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Boyle's Law Calculator

Solve Boyle's law, P₁V₁ = P₂V₂, for the pressure or volume of a gas compressed or expanded at constant temperature.

Level: Grades 10–11

Printable worksheet

Boyle's Law Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

Use absolute pressure, measured from zero. Add the air pressure around you to a gauge reading.

Result

Final pressure (P₂)

2.5 atm

Final pressure (P₂) is 2.5 atm.

In kilopascals
253.3125 kPa
In pounds per square inch
36.7399 psi
Pressure ratio (P₂ ÷ P₁)
2.5
Volume ratio (V₂ ÷ V₁)
0.4Always the pressure ratio flipped upside down.
Constant P × V
10 atm·L

See the step-by-step solution ↓

Step-by-step solution

  1. Pressure × volume stays the same for this gas, so work it out from the starting state, where you know both

    1 atm×10 L=10 atm·L

  2. Divide that product by the final volume to get the missing pressure

    104 L=2.5 atm

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the new pressure or volume of a gas when you squeeze it or let it expand. Boyle's law describes what happens when you do that without changing the gas's temperature. Pressure and volume move in opposite directions. Halve the volume and the pressure doubles. Triple the volume and the pressure falls to a third. Their product, P × V (pressure times volume), stays the same the whole time.

The calculator can solve for any one of four values: the starting or final pressure, or the starting or final volume. Choose one pressure unit and one volume unit for both states. The law only compares the two states, so the units cancel out. The answer comes out in the unit you picked. Pressure results are also shown in kilopascals and psi to save you a step.

Where it's used

Why this math matters outside the classroom:

  • Scuba diving. Divers learn that air in a sealed balloon at 10 m depth, about 2 atm, shrinks to half its surface volume.
  • Syringes. Pulling a sealed syringe plunger from 10 mL to 20 mL halves the pressure of the trapped air if the temperature holds steady.
  • Compressed air. Shops estimate that 1 m³ of air at 1 bar squeezed into a tank at 8 bar takes up 0.125 m³.
  • Weather balloons. A weather balloon swells as it rises because the outside pressure falls and the gas inside expands to match it.
  • Chemistry labs. Students record pressure as they compress air in a syringe and check that P × V stays close to constant.

Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what to solve for.
  2. Pick the pressure unit and volume unit used for both states of the gas.
  3. Enter the three values you know. Pressures must be absolute (measured from zero), not gauge readings.
  4. Read the answer, along with the pressure and volume ratios and the constant product P × V.

What the inputs mean

Volume unit (both volumes)
Both volumes use this unit. So a squeeze from 10 L to 4 L is entered as 10 and 4.
Initial pressure (P₁)
Tire and cylinder gauges show pressure above the air pressure around you. Add about 1 atm (14.7 psi or 101.3 kPa at sea level) to a gauge reading before using it here. Otherwise the answer will be wrong.
Final pressure (P₂)
Absolute pressure, not a gauge reading.

Formula and method

P₁ × V₁ = P₂ × V₂   (constant temperature and amount)
P₂ = P₁ × V₁ ÷ V₂
V₂ = P₁ × V₁ ÷ P₂

P₁ and V₁ are the starting pressure and volume, and P₂ and V₂ are the final ones. Boyle's law is the fixed-temperature case of the ideal gas law, PV = nRT. There, n is the amount of gas, R is a fixed constant and T is the temperature. With n and T held steady, the right-hand side doesn't change. So pressure times volume stays the same, however the gas is squeezed or expanded.

The calculator first works out that constant product from whichever state you know fully. Then it divides by the other known value to find the missing one. Since the law only compares two states, you don't need to convert to standard SI units. Just make sure both pressures use one unit and both volumes use one unit.

Worked example

A cylinder holds 10 L of air at 1 atm. A piston slowly pushes it down to 4 L, slowly enough that the air stays at room temperature. What is the new pressure?

  1. Constant product: P₁ × V₁ = 1 atm × 10 L = 10 atm·L.
  2. P₂ = 10 ÷ 4 = 2.5 atm.
  3. In other units: 2.5 × 101.325 = 253.3125 kPa, about 36.74 psi.

Result: The pressure rises to 2.5 atm. The volume fell to 0.4 of its starting value, so the pressure rose by the flipped factor, 2.5.

Understanding the result

The pressure ratio and the volume ratio are always each other flipped upside down (reciprocals). That makes Boyle's law handy for quick mental estimates. Take a scuba diver at 10 m deep, where the absolute pressure is about 2 atm. The air they breathe is squeezed to roughly half its volume at the surface.

Plot pressure against volume for a gas at one temperature, and its states fall on one curve. That curve is called an isotherm, and its shape is a rectangular hyperbola.

Assumptions and limitations

  • The temperature of the gas stays the same. In practice, that means changing the volume slowly enough for heat to flow in or out.
  • No gas leaks in or out, and the gas behaves ideally, like the textbook model.
  • Pressures are absolute.
  • Fast squeezing heats the gas, as in a bicycle pump, and fast expansion cools it. Then the pressure changes more than Boyle's law predicts.
  • At high pressures, or when a gas is close to turning into liquid, real gases drift away from the law.
  • If the temperature also changes, use the combined gas law or the ideal gas law instead.

Frequently asked questions

Why do I need absolute pressure?

The law compares pressures measured from zero. A gauge reads zero at normal air pressure. So gauge readings shift both pressures by the same amount, and that breaks the ratio. Add the air pressure around you first.

What happens to pressure if the volume is doubled?

It halves. If the volume changes by a factor x, the pressure changes by the factor 1 ÷ x, as long as the temperature and amount stay the same.

Is Boyle's law the same as the ideal gas law?

It's a special case of it. The ideal gas law, PV = nRT, includes temperature and the amount of gas. Boyle's law is what's left when both are held steady.

Why do my ears pop on a plane?

As the cabin pressure drops on the climb, the air trapped behind your eardrum tries to expand, just as Boyle's law predicts. Then the Eustachian tube (a small passage from the ear to the throat) lets some of it out.

How this calculator is checked

Method: Boyle's law P₁V₁ = P₂V₂ for an ideal gas at constant temperature and amount; pressure conversions from the shared exact pressure table (atm = 101,325 Pa). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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