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Combined Gas Law Calculator

Solve the combined gas law P₁V₁/T₁ = P₂V₂/T₂ for any one of the six values, or switch to Boyle's, Charles's or Gay-Lussac's law when one property stays constant. Mix units freely: temperatures are converted to kelvin for you.

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Gas law
Initial state (1)
Final state (2)
Enter your values to see the result.
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How to use the Combined Gas Law Calculator

  1. Choose the law: combined, or a special case where T, P or V is constant.
  2. Pick the unknown in the Solve for list.
  3. Select units for pressure, volume and temperature.
  4. Enter the other values for the initial and final state.
  5. Press Solve and read the answer, the change factors and the steps.

Gas law formulas

LawConstantFormulaRelationship
Combined gas lawamount of gas (n)P₁V₁ / T₁ = P₂V₂ / T₂All three can change
Boyle's lawn and TP₁V₁ = P₂V₂P and V inversely proportional
Charles's lawn and PV₁ / T₁ = V₂ / T₂V proportional to T
Gay-Lussac's lawn and VP₁ / T₁ = P₂ / T₂P proportional to T
Ideal gas law—PV = nRTR = 0.082057 L·atm/(mol·K) = 8.314 J/(mol·K)

Solving for each variable

UnknownRearranged formula
P₂P₂ = P₁V₁T₂ / (V₂T₁)
V₂V₂ = P₁V₁T₂ / (P₂T₁)
T₂T₂ = P₂V₂T₁ / (P₁V₁)
P₁P₁ = P₂V₂T₁ / (V₁T₂)
V₁V₁ = P₂V₂T₁ / (P₁T₂)
T₁T₁ = P₁V₁T₂ / (P₂V₂)

Pressure unit conversions

1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 760 Torr = 14.696 psi. Standard temperature and pressure (STP) is 0 °C (273.15 K) and 1 atm in many textbooks; IUPAC uses 0 °C and 100 kPa (1 bar). Real gases deviate from these laws at high pressure and low temperature, near condensation.

Frequently asked questions

What is the combined gas law?

For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂: pressure times volume divided by absolute temperature stays constant. It combines Boyle's, Charles's and Gay-Lussac's laws and follows from the ideal gas law PV = nRT with n constant.

Why must temperature be in kelvin?

The gas laws are proportional to absolute temperature. Using °C would give wrong answers (and division by zero at 0 °C). The calculator converts °C and °F to kelvin automatically: K = °C + 273.15.

What is Boyle's law?

At constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Squeezing a syringe from 60 mL to 20 mL triples the pressure.

What is Charles's law?

At constant pressure, volume is proportional to absolute temperature: V₁/T₁ = V₂/T₂. A 3.00 L balloon at 22 °C shrinks to about 2.59 L at −18 °C.

What is Gay-Lussac's law?

At constant volume, pressure is proportional to absolute temperature: P₁/T₁ = P₂/T₂. A rigid container heated from 20 °C to 40 °C sees its absolute pressure rise by about 6.8%.

Can I use gauge pressure such as tire pressure?

The gas laws need absolute pressure. Tire gauges show pressure above atmospheric, so add about 14.7 psi (101.3 kPa) before calculating and subtract it afterwards for the most accurate result.

Does the amount of gas have to stay the same?

Yes. The combined gas law assumes a fixed number of moles. If gas is added or escapes, use the ideal gas law PV = nRT instead.

Are all the tools on FreeToolCabin tested for quality and accuracy?

Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.

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