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Combined Gas Calculator | Final pressure from P, V & T

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Solve combined gas law problems — final pressure, volume or temperature — from the other five values, with temperatures converted to kelvin automatically. The P₁V₁/T₁ = P₂V₂/T₂ relationship is applied with every step shown.

Last updated: June 2026 · Free · No sign-up required

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What the Combined Gas Calculator does

Under the hood, this calculator applies P₂ = P₁ × V₁ × T₂ ÷ (T₁ × V₂), temperatures in kelvin, so the combined gas law calculator result you see is genuine math, not a lookup table.

If you are new to combined gas law calculator, start with the worked example in the methodology section below — it walks the formula end-to-end with real numbers — then use the quick-reference table for common scenarios.

From our guides

Quick reference

Held constantLawRelationship
TemperatureBoyleP₁V₁ = P₂V₂
PressureCharlesV₁÷T₁ = V₂÷T₂
VolumeGay-LussacP₁÷T₁ = P₂÷T₂
NothingCombinedP₁V₁÷T₁ = P₂V₂÷T₂

info Combined Gas Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

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info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

ChangeEffect on P₂
Volume halvedPressure doubles (T fixed)
Temperature upPressure rises (V fixed)
Both V↓ and T↑Effects multiply

lightbulb Worked example — a weather balloon rising to altitude

A weather balloon is filled at ground level with 500 L of helium at 101 kPa and 20 °C. It rises to an altitude where the outside temperature is −30 °C and the ambient pressure is 25 kPa. Convert to kelvin: T₁ = 293.15 K, T₂ = 243.15 K.

Result: V₂ = P₁V₁T₂ ÷ (T₁P₂) = (101 × 500 × 243.15) ÷ (293.15 × 25) = 12,279,075 ÷ 7,328.75 = 1,675 L.

What this means: The balloon expands to about 3.35 times its ground volume. The pressure drop (to roughly a quarter) dominates over the cooling (only a 17% drop in absolute temperature), which is why weather balloons swell so dramatically as they climb — and why they are only partly filled at launch.

Formula & methodology

Formula: P₂ = P₁ × V₁ × T₂ ÷ (T₁ × V₂), temperatures in kelvin

How the combined gas law is solved

The combined gas law P₁V₁/T₁ = P₂V₂/T₂ describes a fixed amount of gas moving between two states. Temperatures must be absolute, so any °C input is converted with K = °C + 273.15 before the calculation.

  • Record the initial pressure, volume and absolute temperature.
  • Record the final values, leaving the unknown blank.
  • Rearrange to isolate the unknown — for final pressure: P₂ = P₁V₁T₂ ÷ (T₁V₂).
  • Cross-check by substituting the answer back: P₁V₁/T₁ should equal P₂V₂/T₂.

Special cases: if temperature is constant, the law reduces to Boyle’s law (P₁V₁ = P₂V₂); if pressure is constant, to Charles’s law (V₁/T₁ = V₂/T₂). Example: 1 atm, 2 L, 300 K compressed to 1 L at 350 K → P₂ = (1 × 2 × 350) ÷ (300 × 1) = 2.33 atm.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the combined gas law?
It combines Boyle's, Charles's, and Gay-Lussac's laws into one relationship for a fixed amount of gas: P₁V₁/T₁ = P₂V₂/T₂. Solve for the final pressure with P₂ = P₁ × V₁ × T₂ ÷ (T₁ × V₂), always using temperatures in kelvin. For example, compressing a gas to half its volume while doubling its temperature quadruples the pressure.
Why must temperature be in kelvin?
The Combined Gas Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates combined gas law using P₂ = P₁ × V₁ × T₂ ÷ (T₁ × V₂), temperatures in kelvin, right in your browser. There is no limit on usage, and it works on any device.
What units do pressure and volume need?
The Combined Gas Calculator is a free online tool that calculates combined gas law using p₂ = p₁ × v₁ × t₂ ÷ (t₁ × v₂), temperatures in kelvin, right in your browser. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
How is this different from the ideal gas law?
The combined gas law P₁V₁/T₁ = P₂V₂/T₂ describes how a FIXED amount of gas changes between two states, and it is a special case of the ideal gas law PV = nRT with n and R constant. The ideal gas law is more general — it also solves for the amount of gas or absolute state variables. The combined law is the practical tool for compression and expansion problems.
What if my gas amount changes?
The combined gas law assumes a constant amount of gas; if gas is added or removed, you must include the mole count using the full ideal gas law PV = nRT. When the amount changes, compare states with P₁V₁/(n₁T₁) = P₂V₂/(n₂T₂). The calculator flags this assumption and reminds you to use the ideal gas law for open systems.
What happens to the pressure if I compress a gas AND heat it?
Both effects multiply: halving the volume doubles the pressure, and raising the absolute temperature raises it further by the temperature ratio. Compressing 2 L at 1 atm and 300 K down to 1 L at 350 K gives P₂ = 1 × 2 × 350 ÷ (300 × 1) = 2.33 atm — more than Boyle’s law alone would predict, because the heating contributes its own factor.
Can pressure and volume use different units in the same calculation?
They can, because the units cancel in the ratio — but pressure must use the same unit on both sides, and volume must use the same unit on both sides. Mixing atm with kPa between P₁ and P₂, or litres with millilitres between V₁ and V₂, breaks the ratio. Temperature is the exception: it must be kelvin regardless.
Why does the answer change so much when I forget to convert °C to kelvin?
Because the law depends on the absolute temperature ratio. Heating from 20 °C to 40 °C looks like a doubling in Celsius, but in kelvin it is 293.15 → 313.15, only a 6.8% rise — so pressure rises 6.8%, not 100%. Forgetting the conversion is the single most common error in gas-law problems.
Does the combined gas law work if gas leaks out during the change?
No — it assumes a fixed amount of gas, which is why there is no mole term. If gas is added or vented, use the full ideal gas law PV = nRT with the mole counts included, comparing P₁V₁/(n₁T₁) = P₂V₂/(n₂T₂). A leaky tyre cooling overnight needs the n terms to get the pressure right.

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