
Gasoline expands about 0.1% for every 1 °C. A 60 L tank filled with cold fuel from an underground tank can gain more than 1 L as it warms in the sun.
Does the container expand too?
Yes, but much less. The apparent expansion of a liquid in a container is (β_liquid − β_container)·V₀·ΔT; glass and steel expand roughly 30 times less than gasoline.
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Results assume the idealised textbook model stated above; real systems have losses and tolerances, so verify safety-critical values with measurements or a qualified engineer.