Gas Laws Calculator
Boyle’s, Charles’s, and the combined gas law — solve for the missing variable.
Temperatures must be in kelvin (K = °C + 273.15).
The combined gas law relates two states of a fixed amount of gas: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, with temperature in kelvin. Boyle’s law is the constant-temperature case: 1 atm × 2 L = 2 atm × V₂, so V₂ = (1 × 2) ÷ 2 = 1 L. Pick a law, enter the knowns, and solve for the blank.
Boyle, Charles, and the combined gas law
For a fixed amount of gas, pressure, volume, and absolute temperature are linked. Hold temperature constant and pressure times volume stays constant (Boyle’s law). Hold pressure constant and volume is proportional to temperature (Charles’s law). The combined gas law merges both, letting you compare any two states by setting P₁V₁ ÷ T₁ equal to P₂V₂ ÷ T₂.
Combined gas law — temperatures T₁ and T₂ must be in kelvin (K = °C + 273.15)
Worked example
A gas at 1 atm fills 2 L. The temperature is held constant while it is compressed to 2 atm. Find the new volume using Boyle’s law.
- 1 Convert temperatures to kelvin. Add 273.15 to any Celsius reading: K = °C + 273.15. The law is invalid with Celsius or Fahrenheit.
- 2 Pick the law that matches what is held constant. Constant temperature → Boyle (P₁V₁ = P₂V₂). Constant pressure → Charles (V₁ ÷ T₁ = V₂ ÷ T₂). Both changing → combined.
- 3 Substitute and solve for the unknown. For Boyle: V₂ = (P₁ × V₁) ÷ P₂ = (1 × 2) ÷ 2 = 1 L. Halving the volume doubles the pressure.
The three gas laws
Each law fixes the quantities not shown; all temperatures are absolute (kelvin).
| Law | Held constant | Formula |
|---|---|---|
| Boyle’s law | Temperature, amount | P₁V₁ = P₂V₂ |
| Charles’s law | Pressure, amount | V₁ ÷ T₁ = V₂ ÷ T₂ |
| Combined gas law | Amount only | P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ |
Always use kelvin — and how this ties to PV = nRT
Temperature must be absolute. Charles’s and the combined law multiply and divide by T, so a Celsius value (which can be zero or negative) gives nonsense. Convert first with K = °C + 273.15; this tool guards against T = 0 or negative.
These are special cases of the ideal gas law. Starting from PV = nRT, the quantity PV ÷ T equals nR — a constant for a fixed amount of gas. So PV ÷ T is the same in both states, which is exactly P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂. Boyle and Charles drop out by holding T or P fixed. Use the combined law to compare two states; use PV = nRT when you need an absolute value or the number of moles.