# Ideal gas law calculator

> Solve the ideal gas law PV = nRT for pressure, volume, moles or temperature in any units, or find a new state with the combined gas law.

Interactive version: https://www.calcopenly.com/science/ideal-gas-law-calculator
Subject: Science calculators

The ideal gas law, PV = nRT, links the pressure, volume, amount and absolute temperature of a gas through the molar gas constant R = 8.314 462 618… J/(mol·K). Choose the unknown and enter the other three in any units; the calculator converts to pascals, cubic metres, moles and kelvin before solving. The combined gas law mode holds the amount fixed and uses P₁V₁/T₁ = P₂V₂/T₂ to find a new pressure, volume or temperature.

Students use it to find the volume of gas a reaction gives off, and engineers use it to estimate how much gas a tank holds. With the defaults, 1 mol at 0 °C and 1 atm occupies 22.414 L, the CODATA molar volume of an ideal gas at those conditions.

The law ignores molecular size and attraction. Carbon dioxide at 25 °C and 1 atm deviates from it by about 0.5 %; the calculator warns above 100 bar or below 150 K, where a van der Waals or virial equation fits better.

## Inputs

- **Law** (options: PV = nRT, Combined gas law)
- **Solve for** (options: Pressure, Volume, Amount, Temperature)
- **Pressure P**
- **Volume V**
- **Amount of gas n**
- **Amount unit** (options: µmol, mmol, mol, kmol)
- **Temperature T**
- **Find the new** (options: Pressure, Volume, Temperature)
- **Initial pressure P₁**
- **Initial volume V₁**
- **Initial temperature T₁**
- **New pressure P₂**
- **New volume V₂**
- **New temperature T₂**

## Results

- Volume (L) — main result
- Pressure (kPa)
- Pressure (atm)
- Amount of gas (mol)
- Temperature (K)
- Temperature (°C)
- Molar volume V/n (L/mol)
- Number of molecules

## Formula

$$
PV = nRT,\ R = 8.314\,462\,618\ldots\ \mathrm{J\,mol^{-1}\,K^{-1}}\ (\text{exact});\qquad \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
$$

## Worked examples

### 1 mol at 0 °C and 1 atm

- Law: PV = nRT
- Solve for: Volume
- Pressure P: 1 atm
- Amount of gas n: 1
- Amount unit: mol
- Temperature T: 0 °C
- **Volume: 22.414 L**
- Checked against: CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol

### Pressure of 2 mol in 10 L at 300 K

- Law: PV = nRT
- Solve for: Pressure
- Volume V: 10 L
- Amount of gas n: 2
- Amount unit: mol
- Temperature T: 300 K
- **Pressure: 498.868 kPa**
- Checked against: Python 3.8 decimal: 2 × 8.31446261815324 × 300 / 0.01 = 498867.757 Pa

### Moles in 1 m³ at 100 kPa and 25 °C

- Law: PV = nRT
- Solve for: Amount
- Pressure P: 100 kPa
- Volume V: 1 m³
- Temperature T: 25 °C
- **Amount of gas: 40.3395 mol**
- Checked against: Python 3.8 decimal: 100000 / (8.31446261815324 × 298.15) = 40.3395455

### Temperature of 1 mol in 24.465 L at 1 atm

- Law: PV = nRT
- Solve for: Temperature
- Pressure P: 1 atm
- Volume V: 24.465 L
- Amount of gas n: 1
- Amount unit: mol
- **Temperature: 298.145 K**
- Checked against: Python 3.8 decimal: 101325 × 0.024465 / 8.31446261815324 = 298.14508 K

### Sealed can heated: pressure and temperature both change

- Law: Combined gas law
- Find the new: Temperature
- Initial pressure P₁: 100 kPa
- Initial volume V₁: 2 L
- Initial temperature T₁: 293.15 K
- New pressure P₂: 150 kPa
- New volume V₂: 2 L
- **Temperature: 439.725 K**
- Checked against: Python 3.8 decimal: T₂ = 293.15 × 150 × 2 / (100 × 2) = 439.725 K (Gay-Lussac)

### Double the pressure and the absolute temperature: volume unchanged

- Law: Combined gas law
- Find the new: Volume
- Initial pressure P₁: 1 atm
- Initial volume V₁: 10 L
- Initial temperature T₁: 300 K
- New pressure P₂: 2 atm
- New temperature T₂: 600 K
- **Volume: 10 L**
- Checked against: Combined gas law: V₂ = V₁ (P₁/P₂)(T₂/T₁) = 10 × ½ × 2

## Questions

### What is the value of R in PV = nRT?

R = 8.314 462 618 153 24 J/(mol·K), exact since the 2019 SI revision because it is the product of two fixed constants, the Avogadro constant and the Boltzmann constant. In other units it is 0.082 057 L·atm/(mol·K), 8.314 L·kPa/(mol·K) and 62.364 L·mmHg/(mol·K). Use the version that matches your pressure and volume units, or convert everything to SI as this calculator does.

### What volume does one mole of gas occupy at STP?

It depends on which STP is meant. At 0 °C and 1 atm (101.325 kPa), one mole of ideal gas occupies 22.414 L; at 0 °C and 100 kPa, the standard pressure IUPAC has recommended since 1982, it occupies 22.711 L; at 25 °C and 1 atm it occupies 24.465 L. Check which definition your textbook or exam uses, since the first two differ by 1.3 %.

### Why does temperature have to be in kelvin?

Gas pressure and volume are proportional to absolute temperature, which starts at absolute zero, −273.15 °C. Going from 10 °C to 20 °C looks like doubling, but the absolute temperature only rises from 283.15 K to 293.15 K, a 3.5 % increase, so at constant pressure the gas expands by 3.5 %, not 100 %. The calculator converts °C and °F to kelvin before solving.

### What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. It merges Boyle's law (PV constant at fixed temperature), Charles's law (V/T constant at fixed pressure) and Gay-Lussac's law (P/T constant at fixed volume). Heating a sealed rigid container from 20 °C to 40 °C raises 100 kPa to 106.8 kPa, because the pressure scales with 313.15 K ÷ 293.15 K.

### How accurate is the ideal gas law calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “1 mol at 0 °C and 1 atm” is checked against CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol.

### Where does the method come from?

CODATA 2022 — molar gas constant R and molar volume of an ideal gas (22.413 969 54 L/mol at 273.15 K, 101.325 kPa); OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law.

## Sources

- [CODATA 2022 — molar gas constant R and molar volume of an ideal gas (22.413 969 54 L/mol at 273.15 K, 101.325 kPa)](https://physics.nist.gov/cgi-bin/cuu/Value?mvol)
- [OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law](https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law)