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Ideal Gas Law Calculator

Solves the ideal gas equation PV = nRT for whichever of pressure, volume, amount or temperature is left empty, with pressure in atm, kPa, bar, mmHg or psi and temperature in °C, K or °F.

When to use

You know three of pressure, volume, moles and temperature of a gas and need the fourth, or the molar volume at given conditions.

Do not use when: The gas is near condensation or at very high pressure (use a real-gas equation such as van der Waals), or you need the mass of gas without knowing its molar mass (combine with moles-mass).

Formula

P × V = n × R × T with R = 0.082057366 L·atm/(mol·K) (= 8.314462618 J/(mol·K)); P converted to atm, T to kelvin (K = °C + 273.15)

Ideal-gas behaviour is accurate to about 1% for common gases near room temperature and pressures up to a few atmospheres; deviations grow near the boiling point and above roughly 10 atm.

Inputs

Parameter	Type	Unit	Required	Description
`pressure`	number		no	Gas pressure in the unit given by pressure_unit. Leave empty to solve for it. Range: > 0
`pressure_unit`	enum: atm \| kpa \| bar \| mmhg \| psi		default atm	Unit of the pressure input (1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 14.696 psi).
`volume_l`	number	L	no	Gas volume in litres. Leave empty to solve for it. Range: > 0
`moles`	number	mol	no	Amount of gas in moles. Leave empty to solve for it. Range: > 0
`temperature`	number		no	Gas temperature in the unit given by temperature_unit (must be above absolute zero). Leave empty to solve for it. Range: ≥ -459.67, ≤ 10000000
`temperature_unit`	enum: celsius \| kelvin \| fahrenheit		default celsius	Unit of the temperature input; the calculation uses kelvin.

Outputs

Output	Type	Unit	Description
`solved_for`	string		pressure, volume_l, moles or temperature.
`pressure_atm`	number	atm	Pressure in standard atmospheres.
`pressure_kpa`	number	kPa	Pressure in kilopascals (1 atm = 101.325 kPa).
`pressure_bar`	number	bar	Pressure in bar (1 atm = 1.01325 bar).
`volume_l`	number	L	Gas volume in litres.
`moles`	number	mol	Amount of gas.
`temperature_k`	number	K	Absolute temperature.
`temperature_c`	number	°C	Temperature in degrees Celsius.
`molar_volume_l_per_mol`	number	L/mol	V / n at these conditions (22.414 L/mol at 0 °C and 1 atm).

Example

Molar volume at 0 °C and 1 atm: {"pressure":1,"pressure_unit":"atm","moles":1,"temperature":0,"temperature_unit":"celsius"} → {"solved_for":"volume_l","volume_l":22.414,"molar_volume_l_per_mol":22.414,"temperature_k":273.15,"pressure_kpa":101.325}

Moles in 5 L at 101.325 kPa and 25 °C: {"pressure":101.325,"pressure_unit":"kpa","volume_l":5,"temperature":25} → {"solved_for":"moles","moles":0.20437,"pressure_atm":1,"temperature_k":298.15,"molar_volume_l_per_mol":24.4654}

GET https://tttkmbb.com/api/v1/calculate/ideal-gas-law?pressure=1&pressure_unit=atm&moles=1&temperature=0&temperature_unit=celsius

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/ideal-gas-law (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/ideal-gas-law · Markdown: https://tttkmbb.com/chemistry/ideal-gas-law.md · JSON definition: https://tttkmbb.com/chemistry/ideal-gas-law.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="ideal-gas-law"
OpenAPI operationId: solve_ideal_gas_law
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

Why is the molar volume 22.414 L and not 22.7 L?

22.414 L/mol applies at 0 °C and 1 atm (101.325 kPa). IUPAC's current STP is 0 °C and 1 bar (100 kPa), which gives 22.711 L/mol; enter pressure 1 bar to reproduce it.

Can I enter temperature in Celsius?

Yes, temperature_unit defaults to celsius and the value is converted to kelvin internally; temperatures at or below absolute zero are rejected.

Related calculators

Moles to Grams Calculator — Convert the moles of gas to mass or number of molecules.
Pressure Converter — Pressure expressed in Pa, kPa, bar, psi and atm (or from force and area).
Temperature Converter — Convert between Celsius, Fahrenheit and kelvin.