💨 Combined Gas Law Calculator

P₁V₁/T₁ = P₂V₂/T₂. Solve for any variable (temperatures in Kelvin).

Solve for

P₁ — Initial Pressure

V₁ — Initial Volume

T₁ — Initial Temp (K)

P₂ — Final Pressure

V₂ — Final Volume

T₂ — Final Temp (K)

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How to Use This Calculator

Choose the variable you want to find, fill in the five known values, and click Calculate. Temperatures must be in Kelvin. Pressure and volume can be in any unit, as long as both the initial and final values use the same unit.

Select what you are solving for from the dropdown. You can solve for any of the six variables: P₁, V₁, T₁, P₂, V₂, or T₂.

Enter the five known values. For temperature, always use Kelvin: convert by adding 273.15 to the Celsius value. 0°C = 273.15 K, 100°C = 373.15 K.

Use consistent units for pressure on both sides (both in atm, or both in kPa) and the same rule for volume. You do not need to convert to any particular unit as long as the ratio stays valid.

Click Calculate to get the missing variable. The units on the result match whatever unit you used for the same quantity on the other side.

Combined Gas Law Formula

P₁V₁ / T₁ = P₂V₂ / T₂ Rearranged: V₂ = P₁V₁T₂ / (T₁P₂) (T must be in Kelvin; P and V in any consistent units)

This equation comes from holding the number of moles constant and combining Boyle's Law (P and V at constant T) with Charles's Law (V and T at constant P). The ratio PV/T stays the same for a fixed amount of gas even when all three variables change simultaneously. Unlike the ideal gas law, you do not need to know n or use a specific value of R.

Worked Examples

P₁=1 atm, V₁=5 L, T₁=300 K, P₂=2 atm, T₂=600 K: find V₂5.00 L

P₁=1 atm, V₁=10 L, T₁=273 K, P₂=1 atm, T₂=546 K: find V₂20.00 L

P₁=2 atm, V₁=4 L, T₁=400 K, V₂=2 L, T₂=400 K: find P₂4.00 atm

P₁=1 atm, V₁=3 L, T₁=300 K, P₂=1.5 atm, V₂=2 L: find T₂300 K

Where This Calculation Comes Up

The combined gas law is the go-to tool when a gas sample undergoes a change in conditions and you need to find one missing value. A classic lab scenario is collecting a gas sample at room temperature and pressure, then needing to know its volume at STP (0°C, 1 atm) for comparison with a theoretical calculation. You enter the initial and final temperatures and pressures, and the law gives you the corrected volume directly.

Weather forecasting and meteorology rely on this relationship constantly. A weather balloon filled with helium at ground level (say, 1 atm and 20°C) expands as it rises to altitudes where pressure drops to 0.1 atm and temperature falls to -50°C. The combined gas law predicts the final volume, which engineers use to size the balloon correctly so it does not burst before reaching the target altitude. Similar calculations apply to gas cylinders transported in vehicles, where temperature swings from cold storage to a hot truck can noticeably change internal pressure.

Frequently Asked Questions

What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ — combines Boyle's, Charles's, and Gay-Lussac's Laws. Applies when amount of gas is constant but P, V, and T all change.

When do I use the combined vs ideal gas law?

Use combined when comparing two states of the same gas. Use ideal (PV=nRT) when you need to find moles or when absolute values are needed.

What units should I use?

Pressure in any consistent unit (atm, kPa, mmHg), volume in any consistent unit, temperature MUST be in Kelvin.

Example: A gas at 1 atm, 5 L, 300 K is heated to 600 K at 2 atm. What is V₂?

V₂ = P₁V₁T₂/(T₁P₂) = (1×5×600)/(300×2) = 5 L

What happens if temperature doubles and pressure doubles?

Volume stays the same, since V₂ = V₁×(P₁/P₂)×(T₂/T₁) = V₁×(1/2)×2 = V₁.