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Ideal Gas Law Calculator (PV = nRT)

Solve PV = nRT for pressure, volume, moles or temperature in SI units.

Solved P

101388.1904 Pa

In atm

1.0006 atm

Step-by-step working

PV = nRT, R = 8.314462618 J/(mol·K)
Rearranged for P with the other three values → 101388.1904 Pa

Mathematical Formula

PV = nRT, R = 8.314462618 J/(mol·K) (exact SI value).

Overview & Explanation

The ideal gas law relates the state variables of a dilute gas.

How It Works

Pick the unknown.
Rearrange PV = nRT.
Use kelvin for temperature.

Practical Applications

Chemistry problems.
Tank and balloon estimates.

PV = nRT term by term

P is pressure in pascals, V is volume in cubic metres, n is the amount of gas in moles, T is absolute temperature in kelvin and R = 8.314 J/(mol K) is the gas constant. Temperature must be in kelvin: add 273.15 to degrees Celsius.

Example: 2 mol of gas at 300 K in 0.05 cubic metres has P = 2 x 8.314 x 300 / 0.05 = 99,768 Pa, about 99.8 kPa, just under normal atmospheric pressure.

A useful check

One mole at 273.15 K and 101,325 Pa occupies 8.314 x 273.15 / 101,325 = 0.02241 cubic metres, or about 22.4 L. If your answer for similar conditions is far from this, a unit is probably off.

Example 1: 1 mol at 273.15 K in 22.4 L

≈ 1 atm.

Inputs

Solve for: Pressure P · Volume (m³): 0.0224 · Amount (mol): 1 · Temperature (K): 273.15

= entered

Step 1

PV = nRT, R = 8.314462618 J/(mol·K)

Step 2

Rearranged for P with the other three values → 101388.1904 Pa

Solved P

Result

= 101388.1904 Pa

Example 2: volume of 2 mol at 300 K, 1 atm

Room conditions.

Inputs

Solve for: Volume V · Pressure (Pa): 101325 · Amount (mol): 2 · Temperature (K): 300

= entered

Step 1

PV = nRT, R = 8.314462618 J/(mol·K)

Step 2

Rearranged for V with the other three values → 0.0492 m³

Solved V

Result

= 0.0492 m³

How it's calculated & sources

PV = nRT, R = 8.314462618 J/(mol·K) (exact SI value).

Frequently Asked Questions

Why kelvin?

The law needs absolute temperature; °C + 273.15 = K.

When does it fail?

At high pressure or low temperature; use van der Waals there.

What is R?

8.314462618 J/(mol·K), fixed by the 2019 SI redefinition.

When does the ideal gas law fail?

At high pressure or low temperature, where molecules are close together and their own volume and attractions matter. Real-gas equations such as van der Waals handle these cases better.

Can I use litres and atmospheres?

Yes, if you use the matching constant R = 0.08206 L atm/(mol K).