Combined Gas Law Calculator

Find Final Pressure (P₂)

Enter the initial pressure, volume, and temperature, plus the final volume and temperature, and this calculator solves P₂ = P₁V₁T₂ / (V₂T₁) for you instantly.

Final Pressure Solver

Initial State
Final State
Final Pressure (P₂)

Deriving the Final Pressure Formula

The combined gas law, P₁V₁/T₁ = P₂V₂/T₂, links a gas's pressure, volume, and temperature across two different states. Rearranging it to isolate P₂ gives:

P₂ = P₁V₁T₂ / (V₂T₁)

This single formula already contains Boyle's Law, Charles' Law, and Gay-Lussac's Law as special cases. If T₁ = T₂, the temperature terms cancel and it reduces to Boyle's Law for pressure; the general form simply handles the case where temperature changes too.

This is useful whenever a sealed quantity of gas changes both its container size and its temperature at the same time, and you need to know the resulting pressure. For example, checking whether a tank will exceed a safe pressure limit after being moved to a hotter environment and having some gas released.

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

Know everything about state 1 and the volume/temperature of state 2. Solve for the missing P₂.

Worked Example: Finding P₂ for a Heated, Expanding Gas

Problem: A gas starts at 2.00 atm, 4.00 L, and 280 K. It's heated to 350 K and allowed to expand to 6.00 L. Find P₂.

Given: P₁ = 2.00 atm, V₁ = 4.00 L, T₁ = 280 K, V₂ = 6.00 L, T₂ = 350 K. P₂ = P₁V₁T₂ / (V₂T₁) P₂ = (2.00 × 4.00 × 350) / (6.00 × 280) P₂ ≈ 1.67 atm

Even though heating alone (Gay-Lussac's Law) would raise pressure, the volume increase here (Boyle's Law effect) more than offsets it, so the net result is a lower final pressure than the starting 2.00 atm. This is exactly the kind of combined effect the standalone Boyle's or Charles' Law calculators can't capture on their own, you need all six variables from the combined gas law to get it right.

Common Mistakes When Finding P₂

The most frequent mistake is forgetting to convert both T₁ and T₂ to Kelvin before substituting into P₂ = P₁V₁T₂ / (V₂T₁). Because temperature appears twice in this formula: once in the numerator, once in the denominator, an unconverted Celsius value doesn't just shift the answer slightly, it can distort the ratio significantly, especially for smaller temperature values where the Celsius-to-Kelvin offset of 273.15 is proportionally large.

A second mistake is entering V₁ and V₂ in different units without converting. Since volume appears once in the numerator (V₁) and once in the denominator (V₂), using inconsistent units there directly and silently distorts the pressure ratio, unlike an error that would cause an obviously impossible result.

A third pitfall is applying this five-variable formula to a problem that's actually simpler. If you notice that temperature doesn't change between the two states, you're really looking at a Boyle's Law problem and only need three known values, not five; using the full formula still works, but recognizing the simpler special case saves effort and reduces the chance of an entry error.

Find Final Pressure FAQ

How do I find the final pressure of a gas?
Use the combined gas law rearranged for P₂: P₂ = P₁V₁T₂ / (V₂T₁). You need the initial pressure, volume, and temperature (P₁, V₁, T₁) plus the final volume and temperature (V₂, T₂). Enter all five into the calculator above and P₂ is computed instantly.
Why does this calculator need five values instead of four?
Finding a final pressure specifically from the combined gas law requires knowing both states almost completely, everything except the pressure you're solving for. That's five known quantities (P₁, V₁, T₁, V₂, T₂) to find the sixth (P₂). 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 my problem only involves pressure and volume changing, not temperature?
If temperature does not change between the two states, you have an isothermal process and can use the simpler Boyle's Law calculator (P₁V₁ = P₂V₂) directly. It needs only three known values instead of five, since T 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 a direct/inverse proportion built on absolute temperature, so using Celsius or Fahrenheit values directly in the formula 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 V₁ and V₂. The calculator converts everything internally.
What is a typical scenario where I'd need to find P₂?
A common example: a sealed container of gas at known pressure, volume, and temperature is heated or cooled and also allowed to expand or compress to a new known volume and temperature. You need P₂ to know the resulting pressure, for instance to check it stays within a tank's safe operating limit.
What if V₂ and T₂ describe an impossible or extreme scenario?
The formula itself will still return a mathematical answer for any positive inputs, but always sanity-check the result: if a calculated P₂ comes out unreasonably large, double check that temperature was entered on an absolute scale (K or °R) and that volume and pressure units for state 1 versus state 2 weren't mixed. A tiny error in unit conversion often produces a wildly wrong pressure because pressure and volume are inversely related.
Can this formula be used for gas mixtures, like air?
Yes: the combined gas law applies to any fixed quantity of gas that behaves approximately ideally, regardless of whether it's a pure substance or a mixture like air, as long as no gas is added, removed, or chemically converted between the two states.
What if I already know P₂ and need to find P₁ instead?
This page is dedicated specifically to solving for P₂. To solve for P₁ (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 P₁, and computes it from the other five using the rearranged formula P₁ = P₂V₂T₁ / (V₁T₂).

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