Liquid Thermal Expansion Calculator (Volumetric)
By Santaji GadepatilinUpdated November 2, 2026
Liquids expand far more than solids when heated, which is why fuel tanks, hot-water systems and closed pipelines need expansion space or thermal relief valves. This liquid thermal expansion calculator applies ΔV = β V₀ ΔT to find the volume change, the final volume and the percentage increase.
How to use the liquid thermal expansion calculator
Enter the liquid’s volumetric expansion coefficient β in units of 10⁻⁶ per kelvin, the initial volume and the initial and final temperatures. The calculator returns the volume increase, the final volume and the percentage change. A negative result means the liquid contracts on cooling.
Volumetric expansion formula
ΔV = β × V0 × (T2 − T1) · V1 = V0 + ΔV
Example
A tank is filled with 1,000 L of petrol at 15 °C, which then warms to 35 °C in the sun (β = 950 × 10⁻⁶/K):
- ΔT = 35 − 15 = 20 K
- ΔV = 950 × 10⁻⁶ × 1000 × 20 = 19.0 L
- Final volume = 1,019 L, an increase of 1.9%
Expansion coefficients and volume change per 1,000 L
| Liquid | β (×10⁻⁶/K, near 20 °C) | ΔT = 10 K | ΔT = 20 K | ΔT = 40 K |
|---|---|---|---|---|
| Water (at 20 °C) | 207 | 2.07 L | 4.14 L | 8.28 L |
| Mercury | 181 | 1.81 L | 3.62 L | 7.24 L |
| Glycerine | 505 | 5.05 L | 10.10 L | 20.20 L |
| Petrol (gasoline) | 950 | 9.50 L | 19.00 L | 38.00 L |
| Kerosene / jet fuel | 990 | 9.90 L | 19.80 L | 39.60 L |
| Ethanol | 1090 | 10.90 L | 21.80 L | 43.60 L |
| Acetone | 1430 | 14.30 L | 28.60 L | 57.20 L |
Coefficients are typical values near room temperature; they vary with temperature and composition.
Why it matters
- Blocked-in liquid: a full, closed pipe that warms up builds pressure very quickly because liquids are nearly incompressible — fit a thermal relief valve.
- Tank ullage: leave enough free space for the expansion over the full storage temperature range.
- Custody transfer: fuel volumes are corrected to 15 °C (or 60 °F) using expansion tables.
- For solids (pipes, rails), use the linear thermal expansion calculator.
Frequently asked questions
What is the formula for thermal expansion of a liquid?
ΔV = β × V₀ × ΔT, where β is the volumetric expansion coefficient (per K), V₀ the initial volume and ΔT the temperature rise. The final volume is V₀ (1 + β ΔT).
How much does petrol expand when it warms up?
About 0.095% per °C. 1,000 L delivered at 15 °C becomes about 1,019 L at 35 °C, which is why fuel is traded at a reference temperature of 15 °C.
Why does water expand differently?
Water's β changes strongly with temperature — it is zero at 4 °C (maximum density), about 207 × 10⁻⁶/K at 20 °C and about 750 × 10⁻⁶/K near 100 °C. For large temperature changes use densities from a steam table instead of a single β.
Does the container expansion matter?
Yes. A steel tank's volume grows by about 3α ≈ 36 × 10⁻⁶ per K, so the apparent expansion of the liquid is β − 3α. For most liquids this is a small correction.