Boyle's Law Calculator
Boyle’s law describes how the volume of a fixed amount of gas changes when you change its pressure at constant temperature: P₁V₁ = P₂V₂. Squeeze the gas harder and it shrinks; ease off and it expands, with pressure and volume always inversely proportional. This calculator solves for the final volume V₂ — enter the initial pressure P₁ and volume V₁, then the new pressure P₂, and the result updates instantly. It is built for chemistry homework, physics labs, scuba and diving estimates, and quick engineering sanity checks where temperature stays put.
How to use the Boyle's law calculator
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1
Enter the initial state
Type the starting pressure P₁ and volume V₁ in any consistent units you like.
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2
Enter the final pressure
Add the new pressure P₂ in the same pressure unit you used for P₁.
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3
Read the final volume
The tool computes V₂ = (P₁ · V₁) / P₂ and shows it next to all your inputs.
The Boyle's law formula explained
Boyle’s law states that, at constant temperature, the pressure of a fixed mass of an ideal gas is inversely proportional to its volume. In other words, the product PV stays constant:
P₁ · V₁ = P₂ · V₂
Rearranging to solve for the final volume gives the formula this calculator uses:
V₂ = (P₁ · V₁) / P₂
Pressure and volume can be in any units you like, as long as you keep them consistent between the initial and final state — the ratio P₁/P₂ cancels the pressure units, so V₂ comes out in the same unit as V₁. The only firm requirement is that the temperature and the amount of gas (the number of moles, n) do not change.
Worked example
A syringe holds 2 L of air at 1 atm. You push the plunger until the pressure rises to 2 atm, keeping the temperature steady. What is the new volume?
V₂ = (1 × 2) / 2 = 1 L
Doubling the pressure halves the volume — the classic inverse relationship. Because P × V is conserved, 1 atm × 2 L = 2 atm × 1 L = 2 in both states.
Quick reference
| Quantity | Symbol | Note |
|---|---|---|
| Initial pressure | P₁ | Any pressure unit |
| Initial volume | V₁ | Any volume unit |
| Final pressure | P₂ | Same unit as P₁ |
| Final volume | V₂ | Same unit as V₁ |
Common pitfalls
- Forgetting temperature must be constant. Boyle’s law only holds at fixed temperature. If the gas heats or cools, switch to the combined gas law P₁V₁/T₁ = P₂V₂/T₂ instead.
- Mixing pressure units. If P₁ is in atm, P₂ must also be in atm; do not mix atm with kPa or psi or the ratio will be wrong.
- Treating gauge pressure as absolute. Convert gauge pressure to absolute (add atmospheric pressure ≈ 1 atm) before using it.
- Letting gas escape or be added. The law assumes a sealed, fixed amount of gas (constant n). If moles change, use the full ideal gas law PV = nRT.
Frequently Asked Questions
Boyle’s law states that, at constant temperature, the pressure and volume of a fixed amount of ideal gas are inversely proportional: P₁V₁ = P₂V₂. As pressure goes up, volume goes down by the same factor, so the product PV stays constant.
No. You can use atm, kPa, psi, litres, mL, m³ or any unit, as long as P₁ and P₂ share a pressure unit and V₁ and V₂ share a volume unit. The pressure ratio cancels, so V₂ comes out in the same unit as V₁.
Boyle’s law isolates the pressure–volume relationship by holding temperature fixed (an isothermal process). If the temperature changes, both volume and pressure are affected, so you need the combined gas law P₁V₁/T₁ = P₂V₂/T₂ with temperatures in kelvin.
No. The calculation runs in your browser and the numbers are never sent to a server or saved. Nothing you enter is uploaded, logged or shared.
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