{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"free-fall"},"result":{"entity_type":"calculator","id":"free-fall","calculator_id":"free-fall","canonical_url":"https://tttkmbb.com/physics/free-fall","name":"Free Fall Calculator","title":"Free Fall Calculator – Fall Time, Impact Velocity and Height Without Air Resistance","category":"physics","category_name":"Physics","tool_name":"calculate_free_fall","featured_mcp_tool":false,"description":"Computes the time to fall a given height from rest, or the height fallen in a given time, together with the final (impact) velocity, using h = ½·g·t² with no air resistance.","use_when":"An object is dropped from rest near a planet's surface and you need how long it falls, how far, or how fast it lands (a dropped tool, a stone in a well).","do_not_use_when":"Air drag matters (light or fast objects, skydivers, long falls near terminal velocity), the object has an initial velocity or launch angle (use projectile-motion), or heights are comparable to the planet's radius.","inputs":[{"name":"height_m","label":"Drop height","type":"number","unit":"m","required":false,"min":0,"description":"Height fallen in metres. Give either height_m or time_s.","example":20},{"name":"time_s","label":"Fall time","type":"number","unit":"s","required":false,"min":0,"description":"Fall duration in seconds. Give either height_m or time_s."},{"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":"fall_time_s","label":"Fall time","type":"number","unit":"s","decimals":4,"description":"Time to fall the height from rest: √(2h / g)."},{"name":"height_m","label":"Height fallen","type":"number","unit":"m","decimals":4,"description":"Distance fallen: ½ × g × t²."},{"name":"final_velocity_m_s","label":"Impact velocity","type":"number","unit":"m/s","decimals":4,"description":"Velocity at the end of the fall: g × t = √(2gh)."},{"name":"final_velocity_km_h","label":"Impact velocity","type":"number","unit":"km/h","decimals":4,"description":"Impact velocity in kilometres per hour."},{"name":"average_velocity_m_s","label":"Average velocity","type":"number","unit":"m/s","decimals":4,"description":"Mean velocity over the fall, half the final velocity."}],"input_schema":{"type":"object","properties":{"height_m":{"description":"Height fallen in metres. Give either height_m or time_s. Unit: m.","type":"number","minimum":0,"examples":[20],"x-unit":"m"},"time_s":{"description":"Fall duration in seconds. Give either height_m or time_s. Unit: s.","type":"number","minimum":0,"x-unit":"s"},"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},"output_schema":{"type":"object","properties":{"fall_time_s":{"description":"Time to fall the height from rest: √(2h / g). Unit: s.","type":"number","x-unit":"s"},"height_m":{"description":"Distance fallen: ½ × g × t². Unit: m.","type":"number","x-unit":"m"},"final_velocity_m_s":{"description":"Velocity at the end of the fall: g × t = √(2gh). Unit: m/s.","type":"number","x-unit":"m/s"},"final_velocity_km_h":{"description":"Impact velocity in kilometres per hour. Unit: km/h.","type":"number","x-unit":"km/h"},"average_velocity_m_s":{"description":"Mean velocity over the fall, half the final velocity. Unit: m/s.","type":"number","x-unit":"m/s"}}},"formula":"fall_time_s = √(2 × height_m / g); height_m = ½ × g × time_s²; final_velocity_m_s = g × fall_time_s = √(2 × g × height_m)","method":"Object released from rest in a vacuum (no drag), constant g. In air, drag becomes noticeable for a human after roughly 2–3 s of fall and dominates for light objects.","sources":[{"name":"Wikipedia – Equations for a falling body","url":"https://en.wikipedia.org/wiki/Equations_for_a_falling_body","type":"reference","retrieved_at":"2026-09-23"},{"name":"HyperPhysics – Trajectories","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/traj.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":"Dropped from 20 m","inputs":{"height_m":20},"expected":{"fall_time_s":2.0196,"height_m":20,"final_velocity_m_s":19.8057,"final_velocity_km_h":71.3005,"average_velocity_m_s":9.9029},"url":"https://tttkmbb.com/api/v1/calculate/free-fall?height_m=20"},{"name":"Falling for 3 s","inputs":{"time_s":3},"expected":{"height_m":44.1299,"fall_time_s":3,"final_velocity_m_s":29.42},"url":"https://tttkmbb.com/api/v1/calculate/free-fall?time_s=3"}],"faq":[{"q":"Does the object's mass matter?","a":"Not without air resistance: all masses fall with the same acceleration g. With air, heavier and denser objects are affected less by drag."},{"q":"What if I know both the height and the time?","a":"Provide only one; the other is computed. Giving both returns an INVALID_PARAMETER error because they cannot be independent."}],"tags":["free fall","fall time","drop height","impact velocity","gravity","falling object"],"related":[{"calculator_id":"projectile-motion","reason":"Launched objects with initial speed and angle."},{"calculator_id":"potential-energy","reason":"Energy released by the fall."},{"calculator_id":"acceleration","reason":"General constant-acceleration kinematics."}],"links":{"html":"https://tttkmbb.com/physics/free-fall","markdown":"https://tttkmbb.com/physics/free-fall.md","json":"https://tttkmbb.com/physics/free-fall.json","api":"https://tttkmbb.com/api/v1/calculate/free-fall","schema":"https://tttkmbb.com/api/v1/calculators/free-fall","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:23:50Z"}