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🧪 Gas Laws

Combined Gas Law Calculator

Solve any of pressure, volume or temperature between two states of a fixed gas, using P₁V₁/T₁ = P₂V₂/T₂ — Boyle's, Charles's and Gay-Lussac's laws rolled into one.

P₁V₁/T₁ = P₂V₂/T₂
Solve any of six
Temperature in kelvin
Fixed amount of gas
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Combined gas law — Quick answer

For a fixed amount of gas the group PV/T is constant, linking two states of pressure, volume and absolute temperature.

P₁V₁ / T₁ = P₂V₂ / T₂ (T in kelvin)
V₂ = P₁·V₁·T₂ / (T₁·P₂)

Worked example: 1 atm, 2 L, 300 K → 2 atm, 600 K. V₂ = 1×2×600 / (300×2) = 2 L.

From 1 atm, 2 L, 300 K (PV/T = 0.00667)

New P, TNew volumeNote
2 atm, 600 K2 LP & T double
1 atm, 600 K4 Lheat only
2 atm, 300 K1 Lcompress only

Used for: weather balloons, engines, scuba, gas storage.

🧪 Combined Gas Law Calculator

Leave the one unknown blank. Temperatures in kelvin; both pressures share a unit, both volumes share a unit.

Final pressure P₂
Final volume V₂
Final temp T₂
PV/T constant

⚠️ Temperatures must be in kelvin (°C + 273.15). The law assumes a fixed amount of gas. If the number of moles changes, use the ideal gas law PV = nRT instead.

The combined gas law stitches together the three simple gas laws into a single equation for a fixed amount of gas: P₁V₁/T₁ = P₂V₂/T₂. It says the group PV/T is the same before and after any change, so you can move a gas between two completely different states of pressure, volume and temperature and still tie them together. Hold one variable fixed and it collapses back to Boyle's (constant T), Charles's (constant P) or Gay-Lussac's (constant V) law — this is the master version that handles all three changing at once.

Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the combined gas law derived from PV = nRT.

The combined gas law equations

Combined gas law
P₁V₁ / T₁ = P₂V₂ / T₂ (T in kelvin)
Final volume
V₂ = P₁ × V₁ × T₂ / (T₁ × P₂)
Final pressure
P₂ = P₁ × V₁ × T₂ / (T₁ × V₂)

Because the amount of gas and the gas constant are fixed, the quantity PV/T is conserved between the two states. To solve any one variable, write both PV/T groups, set them equal, and rearrange. Pressure and volume units cancel in their pairs, so you only need consistency within each pair — but temperature, appearing alone in the denominator, must be the absolute kelvin value.

Worked example — two changes at once

Scenario: A gas occupies 2 L at 1 atm and 300 K. It is compressed and heated to 2 atm and 600 K. What is its new volume?

Final volume
V₂ = (1 × 2 × 600) / (300 × 2) = 1200 / 600 = 2 L
Check PV/T
1×2/300 = 0.00667 = 2×2/600 ✓

The doubling of pressure (which would halve the volume) is exactly cancelled by the doubling of absolute temperature (which would double it), so the volume lands back at 2 L. Heat the gas to 600 K without compressing and it expands to 4 L; compress to 2 atm without heating and it shrinks to 1 L. The combined law captures both effects in one step, and the constant PV/T = 0.00667 confirms the answer.

Frequently Asked Questions

What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. The group PV/T stays constant between two states.

How do I solve it?

Rearrange for the unknown, e.g. V₂ = P₁V₁T₂/(T₁P₂). 1×2×600/(300×2) = 2 L.

Why kelvin?

It uses absolute temperature. Add 273.15 to °C. Celsius gives wrong or negative answers.

Combined vs ideal gas law?

Combined compares two states of a fixed gas; ideal (PV=nRT) gives absolute values and handles changing moles.

What stays constant?

The amount of gas (moles) and R. Pressure, volume and temperature may all change.

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