🧮 Combined Gas Law Calculator

The Combined Gas Law merges Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation: P₁V₁ / T₁ = P₂V₂ / T₂. It describes how the pressure, volume, and temperature of a fixed amount of gas all relate to each other when any two of the three variables change simultaneously. If temperature is constant, it reduces to Boyle's Law. If pressure is constant, it becomes Charles's Law. If volume is constant, it simplifies to Gay-Lussac's Law.

This calculator is essential for chemistry students, HVAC engineers, meteorologists, and anyone working with gas processes where pressure, volume, and temperature all change. Enter any five of the six variables—the calculator solves for the sixth automatically. Temperature must be in Kelvin.

The calculator rearranges P₁V₁ / T₁ = P₂V₂ / T₂ to solve for whichever variable is missing. For example, if T₂ is unknown: T₂ = (P₂V₂T₁) / (P₁V₁). If P₂ is unknown: P₂ = (P₁V₁T₂) / (T₁V₂).

The table below shows a worked example: a gas starts at 1.0 atm, 2.0 L, 300 K. What happens when pressure, volume, or temperature changes?

In every case, PV/T = 0.00667 atm·L/K—the constant that defines this gas sample. The combined gas law is a stepping stone to the Ideal Gas Law (PV = nRT), which also accounts for the amount of gas.

1. Convert all temperatures to Kelvin (K = °C + 273.15).
2. Enter any five of the six values: P₁, V₁, T₁, P₂, V₂, T₂.
3. Leave the sixth field blank—that is what will be calculated.
4. Click the Calculate button.
5. Review the result and verify physical plausibility.

How is the Combined Gas Law different from the Ideal Gas Law?

The Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) applies when the amount of gas is constant. It relates two states of the same gas sample. The Ideal Gas Law (PV = nRT) is more general and includes the number of moles (n), so it can handle situations where gas is added or removed.

Do I need to use Kelvin?

Yes. Temperature appears as a ratio (T₁ and T₂ in denominators), so it must be in absolute units. Kelvin is the standard choice. Using Celsius or Fahrenheit would give incorrect results because their zero points are arbitrary.

What units should pressure and volume use?

P₁ and P₂ must share the same unit (e.g. both in atm). V₁ and V₂ must share the same unit (e.g. both in L). The specific units do not matter as long as they are consistent, because they cancel out in the ratio.

Can this calculator handle all three gas laws?

Yes. If temperature is constant (T₁ = T₂), the equation reduces to P₁V₁ = P₂V₂ (Boyle's Law). If pressure is constant (P₁ = P₂), it becomes V₁/T₁ = V₂/T₂ (Charles's Law). If volume is constant (V₁ = V₂), it simplifies to P₁/T₁ = P₂/T₂ (Gay-Lussac's Law).

What if my answer seems wrong?

First check that all temperatures are in Kelvin. Then verify that pressure and volume units are consistent within each pair. Finally, check that the result makes physical sense: increasing temperature should increase pressure or volume, and increasing pressure should decrease volume (at constant temperature).

Does this work for real gases at extreme conditions?

The Combined Gas Law is derived from the ideal gas assumption. At very high pressures (> 10 atm) or very low temperatures (near condensation), real gases deviate. For such conditions, the Van der Waals equation provides corrections for intermolecular forces and molecular volume.

Temperature must always be in Kelvin. Convert using K = °C + 273.15 before entering values. Pressure units must be consistent between P₁ and P₂, and volume units must be consistent between V₁ and V₂—but P and V can use different units from each other. The combined gas law applies to a fixed amount of gas (no leaks, no additions). If the number of moles changes, you need the full Ideal Gas Law (PV = nRT). For scenarios where only one variable changes, our specialized calculators for Boyle's Law, Charles's Law, or Gay-Lussac's Law may be simpler to use.