Combined Gas Law Calculator – Solve P₁V₁/T₁ = P₂V₂/T₂ Instantly
The Combined Gas Law unifies three classical gas laws — Boyle's Law, Charles's Law, and Gay-Lussac's Law — into a single relationship. This free online Combined Gas Law calculator lets you solve for any unknown final-state variable (P₂, V₂, or T₂) given the other five values, with automatic unit conversion across pressure, volume, and temperature scales.
Whether you are studying for a chemistry exam, working on a lab report, or solving an engineering problem, this tool handles all unit conversions automatically so you can focus on the physics.
📘 What is the Combined Gas Law?
The Combined Gas Law describes how the pressure, volume, and absolute temperature of a fixed amount of ideal gas are related when the gas changes from one state to another:
where subscript 1 = initial state, subscript 2 = final state, temperature in Kelvin.
It combines three simpler laws that each hold only one variable constant:
- Boyle's Law (constant T): P₁V₁ = P₂V₂
- Charles's Law (constant P): V₁/T₁ = V₂/T₂
- Gay-Lussac's Law (constant V): P₁/T₁ = P₂/T₂
The Combined Gas Law works for any two-state transition where the amount of gas (moles) stays constant. Unlike the Ideal Gas Law (PV = nRT), you do not need to know the number of moles.
⚙️ Solving for Each Unknown
Rearranging P₁V₁/T₁ = P₂V₂/T₂ for each possible unknown gives three working formulas:
P₂ = (P₁ × V₁ × T₂) / (T₁ × V₂)
V₂ = (P₁ × V₁ × T₂) / (T₁ × P₂)
T₂ = (P₂ × V₂ × T₁) / (P₁ × V₁)This calculator applies the appropriate formula automatically based on your selection. All inputs are converted to SI units (Pa, m³, K) before calculation and converted back to your chosen units for display.
🌡️ Temperature — Why Kelvin Matters
Gas laws are built on the kinetic theory of gases, where temperature represents the average kinetic energy of molecules. This relationship is only proportional on an absolute scale — Kelvin — because it starts at true zero (0 K = −273.15 °C), where molecular motion theoretically stops.
K = °C + 273.15 | K = (°F − 32) × 5/9 + 273.15🧮 Worked Examples
Example 1 — Hot Air Balloon: A balloon contains 1 000 L of air at 1 atm and 300 K. The air is heated to 400 K at the same pressure. What is the new volume?
V₂ = (P₁ × V₁ × T₂) / (T₁ × P₂)
V₂ = (1 atm × 1000 L × 400 K) / (300 K × 1 atm)
V₂ = 1333 LHeating the gas from 300 K to 400 K (a 33 % increase) expands the balloon volume by 33 %, from 1 000 L to 1 333 L.
Example 2 — Scuba Tank to Depth: A gas sample occupies 6 L at 1 atm and 293 K at the surface. At depth, the pressure rises to 3 atm and temperature drops to 278 K. What is the new volume?
V₂ = (1 × 6 × 278) / (293 × 3)
V₂ = 1668 / 879 ≈ 1.90 LBoth higher pressure and lower temperature reduce the gas volume, from 6 L to approximately 1.90 L.
Example 3 — Finding Final Temperature: A gas at 2 atm, 5 L, 300 K is compressed to 4 atm and 3 L. What temperature does it reach?
T₂ = (P₂ × V₂ × T₁) / (P₁ × V₁)
T₂ = (4 × 3 × 300) / (2 × 5)
T₂ = 3600 / 10 = 360 K (≈ 87 °C)💡 Practical Tips
- Verify the PV/T constant: After solving, check that P₁V₁/T₁ ≈ P₂V₂/T₂. Both sides should be equal (within rounding error).
- Sign check for temperature: Ensure the Kelvin value is positive. A negative Kelvin result means the inputs are physically impossible.
- Use at least 4 significant figures for temperature in Kelvin near room temperature — rounding to 2 sig figs introduces noticeable error.
- Moles must stay constant: The Combined Gas Law does not apply if gas is added or removed between states. Use the Ideal Gas Law (PV = nRT) in those situations.
🔗 Related Gas Laws and Tools
The Combined Gas Law is part of a family of foundational gas laws. Use the specialised calculators when one variable is held constant:
- Boyle's Law Calculator — P₁V₁ = P₂V₂ at constant temperature.
- Charles's Law Calculator — V₁/T₁ = V₂/T₂ at constant pressure.
- Ideal Gas Law Calculator — PV = nRT for single-state problems where moles are known.
- Pressure Converter — convert between atm, Pa, kPa, bar, mmHg, and more.