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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)

info Boyle's Law Calculator

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Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

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

lightbulb Worked example

Let's say you are using the Boyle's Law Calculator. Boyle's Law Calculator is a free online calculator that helps you work out boyle's law quickly and accurately, right in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula P1 V1 = P2 V2 (constant temperature and fixed amount of gas) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

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.
What does the Boyle's Law Calculator do?
Boyle's Law Calculator is a free online calculator that helps you work out boyle's law quickly and accurately, right in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Boyle's Law Calculator use?
The Boyle's Law Calculator applies the standard formula: P1 V1 = P2 V2 (constant temperature and fixed amount of gas). The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Boyle's Law Calculator free and private?
Yes — the Boyle's Law Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Boyle's Law Calculator?
The Boyle's Law Calculator applies the standard formula: P1 V1 = P2 V2 (constant temperature and fixed amount of gas). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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