Combined Gas Law Calculator

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How to Use the Combined Gas Law Calculator

1. 1. Choose the law. Use the combined gas law when pressure, volume and temperature all change. If one of them is held constant, choose the matching simple law — Boyle's, Charles's, Gay-Lussac's — and the calculator drops the variables that cancel. Avogadro's law relates volume to the amount of gas.
2. 2. Pick the unknown. Any of the initial or final values can be the answer, not just the final volume.
3. 3. Enter the other values and choose the units. Each variable has one unit shared by both states. Pressure, volume and amount cancel in the ratio, so any unit works; temperature is converted to kelvin first.
4. 4. Check the working. The calculator prints the law, the rearranged equation, any temperature conversion, and your numbers substituted in, so it reads like a worked solution.

The Gas Laws in One Table

All five come from the ideal gas law, PV = nRT. Rearranged to PV/T = nR, the right-hand side is constant for a fixed amount of gas, so PV/T has the same value before and after any change. Hold T constant and you recover Boyle's law; hold P or V constant and you get Charles's or Gay-Lussac's. Because R cancels, you never need its value here — use the Ideal Gas Law Calculator when you need R, or when the amount of gas is the unknown.

Worked Examples

Combined law (the default inputs). A gas occupies 5.00 L at 1.00 atm and 20.0 °C. What is its volume at 2.00 atm and 100. °C? Convert the temperatures: T₁ = 293.15 K and T₂ = 373.15 K. Then V₂ = (P₁ × V₁ × T₂) ÷ (T₁ × P₂) = (1.00 × 5.00 × 373.15) ÷ (293.15 × 2.00) = 3.18 L. Doubling the pressure would halve the volume; heating the gas expands it by a factor of 1.27 and the net change is a factor of 0.636.

Boyle's law. A 5.00 L sample at 1.00 atm is compressed at constant temperature to 2.00 atm. V₂ = P₁V₁ ÷ P₂ = (1.00 × 5.00) ÷ 2.00 = 2.50 L.

Charles's law. A balloon holds 2.50 L at 25.0 °C. Heated to 75.0 °C at constant pressure, V₂ = V₁T₂ ÷ T₁ = (2.50 × 348.15) ÷ 298.15 = 2.92 L. Using Celsius directly would give 7.5 L, which is wrong.

Gay-Lussac's law. A rigid container is at 2.00 atm and 20.0 °C. At 45.0 °C the pressure is P₂ = P₁T₂ ÷ T₁ = (2.00 × 318.15) ÷ 293.15 = 2.17 atm.

Avogadro's law. 0.250 mol of gas fills 5.00 L. At the same pressure and temperature, 0.400 mol fills V₂ = V₁n₂ ÷ n₁ = (5.00 × 0.400) ÷ 0.250 = 8.00 L.

Why Temperature Must Be in Kelvin

Pressure and volume of a gas depend on its absolute temperature, which is measured from zero where ideal gas motion would cease. Celsius and Fahrenheit place their zeros elsewhere, so a ratio of two Celsius values means nothing: 50 °C is not twice as hot as 25 °C. The calculator adds 273.15 to Celsius readings (or converts Fahrenheit) and rejects anything at or below 0 K, because the equation would divide by zero or return a negative volume.

Common Mistakes

• Mixing units between states. The ratio only cancels if both pressures use one unit and both volumes use one. This calculator enforces that by giving each variable a single unit menu.
• Using the wrong law for what is constant. If the container is rigid, volume is constant and Gay-Lussac's law applies; if a piston lets the gas expand against fixed pressure, use Charles's law.
• Changing the amount of gas. The combined law assumes none leaks in or out. If gas is added or a reaction produces some, the amount changes and you need PV/(nT) = constant — the Avogadro setting or the ideal gas law.
• Ignoring significant figures. The answer is shown to the fewest significant figures in your data unless you choose otherwise; check the Significant Figures Calculator if you are unsure how many to keep.

Frequently Asked Questions

What is the combined gas law formula?

P₁V₁/T₁ = P₂V₂/T₂, where P is pressure, V is volume and T is the absolute temperature in kelvin, for a fixed amount of gas in an initial (1) and a final (2) state. It merges Boyle's, Charles's and Gay-Lussac's laws.

How do I solve the combined gas law for V₂?

Rearrange to V₂ = P₁V₁T₂ ÷ (T₁P₂). Convert both temperatures to kelvin, keep both pressures in the same unit, then substitute. The volume comes out in whatever unit V₁ was in.

Do I need the gas constant R for the combined gas law?

No. R cancels because it appears on both sides of PV/T = nR. That is why pressure and volume can stay in any unit, as long as each unit is used consistently for both states.

What is the difference between Boyle's law and Charles's law?

Boyle's law links pressure and volume at constant temperature and is an inverse relationship: pressure up, volume down. Charles's law links volume and temperature at constant pressure and is direct: temperature up, volume up. Both need the same amount of gas.

What is Gay-Lussac's law?

At constant volume and amount, the pressure of a gas is directly proportional to its absolute temperature, P₁/T₁ = P₂/T₂. It explains why a sealed can or a car tyre rises in pressure when heated. The name is also used for the law of combining volumes in some textbooks.

Can the combined gas law be used with Celsius?

Only after converting to kelvin. Add 273.15 to Celsius or use K = (°F + 459.67) × 5/9 for Fahrenheit. The calculator does this for you, and it reports an error for any temperature at or below absolute zero.