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🧪 Gas Laws

Boyle's Law Calculator

Solve any of initial or final pressure and volume for a fixed gas at constant temperature, using P₁V₁ = P₂V₂. Pressure and volume are inversely proportional — squeeze the volume, the pressure rises.

P₁V₁ = P₂V₂
Constant temperature
Solve any value
Any consistent units
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Boyle's Law — Quick answer

At constant temperature, a gas's pressure and volume are inversely proportional. Their product stays constant.

P₁V₁ = P₂V₂
P₂ = P₁·V₁ / V₂ · V₂ = P₁·V₁ / P₂

Worked example: 2 L at 1 atm compressed to 1 L. P₂ = 1 × 2 / 1 = 2 atm.

2 L of gas at 1 atm, compressed

Final volumeFinal pressureNote
2 L1 atmstart
1 L2 atmhalf volume
0.5 L4 atmquarter volume

Used for: syringes, scuba, pumps, lungs, pneumatics.

🧪 Boyle's Law Calculator

Leave the one unknown blank. Keep both pressures in the same unit and both volumes in the same unit.

Initial pressure P₁
Initial volume V₁
Final pressure P₂
Final volume V₂

⚠️ Boyle's Law holds only at constant temperature for a fixed amount of gas. If the temperature changes, use the combined gas law (P₁V₁/T₁ = P₂V₂/T₂) or the ideal gas law PV = nRT instead.

Boyle's Law describes how a fixed amount of gas behaves when you change its volume at constant temperature: the pressure and volume are inversely proportional, so their product never changes — P₁V₁ = P₂V₂. Compress the gas into half the space and the pressure doubles; let it expand to twice the volume and the pressure halves. It is the constant-temperature special case of the ideal gas law and the most intuitive of the gas laws, governing everything from a bicycle pump to the breath in your lungs.

Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Boyle's Law as the isothermal case of PV = nRT.

The Boyle's Law equations

Boyle's Law
P₁ × V₁ = P₂ × V₂
Final pressure
P₂ = P₁ × V₁ / V₂
Final volume
V₂ = P₁ × V₁ / P₂

The product P × V is a constant for the gas as long as temperature and the amount of gas stay fixed. To find any one of the four quantities, set the two products equal and divide. Because pressure appears on both sides — and volume on both sides — the units cancel in pairs, so you can work in atm and litres, kPa and millilitres, or any consistent pair without converting to SI.

Worked example — compressing a gas

Scenario: A 2-litre sample of gas at 1 atm is compressed to 1 litre at the same temperature. What is the new pressure?

Final pressure
P₂ = (1 atm × 2 L) / 1 L = 2 atm
Check the product
1 × 2 = 2 atm·L = 2 × 1 ✓

Halving the volume doubles the pressure to 2 atm — the product P × V stays at 2 atm·L throughout. Push the compression further to 0.5 L and the pressure climbs to 4 atm; expand back out to 4 L and it would fall to 0.5 atm. The inverse relationship is exact at constant temperature, which is why the same 2 atm·L appears in every row.

Frequently Asked Questions

What is Boyle's Law?

At constant temperature, gas pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Half the volume, double the pressure.

How do I find the new pressure?

P₂ = P₁·V₁/V₂. e.g. 1 atm × 2 L ÷ 1 L = 2 atm. New volume is V₂ = P₁·V₁/P₂.

Does temperature have to be constant?

Yes — Boyle's Law is the isothermal case. If T changes, use P₁V₁/T₁ = P₂V₂/T₂ or PV = nRT.

What units should I use?

Any consistent units — atm/kPa/psi for pressure, L/mL for volume. They cancel, so no SI needed.

Why does pressure rise when volume drops?

Same molecules in less space hit the walls more often per area. Half the volume ≈ double the collisions = double pressure.

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