Combined Gas Law Calculator

Find Final Volume (V₂)

Enter the initial pressure, volume, and temperature, plus the final pressure and temperature, and this calculator solves V₂ = P₁V₁T₂ / (P₂T₁) for you instantly.

Final Volume Solver

Initial State
Final State
Final Volume (V₂)

Deriving the Final Volume Formula

Starting from the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, isolating V₂ gives:

V₂ = P₁V₁T₂ / (P₂T₁)

This formula is exactly what's needed whenever a fixed amount of gas moves to a new pressure and temperature and you need to predict how much space it will occupy. The classic weather balloon problem, or estimating how much a sealed gas sample will expand when heated and depressurized at the same time.

If you already know the volume ratio is small or the final state isn't fully specified, consider whether a simpler single-variable law, Boyle's, Charles', or Gay-Lussac's, fits your data better; they need only three known values instead of five.

State 1 → State 2 State 1 P₁, V₁, T₁ State 2 V₂ = ? P₂, T₂

Know everything about state 1 and the pressure/temperature of state 2. Solve for the missing V₂.

Worked Example: A Rising Weather Balloon

Problem: A weather balloon has volume 3.00 m³ at ground level, where P₁ = 1.00 atm and T₁ = 288 K. At altitude, pressure drops to 0.35 atm and temperature falls to 230 K. Find V₂.

Given: P₁ = 1.00 atm, V₁ = 3.00 m³, T₁ = 288 K, P₂ = 0.35 atm, T₂ = 230 K. V₂ = P₁V₁T₂ / (P₂T₁) V₂ = (1.00 × 3.00 × 230) / (0.35 × 288) V₂ ≈ 6.85 m³

The balloon more than doubles in volume, even though it also cooled substantially, the drop in pressure dominates the effect of the drop in temperature. This is exactly why meteorologists must design weather balloons to handle several times their ground-level volume without bursting before they reach their intended altitude.

Common Mistakes When Finding V₂

The most frequent mistake is forgetting to convert both T₁ and T₂ to Kelvin before substituting into V₂ = P₁V₁T₂ / (P₂T₁). As with finding P₂, temperature appears in both the numerator and denominator here, so an unconverted Celsius or Fahrenheit value distorts the ratio rather than just introducing a small error.

A second mistake is mismatching pressure units between P₁ and P₂. Since P₁ sits in the numerator and P₂ in the denominator, using atm for one and kPa for the other without converting will silently scale the final volume by whatever conversion factor was missed.

A third pitfall is misreading which volume is known and which is unknown in a word problem. Double-check whether the problem gives you the starting volume (V₁, a known input) or is actually asking about the starting volume while giving you the final one; a surprisingly common source of wrong answers is simply plugging values into the wrong slots of the formula.

Find Final Volume FAQ

How do I find the final volume of a gas?
Use the combined gas law rearranged for V₂: V₂ = P₁V₁T₂ / (P₂T₁). You need the initial pressure, volume, and temperature (P₁, V₁, T₁) plus the final pressure and temperature (P₂, T₂). Enter all five into the calculator above and V₂ is computed instantly.
Why does this calculator need five values instead of four?
Finding a final volume from the combined gas law requires knowing both states almost completely, everything except the volume you're solving for. That's five known quantities (P₁, V₁, T₁, P₂, T₂) to find the sixth (V₂). If you only have three values total, you likely want a single-law calculator like Boyle's, Charles', or Gay-Lussac's Law instead.
What if pressure doesn't change between the two states?
If pressure stays the same, you have an isobaric process and can use the simpler Charles' Law calculator (V₁/T₁ = V₂/T₂) directly. It needs only three known values instead of five, since P cancels out entirely.
Does temperature need to be in Kelvin?
Yes, internally. But you can type °C or °F into the calculator and it converts to Kelvin automatically before solving. The combined gas law is built on absolute temperature, so plugging in Celsius or Fahrenheit values directly by hand would give an incorrect result.
What units can I use for pressure and volume?
Pressure can be entered in Pa, kPa, MPa, bar, mbar, atm, mmHg, torr, psi, or inHg. Volume can be entered in m³, L, mL, cm³, dm³, ft³, in³, or gal (US). You can mix different units across P₁ and P₂, or choose whichever unit you want for the resulting V₂. The calculator converts everything internally.
What is a typical scenario where I'd need to find V₂?
A common example: a weather balloon released at ground-level pressure, volume, and temperature rises to an altitude with a known lower pressure and colder temperature. You need V₂ to predict how large the balloon will swell, which matters for whether it will burst before reaching its target altitude.
What if the calculated V₂ seems too large or too small?
Double-check that temperature was converted to Kelvin (not left in °C or °F) and that P₁ and P₂ use the same pressure unit, and V₁ uses whatever unit you want V₂ displayed in. A very common source of an unreasonable answer is accidentally leaving a Celsius value in a Kelvin-only formula, which can flip the direction of the temperature effect entirely.
How is this different from simply using Boyle's Law twice?
Boyle's Law alone assumes temperature never changes, so it cannot account for a situation like a weather balloon rising through both changing pressure and changing temperature, where both effects happen together. The combined gas law formula used here handles both simultaneously in a single calculation, rather than requiring two separate, sequential steps.
What if I already know V₂ and need to find V₁ instead?
This page is dedicated specifically to solving for V₂. To solve for V₁ (or any other one of the six combined gas law variables), use the interactive calculator on the homepage. It lets you leave any single variable blank, including V₁, and computes it from the other five using the rearranged formula V₁ = P₂V₂T₁ / (P₁T₂).

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