Combined Gas Law Calculator (Boyle, Charles, Gay-Lussac)

Understanding the combined gas law calculator — concept and principle

The combined gas law predicts how a fixed amount of gas responds when two of its three state variables change at once. You give the starting pressure, volume and temperature, plus the new pressure and new temperature, and the calculator returns the new volume. Typical uses are scuba and compressed-air problems, weather balloons, syringes and piston questions in physics and chemistry classes.

Double pressure halves the gas; the warming (in kelvin) adds back about 10%, giving 5.51 L.

How it is calculated

The law states P₁V₁ / T₁ = P₂V₂ / T₂, so the new volume is V₂ = V₁ × (P₁ / P₂) × (T₂ / T₁).

P₁, P₂: initial and final pressure in kPa (any unit works as long as both use the same one, and both are absolute pressures).
V₁: initial volume in litres; V₂ comes out in the same unit.
T₁, T₂: temperatures entered in °C and converted to kelvin by adding 273.15.

The principle

The combined law is the ideal gas law PV = nRT with the amount n held constant: PV / T equals nR, which does not change. It therefore contains three classic special cases. With T fixed it reduces to Boyle's law (P₁V₁ = P₂V₂), with P fixed to Charles's law (V₁/T₁ = V₂/T₂), and with V fixed to Gay-Lussac's law (P₁/T₁ = P₂/T₂). Writing the answer as V₁ × (P₁/P₂) × (T₂/T₁) makes the logic visible: the pressure ratio squeezes or expands the gas, and the temperature ratio corrects for heating or cooling.

Worked example

Inputs: P₁ = 100 kPa, V₁ = 10 L, T₁ = 20 °C, P₂ = 200 kPa, T₂ = 50 °C.
Convert temperatures: T₁ = 293.15 K, T₂ = 323.15 K.
Pressure factor: 100 / 200 = 0.5, so doubling the pressure alone would give 5 L.
Temperature factor: 323.15 / 293.15 = 1.10234.
V₂ = 10 × 0.5 × 1.10234 = 5.511683439 L.

Each point is the calculator re-run with only “P₂ (kPa)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

P₂ (kPa)	V₂ (L)
50	22.04673375
100	11.02336688
150	7.348911251
200	5.511683439
250	4.409346751
300	3.674455626
400	2.755841719

How to read the result

Pressure and volume pull in opposite directions: doubling P halves V. Temperature works in the same direction as volume, but only through kelvin: going from 20 °C to 50 °C is not a 2.5-fold change but about 10%. If V₂ is bigger than V₁ the gas expanded, which happens when the temperature rise outweighs the pressure rise. A quick sanity check is to estimate each factor separately, as in step 3, before trusting the final figure.

Common mistakes

Using °C directly in the ratio; 50/20 = 2.5 would overstate the effect fourfold.
Using gauge pressure; a tyre at "200 kPa" on a gauge is about 300 kPa absolute.
Applying the law when gas leaks in or out, so the amount is not constant.

Keep in mind: The result assumes ideal-gas behaviour and a sealed, constant amount of gas. At high pressures or near condensation (for example, humid air cooling to its dew point) real gases deviate, and the formula no longer holds exactly.

Frequently asked questions

Can I use bar, atm or psi instead of kPa?

Yes. Only the ratio P₁/P₂ enters, so any pressure unit works if both values use it and both are absolute.

How do I find the new pressure instead of the volume?

Rearrange to P₂ = P₁ × (V₁/V₂) × (T₂/T₁). The same ratios apply in a different order.

Why must temperature be in kelvin?

Gas volume is proportional to absolute temperature, which starts from absolute zero. The Celsius scale has an arbitrary zero, so its ratios have no physical meaning.

Sources: P. Atkins and J. de Paula, Atkins' Physical Chemistry, Oxford University Press · OpenStax, Chemistry 2e, Chapter 9 "Gases", Rice University

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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