Boyle's Law Calculator

About the Boyle's Law Calculator

Squeeze a gas into a smaller space and its pressure rises; give it more room and the pressure falls. Boyle's law makes that relationship exact: for a fixed amount of gas at a constant temperature, pressure and volume are inversely proportional, so their product stays the same. Halve the volume and the pressure doubles; triple the volume and the pressure drops to a third. It explains how syringes, bicycle pumps, lungs and scuba equipment work, and it was one of the first physical laws ever written down as an equation.

This Boyle's law calculator solves P₁V₁ = P₂V₂ for whichever value you need: the final pressure, the final volume, or either starting value. You can work in atmospheres, kilopascals, bar, psi, millimetres of mercury or pascals, and in litres, millilitres, cubic metres or cubic feet. It shows how much the gas was compressed or expanded and checks that the two products match.

How to Use the Boyle's Law Calculator

Choose which value to find: P₂, V₂, P₁ or V₁.

Enter the three values you know.

Choose the pressure unit and volume unit. Both pressures must use the same unit, and both volumes must use the same unit; the calculator does not need them converted to SI because the units cancel.

The Formula

  P₁ × V₁ = P₂ × V₂

  P₂ = P₁V₁ ÷ V₂        V₂ = P₁V₁ ÷ P₂
  P₁ = P₂V₂ ÷ V₁        V₁ = P₂V₂ ÷ P₁

Step-by-Step Examples

Compressing air. Ten litres of air at 1 atm are squeezed into 2.5 litres.

  P₂ = 1 × 10 ÷ 2.5 = 4 atm

The volume is four times smaller, so the pressure is four times higher.

Raising the pressure. Six litres of gas at 100 kPa are put under 150 kPa.

  V₂ = 100 × 6 ÷ 150 = 4 L

Diving. At 20 metres of seawater the absolute pressure is about 3 atm, so 12 litres of air taken from the surface at 1 atm shrinks to 12 × 1 ÷ 3 = 4 litres.

Why Pressure and Volume Are Linked

Gas pressure comes from molecules hitting the walls of their container. If the same molecules are crowded into half the space, each area of wall is hit twice as often, so the pressure doubles. Temperature sets how fast the molecules move; as long as it stays the same, the only thing that changes the rate of collisions is how closely the molecules are packed. That simple picture, part of the kinetic theory of gases, is why the product of pressure and volume stays constant.

Boyle's Law in Everyday Life

Breathing relies on it. When the diaphragm moves down, the chest cavity gets bigger, the pressure in the lungs falls slightly below the air outside, and air flows in. Raising the diaphragm again shrinks the lungs, raises the pressure and pushes the air out. Syringes work the same way: pulling the plunger increases the volume, lowers the pressure and draws liquid in. A sealed bag of crisps swells on an aeroplane because the cabin pressure at altitude is lower than at the ground, so the air inside expands.

Scuba Diving and Boyle's Law

Divers learn Boyle's law early, because pressure changes fastest near the surface. Water adds about one atmosphere of pressure every ten metres, so the absolute pressure doubles between the surface and ten metres, and air in the lungs, ears and mask shrinks to half its volume. On the way up the reverse happens: air expands as the pressure falls. That is why divers must never hold their breath while ascending — the expanding air can damage the lungs — and why they equalise their ears and masks on the way down.

Keeping Temperature Constant

Boyle's law only holds when the temperature does not change. Pumping up a bicycle tyre quickly makes the pump warm, because compressing a gas does work on it and heats it up. While the gas is hot, its pressure is higher than Boyle's law predicts. Once it cools back to the starting temperature, the law applies again. Scientists call a slow, constant-temperature change isothermal. When temperature changes too, use the combined gas law or the ideal gas law instead.

A Brief History

Robert Boyle, an Irish-born scientist working in England, published the law in 1662 after experiments with a J-shaped glass tube. He trapped air in the sealed short end and poured mercury into the long, open end. Each time he doubled the height of mercury — and so the pressure — the trapped air shrank to half its volume. His assistant, Robert Hooke, built the air pump that made many of these experiments possible, and in France the same law is often credited to Edme Mariotte, who found it independently in 1676.

Understanding Your Result

The headline is the pressure or volume you asked for, in your chosen unit.

The change line says by what factor the volume shrank or grew and how the pressure responded.

The check line multiplies out P₁V₁ and P₂V₂ so you can see they match.

When Should You Use This Calculator?

Use it for physics and chemistry homework on the gas laws.

Use it to understand how compressed gas cylinders, pumps and syringes behave.

Use it to see how air volume changes with depth when diving.

Common Mistakes

Mixing units. Both pressures must share a unit, and both volumes too.

Using gauge pressure. Gauges often read pressure above atmospheric; Boyle's law needs absolute pressure.

Forgetting the temperature condition. Rapid compression heats a gas.

Expecting a straight-line relationship. Pressure and volume are inversely proportional, so doubling one halves the other.