What is the combined gas law formula?

The combined gas law states (P₁ × V₁) / T₁ = (P₂ × V₂) / T₂, where P is absolute pressure (kPa), V is volume (L), and T is absolute temperature (K). It merges Boyle's law, Charles' law, and Gay-Lussac's law into one equation valid when the amount of gas (moles) is constant. Rearranging for any one of the six variables gives you all the other gas-law relationships as special cases.

Why must temperature be in Kelvin, not Celsius?

Gas laws are derived from kinetic-molecular theory, where temperature represents the average kinetic energy of molecules. That relationship is only proportional on an absolute (Kelvin) scale. 0 °C = 273.15 K, so a gas at 0 °C still has positive kinetic energy. Using Celsius would introduce a spurious offset and give wrong answers — for example, doubling Celsius temperature from 20 °C to 40 °C does not double the gas volume; doubling Kelvin temperature from 293 K to 586 K does. The calculator accepts Celsius but converts internally to Kelvin before every computation.

What is Boyle's law and when should I use it?

Boyle's law (P₁V₁ = P₂V₂) applies when temperature is held constant (isothermal process). Compressing a gas in a syringe with your thumb while keeping it at room temperature is a classic example. Select the Boyle's law mode when you know three of {P₁, V₁, P₂, V₂} and need the fourth.

What is the difference between Charles' law and Gay-Lussac's law?

Charles' law (V₁/T₁ = V₂/T₂) describes how volume changes with temperature at constant pressure — a balloon expands in a warm room. Gay-Lussac's law (P₁/T₁ = P₂/T₂) describes how pressure changes with temperature at constant volume — a sealed aerosol can explodes if heated because volume cannot change. Both require absolute (Kelvin) temperatures.

What is the ideal gas law and how does it relate to the combined gas law?

The ideal gas law PV = nRT extends the combined gas law by including the amount of gas n (in moles) and the universal gas constant R = 8.314 J/(mol·K). It is valid for an ideal (non-interacting) gas. The combined gas law is simply the ideal gas law applied twice — once for each state — with the nR terms cancelling, so it works for real gases under moderate conditions where n does not change.

What units does this calculator use and can I convert?

Pressures are in kilopascals (kPa). Standard atmospheric pressure is 101.325 kPa. To convert: 1 atm = 101.325 kPa; 1 bar = 100 kPa; 1 mmHg (Torr) ≈ 0.1333 kPa; 1 psi ≈ 6.895 kPa. Volumes are in litres (L). 1 m³ = 1000 L; 1 mL = 0.001 L. Temperatures default to Kelvin but the calculator accepts Celsius and converts automatically. If your textbook uses atm and mL, convert before entering or note that results scale linearly with unit choice.

Combined Gas Law Calculator

The combined gas law unifies three classical gas relationships — Boyle’s law, Charles’ law, and Gay-Lussac’s law — into a single equation that lets you predict what happens to a fixed amount of gas when pressure, volume, and temperature all change simultaneously. This calculator solves for any one of the six variables, shows full step-by-step working, and also handles the ideal gas law (PV = nRT) so you can move between single-state and two-state gas problems without switching tools.

The formula

The combined gas law is written as:

(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂

Where:

P is absolute pressure in kilopascals (kPa)
V is volume in litres (L)
T is absolute temperature in Kelvin (K = °C + 273.15)
Subscript 1 = initial state, subscript 2 = final state

The amount of gas (moles, n) is assumed constant. If n changes, use the ideal gas law PV = nRT separately for each state instead. The universal gas constant is R = 8.314 J/(mol·K).

The three sub-laws follow directly by holding one variable constant:

Law	Fixed	Equation
Boyle’s	Temperature	P₁V₁ = P₂V₂
Charles’	Pressure	V₁/T₁ = V₂/T₂
Gay-Lussac’s	Volume	P₁/T₁ = P₂/T₂

How it works

Select the gas law mode and choose which variable to find. The calculator hides that field and asks for all remaining known values. For temperatures it accepts either Kelvin or Celsius — select your preferred unit and it converts to Kelvin automatically before computing. Pressures must be in kPa and volumes in litres; if your data is in atm, bar, mmHg, or cm³ use the conversion factors in the FAQ before entering. Once all inputs are filled the answer updates in real time. Click Show working to expand a table of the rearranged formula and the substituted numbers at each step.

Worked example

A gas sample initially has pressure P₁ = 150.0 kPa, volume V₁ = 3.0 L, and temperature T₁ = 300 K. The gas is then compressed and cooled to P₂ = 250.0 kPa and T₂ = 240 K. What is the new volume V₂?

Using the combined gas law rearranged for V₂:

V₂ = (P₁ × V₁ × T₂) / (T₁ × P₂)

Substituting:

V₂ = (150.0 × 3.0 × 240) / (300 × 250.0)

V₂ = 108 000 / 75 000 = 1.44 L

The gas volume dropped from 3.0 L to 1.44 L — the pressure increase more than outweighed the volume expansion that would result from cooling alone.

Formula note

Temperature conversions: K = °C + 273.15. Room temperature ≈ 293 K (20 °C). Standard temperature and pressure (STP) is defined as 273.15 K (0 °C) and 100 kPa. Standard ambient temperature and pressure (SATP) is 298.15 K (25 °C) and 100 kPa. One atmosphere = 101.325 kPa. For the ideal gas law mode the constant R = 8.314 J/(mol·K) is used; n is the number of moles of gas. Every calculation runs client-side — no data is sent to any server.