Combined Gas Law Calculator

What is a combined gas law calculator?

A combined gas law calculator solves the equation P₁V₁/T₁ = P₂V₂/T₂ for any one of its six variables when you know the other five. It relates the pressure, volume and absolute temperature of a fixed amount of gas as it moves between two states. Chemistry and physics students, lab technicians and engineers use it to predict how a gas responds when conditions change.

What is the P₁V₁/T₁ = P₂V₂/T₂ formula?

The combined gas law states that for a fixed mass of gas, the quantity pressure × volume ÷ absolute temperature stays constant, so P₁V₁ / T₁ = P₂V₂ / T₂. Each symbol stands for a measurable property in two states — the initial state (subscript 1) and the final state (subscript 2):

• P₁, P₂ — initial and final pressure, in any consistent unit (atm, kPa, mmHg, psi).
• V₁, V₂ — initial and final volume, in any consistent unit (L, mL, m³).
• T₁, T₂ — initial and final temperature, which must be in Kelvin (K = °C + 273.15) and greater than 0.

Pressure and volume can use any units you like, provided both states use the same unit. Temperature is the strict one: it has to be absolute (Kelvin) because the law depends on ratios of temperature, and an absolute scale has no negative values or arbitrary zero point.

To solve for a single unknown, the calculator rearranges the formula algebraically. The six rearrangements are:

Solve for	Rearranged formula
P₂	P₂ = (P₁·V₁·T₂) / (T₁·V₂)
V₂	V₂ = (P₁·V₁·T₂) / (T₁·P₂)
T₂	T₂ = (P₂·V₂·T₁) / (P₁·V₁)
P₁	P₁ = (P₂·V₂·T₁) / (T₂·V₁)
V₁	V₁ = (P₂·V₂·T₁) / (T₂·P₁)
T₁	T₁ = (P₁·V₁·T₂) / (P₂·V₂)

The result is reported to six significant figures.

Worked examples

Each example below uses only the rearrangements above, so you can reproduce every answer by entering the same five values into the calculator.

Example 1 — solve for final temperature (T₂)

A gas starts at P₁ = 1 atm, V₁ = 2 L, T₁ = 273 K. It is then compressed to P₂ = 2 atm and V₂ = 1 L. Find T₂.

T₂ = (P₂·V₂·T₁) / (P₁·V₁) = (2 × 1 × 273) / (1 × 2) = 546 / 2 = 273 K

The temperature is unchanged: doubling the pressure exactly offsets halving the volume.

Example 2 — solve for final volume (V₂)

Using the same starting state (P₁ = 1 atm, V₁ = 2 L, T₁ = 273 K), the gas reaches P₂ = 2 atm at T₂ = 273 K. Find V₂.

V₂ = (P₁·V₁·T₂) / (T₁·P₂) = (1 × 2 × 273) / (273 × 2) = 546 / 546 = 1 L

Doubling the pressure at constant temperature halves the volume — a direct demonstration of Boyle’s law inside the combined formula.

Example 3 — Boyle’s law case (temperature constant)

A gas at P₁ = 1 atm, V₁ = 4 L, T₁ = 300 K is squeezed to P₂ = 2 atm while the temperature is held at T₂ = 300 K. Find V₂.

V₂ = (P₁·V₁·T₂) / (T₁·P₂) = (1 × 4 × 300) / (300 × 2) = 1200 / 600 = 2 L

Because T₁ = T₂, the temperature terms cancel and you are left with Boyle’s law, P₁V₁ = P₂V₂.

Example 4 — Gay-Lussac case (volume constant)

A sealed rigid container holds gas at P₁ = 1 atm, V₁ = 1 L, T₁ = 300 K. It is heated to T₂ = 450 K with V₂ = 1 L (the rigid volume does not change). Find P₂.

P₂ = (P₁·V₁·T₂) / (T₁·V₂) = (1 × 1 × 450) / (300 × 1) = 450 / 300 = 1.5 atm

With volume fixed, pressure rises in step with absolute temperature, which is Gay-Lussac’s law.

Which gas law is each special case?

The combined gas law contains three simpler laws. Whenever one variable is held constant, its terms cancel and the formula collapses into a classic law you may already know.

Held constant	Reduced relationship	Named law	What it describes
Temperature (T)	P₁V₁ = P₂V₂	Boyle’s law	Pressure and volume are inversely related
Pressure (P)	V₁/T₁ = V₂/T₂	Charles’s law	Volume is proportional to temperature
Volume (V)	P₁/T₁ = P₂/T₂	Gay-Lussac’s law	Pressure is proportional to temperature
— (amount added)	PV = nRT	Ideal gas law	Single state with amount n and constant R

Common uses

The combined gas law appears anywhere a fixed quantity of gas changes conditions:

• Chemistry and physics homework — converting a gas sample from lab conditions to standard temperature and pressure (STP).
• Exam and AP problems — solving for an unknown P, V or T when the other five values are given.
• Laboratory work — predicting how a sealed sample’s pressure shifts as the room or a water bath warms.
• Engineering estimates — sizing or checking pressure in tanks, scuba cylinders and pneumatic systems as temperature changes.
• Weather and aviation — understanding how a weather balloon expands as it rises into colder, lower-pressure air.

Tips and common mistakes

• Always convert temperature to Kelvin first. This is the number-one error. Use K = °C + 273.15, so 25°C is 298.15 K. Plugging in Celsius gives a wrong answer, and 0°C entered as 0 would divide by zero.
• Keep units consistent between states. P₁ and P₂ must share a unit; V₁ and V₂ must share a unit. The calculator does not convert atm to kPa for you — it assumes you already matched them.
• You do not need SI units. Because the law uses ratios, atm and litres work fine as long as both states use the same unit. The unit of your answer matches the unit you entered for the same variable.
• Watch the placement in the fraction. When solving for P₂ or V₂, the unknown’s partner sits in the denominator. Mixing up numerator and denominator flips the result.
• Temperature must be greater than 0 K. A non-positive Kelvin value is unphysical, so the tool requires every temperature above absolute zero.
• Six significant figures is precision, not certainty. The display shows six sig figs, but your answer is only as accurate as the measurements you typed in.

Limitations and accuracy

The combined gas law assumes an ideal gas and a fixed amount of gas (no leaks, no chemical reaction, and the same number of molecules in both states). Real gases deviate from ideal behaviour at very high pressures and very low temperatures, where molecular size and intermolecular forces start to matter; near those extremes the result is an approximation. The law also says nothing about how much gas is present — if the amount changes, you need the ideal gas law, PV = nRT, instead. Treat this calculator as an educational and estimation tool: the arithmetic is exact for the inputs given, but match its assumptions to your real-world problem before relying on a number.

For related calculations, try the density calculator for mass and volume, the kinetic energy calculator for the energy of moving particles, or convert lab temperatures with the Celsius to Fahrenheit converter — and browse more in the chemistry and physics category.