This Boyle’s law calculator solves P₁V₁ = P₂V₂ — the inverse relationship between a gas’s pressure and volume at constant temperature. Enter any three values to find the fourth.
What Is Boyle’s Law?
Boyle’s law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: squeeze a gas to half its volume and its pressure doubles. Robert Boyle published it in 1662 — one of the first quantitative laws of science — and it is the constant-temperature slice of the general Ideal Gas Law. This calculator is part of our Physics Calculators collection and a staple of the Chemistry Calculators too.
Worked Example (Verified)
A gas occupies 3.0 L at 2.0 atm. Compress it to 1.5 L at the same temperature:
P₂ = P₁V₁ ÷ V₂ = (2.0 × 3.0) ÷ 1.5 = 4.0 atm. Halved volume, doubled pressure — the inverse relationship in action. Reverse it: expand back to 6.0 L and the pressure falls to 1.0 atm.
Boyle’s Law in Real Life
- Scuba diving: a breath taken at 20 m depth (3 atm) expands to three times its volume at the surface — why divers exhale continuously while ascending; holding that breath can rupture lungs. Boyle’s law is literally life-safety knowledge underwater.
- Syringes and pumps: pulling a plunger doubles the volume and halves the pressure, drawing fluid in.
- Breathing: your diaphragm expands the chest cavity, dropping pressure so air flows in — every breath is a Boyle’s-law demonstration.
- Weather balloons swell as they rise into lower pressure, until they burst — P down, V up.
Conditions and Limits
Boyle’s law requires constant temperature and a fixed amount of gas, and it idealizes the gas as having point-like, non-interacting molecules. At very high pressures real gases compress less than predicted (their own molecular volume matters) — the same limit discussed in the Ideal Gas Law page. Units are free (atm, kPa, mmHg, psi; L, mL, m³) as long as you use the same units on both sides.
Related Tools
- Ideal Gas Law Calculator — the parent law (PV = nRT)
- Physics Calculators — the full collection
- Chemistry Calculators
Frequently Asked Questions
What is the formula for Boyle’s law?
P₁V₁ = P₂V₂, at constant temperature and constant amount of gas.
What happens to pressure when volume is halved?
It doubles. Pressure and volume trade off in inverse proportion — that is the whole law.
Does Boyle’s law work in any units?
Yes, provided pressure units match on both sides and volume units match on both sides. The products P₁V₁ and P₂V₂ are what must be equal.
Why does temperature have to stay constant?
Because heating a gas raises its pressure independently (that is Charles’s/Gay-Lussac’s territory). Boyle’s law isolates the pressure–volume trade by holding temperature fixed.
Is Boyle’s law the same as the ideal gas law?
Boyle’s law is the special case of PV = nRT with n and T constant. The ideal gas law is the general statement; Boyle’s is its oldest slice.
Is this Boyle’s law calculator free?
Yes — free, instant, no sign-up.