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Gas Laws Calculator

Solves the one unknown final pressure, volume or temperature of a fixed amount of gas from its initial state using Boyle's law (P1V1 = P2V2), Charles's law (V1/T1 = V2/T2), Gay-Lussac's law (P1/T1 = P2/T2) or the combined gas law (P1V1/T1 = P2V2/T2).

Gas law (optional)Which relation to apply; the combined law needs all three initial quantities and two of the final ones. Initial pressure (P1) (optional)Initial pressure in pressure_unit (not needed for Charles's law). Initial volume (V1) (optional)Initial volume in any unit shared with final_volume (not needed for Gay-Lussac's law). Initial temperature (T1) (optional)Initial temperature in temperature_unit (not needed for Boyle's law). Final pressure (P2) (optional)Final pressure in pressure_unit. Leave empty to solve for it. Final volume (V2) (optional)Final volume, same unit as initial_volume. Leave empty to solve for it. Final temperature (T2) (optional)Final temperature in temperature_unit. Leave empty to solve for it. Pressure unit (optional)Unit of the pressure inputs (1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 14.696 psi). Temperature unit (optional)Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).

When to use

A closed gas sample changes pressure, volume or temperature and you need the missing final quantity; temperatures may be entered in °C or K and pressures in atm, kPa, bar, mmHg or psi.

Do not use when: The amount of gas is unknown or changes, or you need moles or molar volume (use ideal-gas-law with PV = nRT); the gas is near condensation or above roughly 10 atm where ideal behaviour fails.

Formula

P1 × V1 / T1 = P2 × V2 / T2 with T in kelvin; Boyle drops T, Charles drops P, Gay-Lussac drops V. Solve: P2 = P1V1T2/(V2T1), V2 = P1V1T2/(P2T1), T2 = T1P2V2/(P1V1)

Ratios are unit-independent, so pressure and volume come out in the units entered; temperatures must be absolute, which is why °C inputs are converted to kelvin before dividing. Amount of gas is assumed constant and the gas ideal.

Inputs

Parameter	Type	Required	Description
`law`	enum: boyle \| charles \| gay_lussac \| combined	default combined	Which relation to apply; the combined law needs all three initial quantities and two of the final ones.
`initial_pressure`	number	no	Initial pressure in pressure_unit (not needed for Charles's law). Range: > 0
`initial_volume`	number	no	Initial volume in any unit shared with final_volume (not needed for Gay-Lussac's law). Range: > 0
`initial_temperature`	number	no	Initial temperature in temperature_unit (not needed for Boyle's law).
`final_pressure`	number	no	Final pressure in pressure_unit. Leave empty to solve for it. Range: > 0
`final_volume`	number	no	Final volume, same unit as initial_volume. Leave empty to solve for it. Range: > 0
`final_temperature`	number	no	Final temperature in temperature_unit. Leave empty to solve for it.
`pressure_unit`	enum: atm \| kpa \| bar \| mmhg \| psi	default atm	Unit of the pressure inputs (1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 14.696 psi).
`temperature_unit`	enum: celsius \| kelvin	default celsius	Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).

Outputs

Output	Type	Unit	Description
`solved_for`	string		final_pressure, final_volume or final_temperature.
`law_used`	string		Name and form of the relation applied.
`final_pressure`	number		P2 in the chosen pressure unit (pressure laws only).
`final_pressure_atm`	number	atm	P2 in standard atmospheres.
`final_pressure_kpa`	number	kPa	P2 in kilopascals.
`final_volume`	number		V2 in the unit of initial_volume (volume laws only).
`final_temperature_k`	number	K	T2 in kelvin (temperature laws only).
`final_temperature_c`	number	°C	T2 in degrees Celsius.
`initial_temperature_k`	number	K	T1 in kelvin, as used in the ratio.
`change_factor`	number		Solved final value divided by its initial value.

Example

Boyle: 2.0 L at 760 mmHg compressed to 0.5 L: {"law":"boyle","initial_pressure":760,"initial_volume":2,"final_volume":0.5,"pressure_unit":"mmhg"} → {"solved_for":"final_pressure","final_pressure":3040,"final_pressure_atm":4,"final_pressure_kpa":405.3,"change_factor":4}

Combined: 10 L at 1 atm, 25 °C to 2 atm, 100 °C: {"law":"combined","initial_pressure":1,"initial_volume":10,"initial_temperature":25,"final_pressure":2,"final_temperature":100} → {"solved_for":"final_volume","final_volume":6.2578,"final_temperature_k":373.15,"initial_temperature_k":298.15,"change_factor":0.62578}

GET https://tttkmbb.com/api/v1/calculate/gas-laws?law=boyle&initial_pressure=760&initial_volume=2&final_volume=0.5&pressure_unit=mmhg

Machine access

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

Sources

OpenStax Chemistry 2e – 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (textbook)
Wikipedia – Combined gas law (reference)
Wikipedia – Boyle's law (reference)

FAQ

Why must temperature be in kelvin?

The gas laws are proportionalities to absolute temperature: doubling 25 °C to 50 °C raises T only from 298 K to 323 K (8%), not 100%. Enter °C and the calculator converts, or set temperature_unit=kelvin.

Which inputs does each law need?

Boyle: P1, V1 and one of P2/V2. Charles: V1, T1 and one of V2/T2. Gay-Lussac: P1, T1 and one of P2/T2. Combined: P1, V1, T1 and two of P2/V2/T2. Inputs irrelevant to the chosen law are ignored.

Related calculators

Ideal Gas Law Calculator — Solve PV = nRT when the amount of gas is involved.
Pressure Converter — Convert pressures between Pa, bar, psi, atm and mmHg.
Temperature Converter — Convert between Celsius, Fahrenheit and kelvin.