{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"gas-laws"},"result":{"entity_type":"calculator","id":"gas-laws","calculator_id":"gas-laws","canonical_url":"https://tttkmbb.com/chemistry/gas-laws","name":"Gas Laws Calculator","title":"Gas Laws Calculator – Boyle's, Charles's, Gay-Lussac's and Combined Gas Law for a Fixed Amount of Gas","category":"chemistry","category_name":"Chemistry","tool_name":"solve_gas_laws","featured_mcp_tool":false,"description":"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).","use_when":"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.","inputs":[{"name":"law","label":"Gas law","type":"enum","required":false,"default":"combined","values":[{"value":"boyle","label":"Boyle's law P1V1 = P2V2 (constant T)","aliases":["boyles","boyle's","boyle-mariotte"]},{"value":"charles","label":"Charles's law V1/T1 = V2/T2 (constant P)","aliases":["charles's","charless"]},{"value":"gay_lussac","label":"Gay-Lussac's law P1/T1 = P2/T2 (constant V)","aliases":["gay-lussac","gaylussac","amontons"]},{"value":"combined","label":"Combined gas law P1V1/T1 = P2V2/T2"}],"description":"Which relation to apply; the combined law needs all three initial quantities and two of the final ones.","example":"combined"},{"name":"initial_pressure","label":"Initial pressure (P1)","type":"number","required":false,"exclusive_min":0,"description":"Initial pressure in pressure_unit (not needed for Charles's law).","example":1},{"name":"initial_volume","label":"Initial volume (V1)","type":"number","required":false,"exclusive_min":0,"description":"Initial volume in any unit shared with final_volume (not needed for Gay-Lussac's law).","example":10},{"name":"initial_temperature","label":"Initial temperature (T1)","type":"number","required":false,"description":"Initial temperature in temperature_unit (not needed for Boyle's law).","example":25},{"name":"final_pressure","label":"Final pressure (P2)","type":"number","required":false,"exclusive_min":0,"description":"Final pressure in pressure_unit. Leave empty to solve for it.","example":2},{"name":"final_volume","label":"Final volume (V2)","type":"number","required":false,"exclusive_min":0,"description":"Final volume, same unit as initial_volume. Leave empty to solve for it."},{"name":"final_temperature","label":"Final temperature (T2)","type":"number","required":false,"description":"Final temperature in temperature_unit. Leave empty to solve for it.","example":100},{"name":"pressure_unit","label":"Pressure unit","type":"enum","required":false,"default":"atm","values":[{"value":"atm","label":"atm"},{"value":"kpa","label":"kPa","aliases":["kilopascal"]},{"value":"bar","label":"bar"},{"value":"mmhg","label":"mmHg (Torr)","aliases":["torr"]},{"value":"psi","label":"psi"}],"description":"Unit of the pressure inputs (1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 14.696 psi).","example":"atm"},{"name":"temperature_unit","label":"Temperature unit","type":"enum","required":false,"default":"celsius","values":[{"value":"celsius","label":"°C","aliases":["c"]},{"value":"kelvin","label":"K","aliases":["k"]}],"description":"Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).","example":"celsius"}],"outputs":[{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"final_pressure, final_volume or final_temperature."},{"name":"law_used","label":"Law","type":"string","decimals":4,"description":"Name and form of the relation applied."},{"name":"final_pressure","label":"Final pressure","type":"number","decimals":6,"description":"P2 in the chosen pressure unit (pressure laws only)."},{"name":"final_pressure_atm","label":"Final pressure","type":"number","unit":"atm","decimals":6,"description":"P2 in standard atmospheres."},{"name":"final_pressure_kpa","label":"Final pressure","type":"number","unit":"kPa","decimals":4,"description":"P2 in kilopascals."},{"name":"final_volume","label":"Final volume","type":"number","decimals":6,"description":"V2 in the unit of initial_volume (volume laws only)."},{"name":"final_temperature_k","label":"Final temperature","type":"number","unit":"K","decimals":3,"description":"T2 in kelvin (temperature laws only)."},{"name":"final_temperature_c","label":"Final temperature","type":"number","unit":"°C","decimals":3,"description":"T2 in degrees Celsius."},{"name":"initial_temperature_k","label":"Initial temperature","type":"number","unit":"K","decimals":3,"description":"T1 in kelvin, as used in the ratio."},{"name":"change_factor","label":"Change factor","type":"number","decimals":6,"description":"Solved final value divided by its initial value."}],"input_schema":{"type":"object","properties":{"law":{"description":"Which relation to apply; the combined law needs all three initial quantities and two of the final ones.","type":"string","enum":["boyle","charles","gay_lussac","combined"],"default":"combined","examples":["combined"]},"initial_pressure":{"description":"Initial pressure in pressure_unit (not needed for Charles's law).","type":"number","exclusiveMinimum":0,"examples":[1]},"initial_volume":{"description":"Initial volume in any unit shared with final_volume (not needed for Gay-Lussac's law).","type":"number","exclusiveMinimum":0,"examples":[10]},"initial_temperature":{"description":"Initial temperature in temperature_unit (not needed for Boyle's law).","type":"number","examples":[25]},"final_pressure":{"description":"Final pressure in pressure_unit. Leave empty to solve for it.","type":"number","exclusiveMinimum":0,"examples":[2]},"final_volume":{"description":"Final volume, same unit as initial_volume. Leave empty to solve for it.","type":"number","exclusiveMinimum":0},"final_temperature":{"description":"Final temperature in temperature_unit. Leave empty to solve for it.","type":"number","examples":[100]},"pressure_unit":{"description":"Unit of the pressure inputs (1 atm = 101.325 kPa = 1.01325 bar = 760 mmHg = 14.696 psi).","type":"string","enum":["atm","kpa","bar","mmhg","psi"],"default":"atm","examples":["atm"]},"temperature_unit":{"description":"Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).","type":"string","enum":["celsius","kelvin"],"default":"celsius","examples":["celsius"]}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"solved_for":{"description":"final_pressure, final_volume or final_temperature.","type":"string"},"law_used":{"description":"Name and form of the relation applied.","type":"string"},"final_pressure":{"description":"P2 in the chosen pressure unit (pressure laws only).","type":"number"},"final_pressure_atm":{"description":"P2 in standard atmospheres. Unit: atm.","type":"number","x-unit":"atm"},"final_pressure_kpa":{"description":"P2 in kilopascals. Unit: kPa.","type":"number","x-unit":"kPa"},"final_volume":{"description":"V2 in the unit of initial_volume (volume laws only).","type":"number"},"final_temperature_k":{"description":"T2 in kelvin (temperature laws only). Unit: K.","type":"number","x-unit":"K"},"final_temperature_c":{"description":"T2 in degrees Celsius. Unit: °C.","type":"number","x-unit":"°C"},"initial_temperature_k":{"description":"T1 in kelvin, as used in the ratio. Unit: K.","type":"number","x-unit":"K"},"change_factor":{"description":"Solved final value divided by its initial value.","type":"number"}}},"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)","method":"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.","sources":[{"name":"OpenStax Chemistry 2e – 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law","url":"https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law","type":"textbook","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Combined gas law","url":"https://en.wikipedia.org/wiki/Combined_gas_law","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Boyle's law","url":"https://en.wikipedia.org/wiki/Boyle%27s_law","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Boyle: 2.0 L at 760 mmHg compressed to 0.5 L","inputs":{"law":"boyle","initial_pressure":760,"initial_volume":2,"final_volume":0.5,"pressure_unit":"mmhg"},"expected":{"solved_for":"final_pressure","final_pressure":3040,"final_pressure_atm":4,"final_pressure_kpa":405.3,"change_factor":4},"url":"https://tttkmbb.com/api/v1/calculate/gas-laws?law=boyle&initial_pressure=760&initial_volume=2&final_volume=0.5&pressure_unit=mmhg"},{"name":"Combined: 10 L at 1 atm, 25 °C to 2 atm, 100 °C","inputs":{"law":"combined","initial_pressure":1,"initial_volume":10,"initial_temperature":25,"final_pressure":2,"final_temperature":100},"expected":{"solved_for":"final_volume","final_volume":6.2578,"final_temperature_k":373.15,"initial_temperature_k":298.15,"change_factor":0.62578},"url":"https://tttkmbb.com/api/v1/calculate/gas-laws?law=combined&initial_pressure=1&initial_volume=10&initial_temperature=25&final_pressure=2&final_temperature=100"}],"faq":[{"q":"Why must temperature be in kelvin?","a":"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."},{"q":"Which inputs does each law need?","a":"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."}],"tags":["boyle's law","charles's law","gay-lussac's law","combined gas law","gas pressure volume temperature","p1v1 = p2v2"],"related":[{"calculator_id":"ideal-gas-law","reason":"Solve PV = nRT when the amount of gas is involved."},{"calculator_id":"pressure","reason":"Convert pressures between Pa, bar, psi, atm and mmHg."},{"calculator_id":"temperature","reason":"Convert between Celsius, Fahrenheit and kelvin."}],"links":{"html":"https://tttkmbb.com/chemistry/gas-laws","markdown":"https://tttkmbb.com/chemistry/gas-laws.md","json":"https://tttkmbb.com/chemistry/gas-laws.json","api":"https://tttkmbb.com/api/v1/calculate/gas-laws","schema":"https://tttkmbb.com/api/v1/calculators/gas-laws","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:49:58Z","next_actions":[{"tool":"run_calculator","calculator_id":"gas-laws","reason":"Run Gas Laws Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/chemistry/gas-laws.md"}}