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Free Fall Calculator

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.

When to use

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.

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)

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.

Inputs

Parameter	Type	Unit	Required	Description
`height_m`	number	m	no	Height fallen in metres. Give either height_m or time_s. Range: ≥ 0
`time_s`	number	s	no	Fall duration in seconds. Give either height_m or time_s. Range: ≥ 0
`gravity_m_s2`	number	m/s²	default 9.80665	Local gravitational acceleration. Default is standard gravity g_n = 9.80665 m/s² (Moon ≈ 1.62, Mars ≈ 3.72, Jupiter ≈ 24.8). Range: > 0, ≤ 10000

Outputs

Output	Type	Unit	Description
`fall_time_s`	number	s	Time to fall the height from rest: √(2h / g).
`height_m`	number	m	Distance fallen: ½ × g × t².
`final_velocity_m_s`	number	m/s	Velocity at the end of the fall: g × t = √(2gh).
`final_velocity_km_h`	number	km/h	Impact velocity in kilometres per hour.
`average_velocity_m_s`	number	m/s	Mean velocity over the fall, half the final velocity.

Example

Dropped from 20 m: {"height_m":20} → {"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}

Falling for 3 s: {"time_s":3} → {"height_m":44.1299,"fall_time_s":3,"final_velocity_m_s":29.42}

GET https://tttkmbb.com/api/v1/calculate/free-fall?height_m=20

Machine access

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

Sources

Wikipedia – Equations for a falling body (reference)
HyperPhysics – Trajectories (reference)
NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s² (standard)

FAQ

Does the object's mass matter?

Not without air resistance: all masses fall with the same acceleration g. With air, heavier and denser objects are affected less by drag.

What if I know both the height and the time?

Provide only one; the other is computed. Giving both returns an INVALID_PARAMETER error because they cannot be independent.

Related calculators

Projectile Motion Calculator — Launched objects with initial speed and angle.
Potential Energy Calculator — Energy released by the fall.
Acceleration Calculator — General constant-acceleration kinematics.