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Boyle's Law Calculator

Chemistry

Solve for any variable in Boyle's Law (P₁V₁ = P₂V₂). Select which variable to find, enter the other three values, and adjust units as needed.

Quick Examples:

Calculator Settings

Input Values

Enter three known values — the fourth will be calculated.

Ready to Calculate
Select what to solve for, then enter the three known values above.

About This Tool

Boyle's Law Calculator – Solve P₁V₁ = P₂V₂

This free online Boyle's Law calculator lets you solve for any one of the four variables in the equation P₁V₁ = P₂V₂: initial pressure (P₁), initial volume (V₁), final pressure (P₂), or final volume (V₂). Simply select what you want to find, input the three known values, and get an instant result alongside a step-by-step derivation.

The tool supports 7 pressure units (atm, Pa, kPa, bar, mmHg, torr, psi) and 6 volume units (L, mL, m³, cm³, ft³, in³), making it ideal for chemistry students, physics learners, and engineering professionals worldwide.

What Is Boyle's Law?

Boyle's Law is one of the foundational gas laws in chemistry and physics. Formulated by Robert Boyle in 1662, it states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. In plain language: if you compress a gas into a smaller space (decrease its volume), the pressure rises; if you let it expand, the pressure falls.

This relationship holds for ideal gases — a theoretical model that is an excellent approximation for real gases at moderate pressures and temperatures far above their boiling points.

The Formula

The mathematical expression of Boyle's Law is:

P₁ × V₁ = P₂ × V₂

Where:

  • P₁ — the initial (starting) pressure of the gas
  • V₁ — the initial (starting) volume of the gas
  • P₂ — the final (ending) pressure of the gas
  • V₂ — the final (ending) volume of the gas

Since P × V equals a constant (at constant temperature), you can rearrange the equation to isolate any unknown variable:

P₁ = (P₂ × V₂) / V₁
V₁ = (P₂ × V₂) / P₁
P₂ = (P₁ × V₁) / V₂
V₂ = (P₁ × V₁) / P₂

Real-World Applications

Boyle's Law has wide-ranging, practical applications across many fields:

  • Scuba diving: A diver's lungs hold a fixed amount of air at the surface (1 atm). At 30 m depth the pressure is about 4 atm, so that same air now occupies roughly one-quarter of its original volume — critical knowledge for safe ascents.
  • Syringe and pump design: Pulling back a syringe plunger increases the volume inside, reducing pressure and drawing fluid in. Pushing it forward compresses the gas and expels the fluid.
  • Breathing physiology: When the diaphragm expands the chest cavity, lung volume increases and pressure drops below atmospheric, pulling air in — a direct application of Boyle's Law.
  • Automotive engineering: Internal combustion engines rely on rapid compression of an air–fuel mixture to raise its pressure before ignition.
  • Weather balloons: As a balloon ascends and atmospheric pressure decreases, the gas inside expands — eventually causing the balloon to burst at altitude.

How to Use This Calculator

Step-by-step guide
  1. Select the variable to solve for from the "Solve For" dropdown (P₁, V₁, P₂, or V₂).
  2. Choose your units — pick a pressure unit (e.g., atm) and a volume unit (e.g., L) from the settings dropdowns.
  3. Enter the three known values into the corresponding input fields. The field for the unknown variable is disabled and will display the calculated result automatically.
  4. Review the step-by-step solution to see exactly how the result was derived with unit conversions shown in SI (Pa, m³).

Worked Examples

Example 1 — Gas compression: A gas occupies 10 L at 1 atm. What is the pressure if the volume is compressed to 5 L?

P₁ × V₁ = P₂ × V₂
1 atm × 10 L = P₂ × 5 L
P₂ = 10 / 5 = 2 atm

Example 2 — Scuba dive: A diver holds 6 L of air at 1 atm on the surface. At 30 m depth the pressure is 4 atm. What is the new air volume?

V₂ = (P₁ × V₁) / P₂
V₂ = (1 atm × 6 L) / 4 atm
V₂ = 1.5 L

Example 3 — Find initial volume: A gas is at 3 atm with a volume of 4 L. If the pressure drops to 1 atm, what was the initial volume before the expansion?

V₁ = (P₂ × V₂) / P₁
V₁ = (1 atm × 4 L) / 3 atm
V₁ ≈ 1.333 L

Pressure & Volume Units Explained

Depending on your field or region, Boyle's Law problems may use different units. This calculator converts internally to SI units (Pascals for pressure, cubic metres for volume) before computing, then converts the result back to your chosen unit.

Pressure units

  • atm (atmosphere): The average air pressure at sea level; 1 atm = 101,325 Pa. Common in chemistry textbooks.
  • Pa / kPa (Pascal / kilopascal): The SI unit. 1 kPa = 1,000 Pa.
  • bar: Roughly equal to 1 atm; 1 bar = 100,000 Pa. Common in meteorology.
  • mmHg / torr: Based on mercury column height; 1 torr = 133.322 Pa. Used in medical and laboratory settings.
  • psi (pounds per square inch): Common in US engineering contexts; 1 psi ≈ 6,895 Pa.

Volume units

  • L (litre): Most common unit in chemistry lab problems. 1 L = 0.001 m³.
  • mL (millilitre): 1 mL = 0.001 L = 1 cm³.
  • m³ (cubic metre): The SI unit for volume.
  • ft³ / in³: Imperial volume units common in US engineering.

Limitations and Assumptions

Boyle's Law is derived under the ideal gas assumption: gas molecules have negligible volume and no intermolecular forces. In practice, it is highly accurate for gases such as oxygen, nitrogen, and air under common laboratory conditions. It becomes less accurate at very high pressures (where molecules are crowded) or near the condensation point of a gas.

Crucially, the law holds only when temperature is constant (isothermal process). For processes involving temperature changes, consider using the combined gas law or the ideal gas law (PV = nRT).

Related Gas Laws

Boyle's Law is one of three classical gas laws, each isolating one pair of variables at constant conditions:

  • Charles's Law: Volume is proportional to temperature at constant pressure (V₁/T₁ = V₂/T₂).
  • Gay-Lussac's Law: Pressure is proportional to temperature at constant volume (P₁/T₁ = P₂/T₂).
  • Ideal Gas Law: Combines all three — PV = nRT — where n is moles of gas and R is the universal gas constant.

Frequently Asked Questions

Is the Boyle's Law Calculator free?

Yes, Boyle's Law Calculator is totally free :)

Can I use the Boyle's Law Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Boyle's Law Calculator?

Yes, any data related to Boyle's Law Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

What is Boyle's Law?

Boyle's Law states that at constant temperature, the pressure and volume of a fixed amount of gas are inversely proportional. That is, P₁ × V₁ = P₂ × V₂. When pressure doubles, volume halves, and vice versa.

How does this Boyle's Law calculator work?

Select which variable you want to solve for (P₁, V₁, P₂, or V₂), then enter the three known values along with their units. The calculator applies the formula P₁V₁ = P₂V₂, converts all values to SI units internally, and returns the unknown variable in your chosen unit with a step-by-step solution.

What pressure and volume units are supported?

Pressure units include atm, Pa, kPa, bar, mmHg, torr, and psi. Volume units include L (litres), mL, m³, cm³, ft³, and in³. All values are converted to Pascals and m³ internally before calculation, then converted back to your selected unit.

Does Boyle's Law apply to all gases?

Boyle's Law applies accurately to ideal gases at moderate pressures and temperatures well above the gas's liquefaction point. For real gases at very high pressures or near their boiling point, deviations occur and the van der Waals equation provides better accuracy.

What are some real-world examples of Boyle's Law?

Common examples include syringes (pulling the plunger reduces pressure, increasing volume), scuba diving (compressed air tanks store gas at high pressure in a small volume), and weather balloons (air pressure decreases with altitude, causing the balloon to expand).

What is the PV constant shown in the result?

The PV constant (k = P × V) is an invariant for a given gas sample at constant temperature. It equals P₁V₁ and also P₂V₂. The value is shown in SI units (Pa·m³), which is equivalent to Joules, representing the work done on or by the gas.