Boyle's Law states that for a fixed amount of an ideal gas held at constant temperature, the pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Doubling the pressure halves the volume, and vice versa.

What are the units for Boyle's Law?

Pressure can be expressed in Pa, kPa, atm, bar, mmHg (torr), or psi. Volume can be in litres (L), millilitres (mL), cubic metres (m³), or cubic centimetres (cm³). Both sides of the equation must use the same units, which this calculator enforces automatically.

Does Boyle's Law work for real gases?

Boyle's Law is exact only for ideal gases. Real gases deviate at high pressures and low temperatures where intermolecular forces and molecular volume matter. For most lab conditions (low pressure, room temperature) the deviation is small and the law is a reliable approximation.

What does constant temperature mean here?

Boyle's Law applies to isothermal processes — the temperature must not change between the initial and final states. If temperature changes too, you need the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) or the Ideal Gas Law (PV = nRT) instead.

How is P·V a constant?

Because P and V are inversely proportional, their product P·V equals nRT — a fixed value when n (moles), R (8.314 J/mol·K), and T (temperature in kelvin) are all constant. The calculator shows this constant product in pascal-litres as a verification check.

Can I use this for scuba diving calculations?

Yes. Boyle's Law directly governs how air in a scuba tank and a diver's lungs changes with depth, since pressure increases by roughly 1 atm per 10 m of sea water. Enter depth pressures in atm and lung volumes in litres to see how volume changes with depth.

Boyle's Law Calculator

Boyle’s Law is one of the foundational relationships in chemistry and physics. It describes how the pressure and volume of a gas change with each other when the temperature and the amount of gas are both held fixed. The law was first published by Robert Boyle in 1662 based on his careful experiments with a J-shaped glass tube, and it remains a cornerstone of every introductory chemistry and physics course today.

This calculator lets you solve for any one of the four quantities — P₁, V₁, P₂, or V₂ — given the other three. It supports six pressure units (Pa, kPa, atm, bar, mmHg, psi) and four volume units (L, mL, m³, cm³), performs all unit conversions internally, and shows you the full algebraic working so you can see exactly how the answer was reached.

How it works

The governing equation is:

P₁ · V₁ = P₂ · V₂

where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. The product P·V is constant because, from the Ideal Gas Law PV = nRT, the right-hand side (nRT) does not change when temperature T, moles n, and the gas constant R = 8.314 J/(mol·K) are all fixed. Rearranging for each unknown:

Solve for P₂: P₂ = P₁ · V₁ ÷ V₂
Solve for V₂: V₂ = P₁ · V₁ ÷ P₂
Solve for P₁: P₁ = P₂ · V₂ ÷ V₁
Solve for V₁: V₁ = P₂ · V₂ ÷ P₁

The calculator converts all inputs to Pa and litres internally before computing, then converts the result back to your chosen display unit. The constant product P·V is also shown in Pa·L so you can verify the conservation relationship by eye.

Worked example

A gas sample has an initial pressure of 1.00 atm and an initial volume of 4.00 L. The piston is pushed in until the volume falls to 1.50 L. What is the new pressure?

Using P₂ = P₁ · V₁ ÷ V₂:

P₂ = 1.00 atm × 4.00 L ÷ 1.50 L = 2.667 atm

The gas has been compressed to 37.5 % of its original volume, so pressure has risen by a factor of 1/0.375 = 2.667. The constant product P·V = 4.00 atm·L in both states.

P₁ (atm)	V₁ (L)	P₂ (atm)	V₂ (L)
1.00	4.00	2.00	2.00
1.00	4.00	2.667	1.50
101.325 kPa	2.00	202.65 kPa	1.00
760 mmHg	500 mL	380 mmHg	1000 mL

Formula note

The law holds rigorously only for ideal gases (no intermolecular forces, negligible molecular volume). At everyday lab pressures (<10 atm) and room temperature, real gases (N₂, O₂, CO₂, He) deviate by less than 1–2 %, making Boyle’s Law highly accurate for most practical calculations. At very high pressures or near the condensation point of the gas, use the van der Waals equation instead: (P + a·n²/V²)(V − nb) = nRT.