Boyle's Law Calculator
At constant temperature and constant amount of gas, pressure × volume stays constant. Enter any 3 of P₁, V₁, P₂, V₂ below and the calculator solves the missing one instantly — with exact unit conversions.
Fill any 3 of the 4 fields — the empty one is solved automatically.
Boyle constant k = P₁V₁ = — Pa·m³ (joule)
How it works — worked example
- Compute the Boyle constant: k = P₁ × V₁ = 100 kPa × 2.0 L = 200 kPa·L.
- Rearrange for the unknown: P₂ = k / V₂ = 200 / 0.5 = 400 kPa.
- Quartering the volume from 2.0 L to 0.5 L (a factor of 4) quadruples the pressure from 100 kPa to 400 kPa — the inverse relationship at the heart of Boyle's law.
Assumptions: temperature and the amount of gas stay constant (a sealed container), and the gas behaves ideally. Real gases deviate at very high pressures — see the FAQ.
Frequently asked questions
What is Boyle’s law?
Boyle’s law says that for a fixed amount of gas at constant temperature, pressure times volume is constant: P₁V₁ = P₂V₂. Compress a gas to half its volume and its pressure doubles; let it expand to twice the volume and the pressure halves. It was published by Robert Boyle in 1662 and is one of the three classical gas laws.
How do you calculate the final pressure (P₂) with Boyle’s law?
Rearrange the law to P₂ = P₁V₁ / V₂. Example: 100 kPa × 2.0 L of gas is compressed to 0.5 L, so P₂ = (100 × 2.0) / 0.5 = 400 kPa — the pressure quadruples because the volume shrank to one quarter. Enter any three values in the calculator above and it solves the fourth.
How do you find the final volume (V₂)?
Use V₂ = P₁V₁ / P₂. Example: 14.7 psi × 10 ft³ of gas is compressed until the pressure reaches 29.4 psi, so V₂ = (14.7 × 10) / 29.4 = 5.0 ft³ — doubling the pressure halves the volume. The calculator above does this with automatic unit conversion.
What units can I use for pressure and volume?
Pressure: Pa, kPa, bar, psi, atm or mmHg. Volume: m³, L, mL or ft³ — you can even mix units, e.g. P₁ in atm with V₁ in ft³, because everything is converted to SI internally. Exact references: 1 atm = 101325 Pa = 101.325 kPa = 1.01325 bar = 14.696 psi = 759.9999 mmHg (about 760); 1 bar = 100 kPa = 14.5038 psi; 1 ft³ = 28.3168 L = 28316.8 mL.
What must stay constant for Boyle’s law to apply?
Two things: the temperature and the amount of gas (a sealed container with no leaks). If the gas heats up while you compress it, or gas escapes, P₁V₁ will not equal P₂V₂ and the calculator’s consistency check will flag the mismatch.
When does Boyle’s law break down for real gases?
Real gases deviate at very high pressures and low temperatures, where the molecules’ own volume and intermolecular attractions stop being negligible — this is described more accurately by the van der Waals equation. For everyday pressures (around 1 atm) and moderate temperatures, Boyle’s law is an excellent approximation.
Can pressure or volume be zero or negative in the calculator?
No — all four values must be positive numbers. Zero volume would mean dividing by zero, and negative pressure has no physical meaning here, so the calculator rejects both with an error message.
Where is Boyle’s law used in real life?
Everywhere gases get squeezed: syringes and bicycle pumps, scuba diving (a lungful of air compresses as you descend and expands as you ascend), human breathing (the diaphragm changes chest volume to move air), spray cans and air compressors. Engineers use it to size pressure vessels and pneumatic systems.
Free tool by NRTechStudio