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Boyle’s Law Calculator | Relate pressure and volume (Boyle’s Law)

Solve Boyle's law P₁V₁ = P₂V₂ for any pressure or volume change at constant temperature, with the inverse relationship explained. Enter three of the four values and get the fourth — the standard tool for gas compression and expansion problems in physics and chemistry.

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

atm
L
atm
Results

Enter values above and click Calculate to see your result instantly.

Quick reference

If volume…Then pressure…
HalvesDoubles
DoublesHalves
x 1/3x 3
ConstantConstant (T fixed)

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Interpretation guide

Solve forRearranged
P2P2 = P1 V1 / V2
V2V2 = P1 V1 / P2
ConditionTemperature and amount held constant

lightbulb Worked example — inflating a weather balloon at ground level

A high-school physics class fills a weather balloon with 12.0 litres of helium at an outside pressure of 0.95 atm on a calm day. The team wants to know what the gas pressure will be if the balloon is allowed to expand to 18.0 litres before launch, with the temperature held constant at 25 °C.

Result: P₂ = P₁V₁ ÷ V₂ = (0.95 × 12.0) ÷ 18.0 = 11.4 ÷ 18.0 = 0.63 atm.

What this means: Expanding the balloon by 50% (from 12.0 to 18.0 L) drops the pressure to two-thirds of its original value — exactly what the inverse relationship predicts. The students can compare this against a gauge reading; a large mismatch usually means the temperature was not actually constant during the expansion.

Formula & methodology

Formula: P1 V1 = P2 V2 (constant temperature and fixed amount of gas)

How Boyle's law works

The tool applies P₁V₁ = P₂V₂ for a fixed amount of gas at constant temperature: pressure and volume are inversely proportional, so halving the volume doubles the pressure. Enter three of the four values and the calculator solves for the missing one, with the initial state clearly identified.

Example: a gas at 1.0 atm in a 4 L container compressed to 2 L reaches P₂ = P₁V₁ ÷ V₂ = 1.0 × 4 ÷ 2 = 2.0 atm.

Reading the result: the inverse relationship is why scuba tanks, syringes, and pressure cookers behave the way they do. The law assumes constant temperature — compression heats the gas in reality, which is why fast pump strokes feel warm. For temperature changes, use the combined gas law instead.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is Boyle's law?
Boyle's law states that at constant temperature, the pressure and volume of a fixed amount of gas are inversely proportional: P1V1 = P2V2. If you halve the volume, the pressure doubles, and vice versa. It describes how gases respond to compression or expansion when temperature does not change.
How do you calculate Boyle's law?
Use P1V1 = P2V2 and solve for the unknown. To find a new pressure: P2 = P1V1/V2. To find a new volume: V2 = P1V1/P2. For example, compressing 2.0 L at 1.0 atm down to 0.5 L gives P2 = (1.0 x 2.0)/0.5 = 4.0 atm.
Why are pressure and volume inversely related?
Squeezing a gas into a smaller volume packs the molecules closer, so they strike the container walls more often, raising the pressure. Expand the volume and collisions become less frequent, lowering the pressure. With temperature fixed, the product of pressure and volume stays constant.
Does Boyle's law require constant temperature?
Yes. Boyle's law only holds when temperature and the amount of gas are constant. If the temperature also changes, you must use the combined gas law (P1V1/T1 = P2V2/T2), which accounts for the temperature effect along with the pressure-volume relationship.
What are real-life examples of Boyle's law?
Breathing (your diaphragm expands the lungs, lowering pressure so air flows in), a syringe (pulling the plunger increases volume and draws fluid), a bicycle pump (compressing air raises its pressure), and scuba diving (gas volume changes with depth pressure) all demonstrate Boyle's law in action.
Why does halving the volume exactly double the pressure?
Because their product is constant: P₁V₁ = P₂V₂. If V₂ = V₁/2, then P₂ = P₁V₁/(V₁/2) = 2P₁. This only holds when the temperature and gas amount stay fixed — in fast real compressions the gas warms up, which pushes the pressure a little higher than the law predicts.
Can I mix units like atm and litres in one calculation?
Yes — as long as both volumes use the same unit and both pressures use the same unit, the units cancel out in P₁V₁ = P₂V₂. So 1.0 atm with 4.0 L gives the same answer as 760 mmHg with 4000 mL. You cannot mix atm with kPa for pressure, or litres with millilitres for volume, within one calculation.
What does “constant temperature” mean for a bicycle pump?
It means the gas must have time to cool back to its starting temperature. When you pump fast, the air inside heats up and the pressure rises above the Boyle’s-law prediction — that is why the pump barrel gets warm. Pump slowly, or pause between strokes, and the calculation matches the gauge closely.
When should I use the combined gas law instead?
Whenever the temperature also changes between the two states. Boyle’s law is the special case of P₁V₁/T₁ = P₂V₂/T₂ with T₁ = T₂. A weather balloon rising into colder air, or a gas sample moved from an ice bath to room temperature, needs the combined form because the temperature change shifts the pressure on its own.

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