What is the combined gas law?

The combined gas law unifies Boyle's, Charles', and Gay-Lussac's laws into one equation: P₁V₁/T₁ = P₂V₂/T₂. It describes how the pressure, volume, and temperature of a fixed mass of gas relate when all three can vary.

When should I use the combined gas law instead of Charles' law?

Use the combined gas law whenever both temperature AND pressure change. Use Charles' law only when pressure stays constant; use Boyle's law only when temperature stays constant.

Do I need to convert temperature to Kelvin?

Yes. Temperatures must be in Kelvin because the law depends on absolute temperature. Convert °C by adding 273.15, and °F by K = (°F − 32) × 5/9 + 273.15.

Does the combined gas law assume a constant amount of gas?

Yes. The amount of gas (number of moles n) must be constant. If n changes, you need the full Ideal Gas Law PV = nRT.

What units should pressure and volume be in?

Any consistent units. The calculator handles Pa, kPa, atm, mmHg, psi for pressure and L, mL, m³, ft³ for volume, converting internally.

How is the combined gas law derived?

Combine Boyle (PV = const at fixed T), Charles (V/T = const at fixed P), and Gay-Lussac (P/T = const at fixed V). The product gives PV/T = const, hence P₁V₁/T₁ = P₂V₂/T₂.

Does the combined gas law work for any gas?

Yes, as a close approximation for real gases such as air, nitrogen, and oxygen at moderate pressure and temperature. It is exact only for an ideal gas; at high pressure or near condensation, use the Van der Waals equation instead.

Combined Gas Law Calculator

Solve P₁V₁/T₁ = P₂V₂/T₂ by entering any 5 of the 6 values. The calculator computes the missing one in real time.

Combined Gas Law Calculator

Enter any 5 of 6 values, and the missing one is computed.

P₁

V₁

T₁

P₂

V₂ (solving for this)

T₂

V₂

1.167 L

V₂ = P₁V₁T₂ / (T₁P₂) = 1.167 L

How the Combined Gas Law Unifies Three Earlier Laws

The combined gas law collapses three separate single-variable laws into one general expression. Boyle's law (P₁V₁ = P₂V₂ at constant T) captures the pressure-volume relationship. Charles' law (V₁/T₁ = V₂/T₂ at constant P) captures the volume-temperature relationship. Gay-Lussac's law (P₁/T₁ = P₂/T₂ at constant V) captures the pressure-temperature relationship. Multiplying their proportionalities together gives PV/T = constant, which leads directly to P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas.

This single equation is the workhorse of practical gas-law problems because real processes rarely hold one variable perfectly constant. Compressing a gas while it cools, heating a sealed-but-flexible container, or analysing a weather balloon's ascent. All of these involve simultaneous changes in P, V, and T, and the combined gas law handles them directly.

Combined Gas Law Formula and Rearrangements

The formula is P₁V₁/T₁ = P₂V₂/T₂. Rearranged for each variable:

P₂ = P₁V₁T₂ / (T₁V₂)
V₂ = P₁V₁T₂ / (T₁P₂)
T₂ = P₂V₂T₁ / (P₁V₁)
P₁ = P₂V₂T₁ / (T₂V₁)
V₁ = P₂V₂T₁ / (T₂P₁)
T₁ = P₁V₁T₂ / (P₂V₂)

Temperatures must be expressed in Kelvin. Pressure and volume can be in any units as long as the two pressures share a unit and the two volumes share a unit. This calculator normalises units automatically.

Worked Example 1: Weather Balloon

A weather balloon contains 4.0 L of helium at 1.0 atm and 295 K at ground level. It rises to where the pressure is 0.30 atm and the temperature is 250 K. What is the new volume?

V₂ = P₁V₁T₂ / (T₁P₂) = (1.0 × 4.0 × 250) / (295 × 0.30) = 11.3 L.

The balloon nearly triples in size, primarily because the surrounding pressure dropped sharply, partially offset by the cooler temperature.

Worked Example 2: Compressed Air in a Heated Cylinder

A cylinder of air at 100 kPa and 300 K is compressed to 250 kPa while the temperature rises to 400 K. The starting volume is 2.0 L. Find the final volume.

V₂ = (100 × 2.0 × 400) / (300 × 250) = 1.07 L. The gas occupies roughly half its starting volume despite being hotter, because the pressure increase dominates.

When to Use Combined Gas Law vs Ideal Gas Law

Use the combined gas law to compare two states of the same fixed amount of gas. Use the Ideal Gas Law (PV = nRT) when you need the absolute pressure, volume, temperature, or moles at a single state, or when the amount of gas is changing. The combined gas law is a ratio of two states; the ideal gas law is the underlying equation that both states satisfy. Because moles and the gas constant (R = 8.314 J/(mol·K)) cancel out of the ratio, the combined gas law works without ever needing to know how much gas is present, which is why it is often the fastest route to an answer.

Combined Gas Law Symbols and Units

Symbol	Meaning	Common units
P₁, P₂	Initial and final pressure	Pa, kPa, atm, mmHg, psi
V₁, V₂	Initial and final volume	L, mL, m³
T₁, T₂	Initial and final temperature	Kelvin (K)

Pick any pressure unit and any volume unit you like, as long as each one stays the same between state 1 and state 2. Temperature is the one variable that has no flexibility: it must be Kelvin on both sides of the equation, because the law depends on absolute temperature, not on the size of a degree.

Related Laws

See the individual laws this one unifies: Charles' law (isobaric, constant pressure), Boyle's law (isothermal, constant temperature), and Gay-Lussac's law (isochoric, constant volume). The temperature converter and volume converter handle any unit conversion these problems need.