Boyle's Law Calculator

Calculate the inverse relationship between Pressure and Volume ($P_1V_1 = P_2V_2$).

Initial State (1)

Final State (2)

Visualizing Relationship

Fill in 3 values to find the 4th
V₁
V₂
Notice: As Volume decreases (piston goes down), Pressure (density) increases.

The Physics of Squeezing

Boyle's Law is the reason you can breathe and the reason scuba divers must ascend slowly. It describes the fundamental battle between space (Volume) and force (Pressure).

Inverse Proportionality

P1V1
=
P2V2

If Pressure doubles, Volume must cut in half.

How You Breathe

Humans are negative-pressure breathers.

  • Inhale
    Your diaphragm moves down. Lung volume expands (V↑). Pressure drops (P↓). Air rushes in to fill the vacuum.
  • Exhale
    Your diaphragm relaxes up. Lung volume shrinks (V↓). Pressure rises (P↑). Air is pushed out.

The Hyperbola

Unlike Charles's Law (a straight line), Boyle's Law creates a curve.

You can never squeeze a gas to **zero volume** (unless you make a black hole), and you can never expand it to **zero pressure** (unless you have infinite space). The curve approaches both axes but never touches them (asymptotes).

Scuba Safety

Never hold your breath while ascending! As you rise, water pressure drops. The air in your lungs expands. If you don't exhale, your lungs can rupture (barotrauma).

Medical Syringes

Pulling the plunger increases the volume inside the chamber. This creates a low-pressure zone. Liquids naturally flow from high pressure (the vial) to low pressure (the syringe).

Bubble Wrap

Pop! When you squeeze a bubble, you decrease its volume violently. The pressure spikes until the plastic can't hold it anymore, and it ruptures with a snap.

Explore More Chemistry Tools

Charles' Law

Volume vs Temperature.

Ideal Gas Law

PV = nRT.

Combined Gas Law

P, V, and T together.

Frequently Asked Questions

What is Boyle's Law?

Boyle's Law deals with the pressure-volume relationship. It states that for a fixed amount of gas at a constant temperature, pressure and volume are inversely proportional. Squeeze the space (V↓), and the pressure shoots up (P↑).

What is the formula?

The formula is P1V1 = P2V2. You can also write it as P × V = k (a constant).

Why is the relationship inverse?

Imagine a box with bouncing balls (gas particles). If you shrink the box to half its size, the balls hit the walls twice as often because they have less room to travel. This doubled impact frequency is measured as doubled pressure.

Does temperature need to be constant?

Yes. This is an isothermal law. If the temperature changes, the particles would speed up or slow down, which would also affect pressure. To handle T changes, use the Combined Gas Law.

What are real-world examples?
  1. Breathing: Your diaphragm drops, expanding your lungs (V↑). This creates low pressure (P↓) inside, sucking air in.
  2. Deep Sea Fish: Fish with swim bladders can explode if brought to the surface too fast. The drop in pressure causes the gas in their bladder to expand massively.
What is 'The Bends'?

Decompression Sickness. If a diver surfaces too fast, the pressure drops rapidly. Nitrogen gas dissolved in the blood expands into bubbles (like opening a soda), blocking blood flow. This is a deadly application of Boyle's Law.

Who discovered it?

Robert Boyle, an Anglo-Irish chemist, published it in 1662 in his book The Spring and Weight of the Air. It is one of the oldest gas laws.

How do I solve for Volume (V2)?

Rearrange the formula: V2 = (P1 × V1) / P2. Just multiply the initial state and divide by the new pressure.

What does the graph look like?

If you plot Pressure (y-axis) vs Volume (x-axis), it forms a hyperbola (a curve that slides down and to the right). It never touches zero.

Why can't I use this for liquids?

Liquids are incompressible. You can push on a piston full of water with immense force, but its volume won't shrink (much). Gas laws rely on the empty space between molecules.

What units should I use?

The beauty of Boyle's Ratio is that units don't matter as long as they match. You can use psi, atm, mmHg, or Pa. Just don't mix them (e.g. don't use atm for P1 and psi for P2).

What if the gas becomes a liquid?

Boyle's Law fails at high pressures where gas turns to liquid. It only works for 'Ideal Gases' where particles don't stick to each other.

How does a syringe work?

Pulling the plunger increases volume inside the barrel. Pressure inside drops below atmospheric pressure. The outside air pushes the liquid into the needle to fill the void.

Is P1V1 always equal to P2V2?

For an ideal gas in a closed system, yes. The product of pressure and volume represents a constant energy state.

What is a 'Closed System'?

It means no gas can enter or escape. If your balloon has a leak (mass changes), Boyle's Law no longer works.