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Solve Boyle's Law instantly with our free online pressure volume ratio calculator. Enter any three of P1, V1, P2, V2 — leave the unknown blank — and get the missing value with full unit support: atm, kPa, psi, mmHg for pressure and liters or milliliters for volume.
Solve Boyle's LawInteractive Pressure Volume Ratio Calculator
Enter any three values and leave the unknown blank — the calculator solves for it.
Boyle's Law Result
How the Pressure Volume Calculator Works
Four values, one equation — leave a blank and let Boyle's Law fill it.
Enter Three Known Values
Type the initial pressure (P1), initial volume (V1), and whichever final value you know. Pick matching units from the dropdowns — atm, kPa, psi, or mmHg for pressure; liters or milliliters for volume.
Leave the Unknown Blank
Leave exactly one field empty — that is the variable the calculator solves for. Entering all four (or fewer than three) triggers a guidance message instead.
Get the Missing Value
The calculator converts everything to base units, applies P1×V1=P2×V2, and returns the answer in your chosen unit — plus conversions to every other unit.
Read the Interpretation
See whether the gas was compressed or expanded, and review the worked equation so you can follow every step of the calculation.
Boyle's Law Formulas
Published by Robert Boyle in 1662, this law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature.
The Core Equation
Pressure times volume stays constant. Squeeze the volume down and the pressure rises by exactly the same factor.
Solving for Final Pressure
Example: 1.0 atm × 2.0 L compressed into 1.0 L gives P2 = 2.0 atm — halving the volume doubles the pressure.
Solving for Final Volume
Example: the same gas released from 2.0 atm back to 1.0 atm expands to V2 = 2.0 L.
Solving for Initial Values
Any variable can be isolated — the calculator detects your blank field and applies the right rearrangement automatically.
Key Assumption
Boyle's Law holds when temperature and gas amount are constant. If temperature changes too, use the Combined Gas Law form instead: (P1×V1)/T1 = (P2×V2)/T2.
Pressure and Volume Unit Conversions
The calculator converts internally, but this table helps you sanity-check results across unit systems.
| Unit | Equals | Common Use |
|---|---|---|
| 1 atm (atmosphere) | 101.325 kPa = 14.696 psi = 760 mmHg | Chemistry, diving |
| 1 kPa (kilopascal) | 0.00987 atm = 0.145 psi = 7.501 mmHg | Engineering, SI contexts |
| 1 psi (pounds/in²) | 0.068 atm = 6.895 kPa = 51.715 mmHg | Tires, US industry |
| 1 mmHg (torr) | 0.00132 atm = 0.133 kPa = 0.0193 psi | Vacuum, medicine |
| 1 L (liter) | 1000 mL | Lab gas volumes |
| 1 mL (milliliter) | 0.001 L = 1 cm³ | Syringes, small samples |
Where Boyle's Law Shows Up in Real Life
Scuba Diving
At 10 m depth, pressure doubles to 2 atm and a diver's air spaces halve in volume — the reason divers equalize ears and never hold their breath on ascent. Dive tables are applied Boyle's Law.
Syringes and Medical Devices
Pulling a syringe plunger expands the volume and drops internal pressure, drawing fluid in. Every injection is a live P1V1=P2V2 demonstration.
Breathing
Your diaphragm expands the chest cavity (V up, P down) and air flows in; exhaling reverses it. Respiratory physiology runs on Boyle's Law with every breath.
Spray Cans and Carbonation
Aerosols and soda bottles hold gas at high pressure in small volumes; releasing them lets the gas expand. Engineers size these containers using exactly this equation.
For the underlying physics, see the Boyle's Law article and the broader ideal gas law reference.
Boyle's Law vs. the Other Gas Laws
Boyle's Law is one of three simple gas laws that combine into the ideal gas law. Knowing which to use when is half the battle in chemistry problems.
Charles's Law (Volume-Temperature)
At constant pressure, volume is directly proportional to absolute temperature: V1/T1 = V2/T2. Heat a balloon and it expands. Note that temperature must be in Kelvin — a common exam trap.
Gay-Lussac's Law (Pressure-Temperature)
At constant volume, pressure is directly proportional to absolute temperature: P1/T1 = P2/T2. This is why tire pressure rises on hot days and why aerosol cans warn against heat.
The Combined Gas Law
When pressure, volume, and temperature all change, this is the tool. Boyle's Law is just the combined law with T1 = T2 (temperature cancels out).
The Ideal Gas Law
With R = 0.08206 L·atm/(mol·K), this single equation subsumes all three simple laws and adds the mole count. Use it when the amount of gas changes or when you need absolute rather than relative answers.
| Use This Law | When | Constant |
|---|---|---|
| Boyle's (P1V1=P2V2) | Only P and V change | n, T |
| Charles's (V1/T1=V2/T2) | Only V and T change | n, P |
| Gay-Lussac's (P1/T1=P2/T2) | Only P and T change | n, V |
| Combined | P, V, T all change | n |
| Ideal (PV=nRT) | Amount changes, or absolute values needed | R |
Pressure Volume Ratio FAQs
For a fixed amount of gas at constant temperature, pressure and volume are inversely related: squeeze the volume in half and the pressure doubles. The equation P1×V1=P2×V2 lets you compute any one of the four values from the other three.
P1 and P2 must share units, and V1 and V2 must share units — but pressure and volume units are independent of each other. So P in psi with V in mL works fine. This calculator converts your selections automatically.
It assumes constant temperature and a fixed amount of gas, and it describes ideal gases best. At very high pressures or near condensation, real gases deviate. For changing temperatures, use the combined gas law: (P1×V1)/T1 = (P2×V2)/T2.
Mathematically the equation allows approaching zero, but a true zero pressure (perfect vacuum) with finite gas is unphysical, and division by zero breaks the rearranged forms. Enter small positive values for vacuum-range problems instead.
Divide psi by 14.696. So 29.4 psi ≈ 2.0 atm. To go the other way, multiply atm by 14.696. The calculator's conversion readout does this for every supported unit automatically.
Rapid compression does work on the gas, adding energy that shows up as temperature — Boyle's Law strictly applies to slow (isothermal) changes where heat escapes. This is why bicycle pumps get warm.
Boyle's Law links pressure and volume at constant temperature (P1V1=P2V2). Charles's Law links volume and temperature at constant pressure (V1/T1=V2/T2). Together with Gay-Lussac's Law they form the combined gas law.
Every 10 m of seawater adds ~1 atm. At 20 m (3 atm), a given air mass occupies one-third its surface volume. Divers learn never to hold their breath ascending: expanding air must escape or it over-pressurizes the lungs — a direct, life-critical application of P1V1=P2V2.
Worked Example: Compressing a Gas Sample
A chemistry student has 2.0 L of gas at 1.0 atm and compresses it to 0.5 L at constant temperature. What is the new pressure?
Step 1: Identify knowns — P1 = 1.0 atm, V1 = 2.0 L, V2 = 0.5 L, solve for P2.
Step 2: Rearrange — P2 = (P1 × V1) ÷ V2.
Step 3: Substitute — P2 = (1.0 × 2.0) ÷ 0.5 = 4.0 atm.
Step 4: Sanity check — volume shrank by a factor of 4, so pressure grew by a factor of 4. ✓
Try it in the calculator above: enter 1.0 atm, 2.0 L, leave P2 blank, enter 0.5 L — you will get 4.0 atm with conversions to kPa (405.3), psi (58.8), and mmHg (3040).