Combined Gas Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/8/2026
The combined gas law relates two states of the same gas without needing to know its amount of substance: (P₁V₁) ÷ T₁ = (P₂V₂) ÷ T₂. For a gas going from 100 kPa and 2 L at 300 K, to 1 L at 350 K, the new pressure is about 233.33 kPa.
Explanation
This law directly combines the three individual gas laws already published on this site — Boyle's law (pressure and volume at constant temperature), Charles's law (volume and temperature at constant pressure), and Gay-Lussac's law (pressure and temperature at constant volume) — into a single relationship valid even when all three quantities change simultaneously between two states of the same gas. Unlike the ideal gas law (PV = nRT), it never requires knowing the amount of substance n or the ideal gas constant R: these two quantities, constant for the same gas sample whose composition does not change, naturally cancel out of the calculation when comparing two states. This is why this law is particularly practical for everyday use — a diver wanting to estimate the pressure remaining in a tank after a temperature change, or the pressure of a tire warming up. Each of the three individual laws is found as a special case of this general law, by holding one of the three quantities constant between the two states: for example, if the volume does not change (V₁ = V₂), the formula simplifies exactly to Gay-Lussac's law, P₂ = P₁ × (T₂ ÷ T₁).
Example: from 100 kPa/2 L/300 K to 1 L/350 K
Inputs
Initial state: 100 kPa, 2 L, 300 K. Final state: 1 L, 350 K.
Calculation
P₂ = (100 × 2 × 350) ÷ (300 × 1) = 70,000 ÷ 300 ≈ 233.33 kPa.
Result
This gas's final pressure is about 233.33 kPa.
Frequently asked questions
Why isn't the amount of gas (number of moles) needed?
Because the combined gas law compares two states of the same gas sample, whose amount of substance does not change between the two measurements: in the full equation PV = nRT applied twice, n and R appear identically on both sides and cancel out when taking the ratio of the two states, leaving only P, V, and T.
How do you get back to Gay-Lussac's law from this formula?
By holding volume constant (V₁ = V₂ in this formula), both volumes fully cancel out, leaving P₁ ÷ T₁ = P₂ ÷ T₂ — exactly Gay-Lussac's law. This is the simplification confirmed by this calculator's second test case: at constant volume, doubling the absolute temperature exactly doubles the pressure.
Must temperatures be in Kelvin?
Yes, absolutely: this law relies on a direct proportionality with absolute temperature, which only holds in Kelvin (where 0 K corresponds to absolute zero). Using degrees Celsius directly in this formula would give a wrong result, since 0°C does not correspond to an absence of thermal energy — add 273.15 to a temperature in °C to get its value in Kelvin.