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Combined Gas Law Calculator

Calculate initial and final pressure, volume, and temperature of a gas system using the Combined Gas Law (P1V1/T1 = P2V2/T2) with automatic Kelvin conversion.

Gas Settings

Initial State (1)

Final State (2)

Calculated Value

Final Volume (V₂)1.3333L
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What is Combined Gas Law (Pressure-Volume-Temperature)?

The Combined Gas Law merges Boyle's Law (P vs V), Charles's Law (V vs T), and Gay-Lussac's Law (P vs T) into a single equation: (P₁V₁)/T₁ = (P₂V₂)/T₂. It describes the behavior of a fixed amount of ideal gas when pressure, volume, and temperature all change simultaneously. This is the most general form of the simple gas laws and reduces to any individual law when one variable is held constant.

Mathematical Foundation

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
P1P_1= Initial pressure (atm, kPa, mmHg, or torr). Must match P₂ units.
V1V_1= Initial volume (L, mL, or m³). Must match V₂ units.
T1T_1= Initial absolute temperature in Kelvin. Convert: K = °C + 273.15 or K = (°F − 32) × 5/9 + 273.15.
P2P_2= Final pressure in the same units as P₁.
V2V_2= Final volume in the same units as V₁.
T2T_2= Final absolute temperature in Kelvin. Must be > 0 K.

Laws & Principles

  • Kelvin Only: Temperature MUST be in Kelvin. Using Celsius or Fahrenheit in the ratio produces catastrophically wrong results because those scales have arbitrary zero points. This calculator converts automatically, but always verify.
  • Unit Consistency: P₁ and P₂ must use the same pressure unit. V₁ and V₂ must use the same volume unit. The Combined Gas Law does not perform unit conversion — it assumes both sides use matched units.
  • Fixed Amount of Gas: The law assumes no gas is added or removed. If gas leaks from the system or more gas is injected, the Ideal Gas Law (PV = nRT) is needed instead.
  • Ideal Gas Assumption: Real gases deviate at very high pressures (>100 atm) or near their liquefaction point. For those cases, use the van der Waals equation with gas-specific correction constants.

Step-by-Step Example Walkthrough

" A weather balloon at sea level holds 2 L of helium at 1 atm and 300 K. It rises to an altitude where pressure drops to 0.5 atm and temperature drops to 250 K. What is the new volume? "

  1. 1. Identify knowns: P₁ = 1 atm, V₁ = 2 L, T₁ = 300 K, P₂ = 0.5 atm, T₂ = 250 K.
  2. 2. Rearrange for V₂: V₂ = (P₁ × V₁ × T₂) / (T₁ × P₂) = (1 × 2 × 250) / (300 × 0.5).
  3. 3. Calculate: V₂ = 500 / 150 = 3.333 L.
Final Result: The balloon expands from 2 L to 3.33 L. The lower pressure allows expansion (Boyle's effect), but the lower temperature partially counteracts it (Charles's effect). Without the temperature drop, it would have expanded to 4 L.

Quick Answer: What is the Combined Gas Law?

The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's Laws into one equation: (P1 x V1) / T1 = (P2 x V2) / T2. It predicts how a fixed amount of gas behaves when pressure, volume, and temperature all change simultaneously. If you hold one variable constant, the equation reduces to eachindividual law. Temperature must always be in Kelvin for the math to work correctly.

How It Reduces to Individual Gas Laws

The Combined Gas Law is the parent equation. When you lock one variable, it simplifies to a named law:

Hold Constant Reduces To Formula Real-World Example
TemperatureBoyle's LawP1V1 = P2V2Squeezing a syringe (isothermal compression)
PressureCharles's LawV1/T1 = V2/T2Hot air balloon expanding as air is heated
VolumeGay-Lussac's LawP1/T1 = P2/T2Pressure cooker heating in a rigid container
NoneCombined Gas LawP1V1/T1 = P2V2/T2Weather balloon rising (P drops, T drops, V changes)

Pro Tips & Common Chemistry Mistakes

Do This

  • ✓Always convert to Kelvin before plugging in. K = C + 273.15. A gas at 25C is 298.15 K. Plugging 25 into the formula instead of 298 produces an answer off by a factor of ~12. This calculator auto-converts, but understanding the why is essential for exams and lab work.
  • ✓Match pressure and volume units on both sides. If P1 is in atm, P2 must also be in atm. If V1 is in liters, V2 must be in liters. The law does not convert units for you.

Avoid This

  • ✗Do not apply when gas is added or removed. The Combined Gas Law assumes a fixed quantity (moles) of gas. If you are filling a tire (adding gas) or a balloon is leaking, you need the full Ideal Gas Law (PV = nRT) which accounts for changing n.
  • ✗Do not use near phase transitions. If a gas is being cooled toward its condensation point (e.g., water vapor near 100C), it stops behaving ideally. The volume collapses as gas liquefies, and the Combined Gas Law no longer applies.

Frequently Asked Questions

When should I use the Combined Gas Law vs. the Ideal Gas Law?

Use the Combined Gas Law when you have a fixed amount of gas changing between two known states (before and after). Use PV = nRT when you need to calculate the number of moles, or when gas is being added or removed from the system. The Combined Gas Law is derived from PV = nRT by setting n and R as constants and comparing two states.

Can I use different temperature units for T1 and T2?

Yes, this calculator supports independent temperature unit selection for T1 and T2. You can enter T1 in Celsius and T2 in Fahrenheit if desired. The calculator converts both to Kelvin internally before performing the calculation. The key requirement is that the math is always done in Kelvin. Both sides of the equation must use the same absolute scale.

Why does this calculator let me solve for any of the 6 variables?

The Combined Gas Law has 6 variables (P1, V1, T1, P2, V2, T2). If you know any 5, the 6th is algebraically determined. In real-world problems, the unknown variable differs by scenario: a chemist might know initial conditions and final P/T but need V2 (balloon problem); an engineer might know both volumes and temperatures but need the final pressure (piston design).

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