{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"potential-energy"},"result":{"entity_type":"calculator","id":"potential-energy","calculator_id":"potential-energy","canonical_url":"https://tttkmbb.com/physics/potential-energy","name":"Potential Energy Calculator","title":"Gravitational Potential Energy Calculator – PE = m·g·h in Joules, kJ and kWh","category":"physics","category_name":"Physics","tool_name":"calculate_potential_energy","featured_mcp_tool":false,"description":"Computes the gravitational potential energy of a mass raised to a height near a planet's surface with PE = m·g·h (standard gravity by default), and the speed the mass would reach if it fell that height freely.","use_when":"You need the energy stored by lifting a mass to a height, the minimum work to lift it, or the energy released when it falls (lifted loads, pumped hydro, dropped objects).","do_not_use_when":"Heights are a significant fraction of the planet's radius (g is not constant; use gravitational-force), or you need elastic energy (use hookes-law) or energy of motion (use kinetic-energy).","inputs":[{"name":"mass_kg","label":"Mass","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"Mass of the object in kilograms.","example":70},{"name":"height_m","label":"Height","type":"number","unit":"m","required":true,"min":0,"description":"Height above the reference level (ground) in metres.","example":10},{"name":"gravity_m_s2","label":"Gravitational acceleration","type":"number","unit":"m/s²","required":false,"default":9.80665,"max":10000,"exclusive_min":0,"description":"Local gravitational acceleration. Default is standard gravity g_n = 9.80665 m/s² (Moon ≈ 1.62, Mars ≈ 3.72, Jupiter ≈ 24.8).","example":9.80665}],"outputs":[{"name":"potential_energy_j","label":"Potential energy","type":"number","unit":"J","decimals":4,"description":"PE = m × g × h."},{"name":"potential_energy_kj","label":"Potential energy","type":"number","unit":"kJ","decimals":6,"description":"Potential energy in kilojoules."},{"name":"potential_energy_kwh","label":"Potential energy","type":"number","unit":"kWh","decimals":6,"description":"Potential energy in kilowatt-hours (J ÷ 3,600,000)."},{"name":"fall_speed_m_s","label":"Speed after falling this height","type":"number","unit":"m/s","decimals":4,"description":"√(2·g·h): speed reached if all the potential energy became kinetic energy (no air resistance)."}],"input_schema":{"type":"object","properties":{"mass_kg":{"description":"Mass of the object in kilograms. Unit: kg.","type":"number","exclusiveMinimum":0,"examples":[70],"x-unit":"kg"},"height_m":{"description":"Height above the reference level (ground) in metres. Unit: m.","type":"number","minimum":0,"examples":[10],"x-unit":"m"},"gravity_m_s2":{"description":"Local gravitational acceleration. Default is standard gravity g_n = 9.80665 m/s² (Moon ≈ 1.62, Mars ≈ 3.72, Jupiter ≈ 24.8). Unit: m/s².","type":"number","maximum":10000,"exclusiveMinimum":0,"default":9.80665,"examples":[9.80665],"x-unit":"m/s²"}},"additionalProperties":false,"required":["mass_kg","height_m"]},"output_schema":{"type":"object","properties":{"potential_energy_j":{"description":"PE = m × g × h. Unit: J.","type":"number","x-unit":"J"},"potential_energy_kj":{"description":"Potential energy in kilojoules. Unit: kJ.","type":"number","x-unit":"kJ"},"potential_energy_kwh":{"description":"Potential energy in kilowatt-hours (J ÷ 3,600,000). Unit: kWh.","type":"number","x-unit":"kWh"},"fall_speed_m_s":{"description":"√(2·g·h): speed reached if all the potential energy became kinetic energy (no air resistance). Unit: m/s.","type":"number","x-unit":"m/s"}}},"formula":"PE = mass_kg × gravity_m_s2 × height_m; fall_speed_m_s = √(2 × gravity_m_s2 × height_m)","method":"Valid where g can be treated as constant (heights small compared with the planet's radius, i.e. within a few tens of kilometres of Earth's surface).","sources":[{"name":"HyperPhysics – Gravitational potential energy","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html","type":"reference","retrieved_at":"2026-09-23"},{"name":"NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s²","url":"https://physics.nist.gov/cgi-bin/cuu/Value?gn","type":"standard","retrieved_at":"2026-09-23"}],"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":"70 kg lifted 10 m","inputs":{"mass_kg":70,"height_m":10},"expected":{"potential_energy_j":6864.655,"potential_energy_kj":6.864655,"potential_energy_kwh":0.001907,"fall_speed_m_s":14.0047},"url":"https://tttkmbb.com/api/v1/calculate/potential-energy?mass_kg=70&height_m=10"},{"name":"2 kg at 1.5 m with g = 9.81","inputs":{"mass_kg":2,"height_m":1.5,"gravity_m_s2":9.81},"expected":{"potential_energy_j":29.43,"fall_speed_m_s":5.4249},"url":"https://tttkmbb.com/api/v1/calculate/potential-energy?mass_kg=2&height_m=1.5&gravity_m_s2=9.81"}],"faq":[{"q":"Which reference level should I use?","a":"Any level you choose; only differences in potential energy matter. Height is measured from that reference, and objects below it have negative potential energy."},{"q":"Should I use 9.81 or 9.80665?","a":"9.80665 m/s² is the defined standard gravity; the actual value varies from about 9.78 at the equator to 9.83 at the poles. The difference is under 0.3 %."}],"tags":["potential energy","gravitational potential energy","mgh","energy of height","joules"],"related":[{"calculator_id":"kinetic-energy","reason":"Energy of motion gained when the object falls."},{"calculator_id":"free-fall","reason":"Fall time and impact speed from the same height."},{"calculator_id":"work-power","reason":"Power needed to lift the mass in a given time."}],"links":{"html":"https://tttkmbb.com/physics/potential-energy","markdown":"https://tttkmbb.com/physics/potential-energy.md","json":"https://tttkmbb.com/physics/potential-energy.json","api":"https://tttkmbb.com/api/v1/calculate/potential-energy","schema":"https://tttkmbb.com/api/v1/calculators/potential-energy","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:30:17Z","next_actions":[{"tool":"run_calculator","calculator_id":"potential-energy","reason":"Run Potential Energy Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/potential-energy.md"}}