Free Fall Time Calculator
Free fall is the motion of an object under gravity alone, starting from rest with no air resistance. The time to fall a height h is t = sqrt(2h / g), and the velocity at impact is v = sqrt(2gh). These formulas come directly from the kinematics equation h = (1/2) g t² applied with zero initial velocity. Enter the drop height and the local gravitational acceleration (9.81 m/s² at Earth's surface) to find the fall time and impact speed. Results assume vacuum conditions; real-world falls in air will take longer and reach terminal velocity.
Free fall formulas
t = √(2h / g) | v = √(2gh)
Where h is height (m), g is gravitational acceleration (m/s²), t is fall time (s), and v is impact velocity (m/s). These assume the object starts from rest (initial velocity = 0) in a vacuum.
Free fall reference examples
- 1 m (3.3 ft) drop: t = 0.45 s, v = 4.43 m/s (15.9 km/h)
- 10 m (33 ft) drop: t = 1.43 s, v = 14.0 m/s (50.5 km/h)
- 100 m drop: t = 4.52 s, v = 44.3 m/s (159 km/h)
- Niagara Falls (57 m): t = 3.41 s, v = 33.4 m/s (120 km/h)
- Skydive exit at 4,000 m altitude (vacuum only): t = 28.6 s (real-world terminal velocity is reached around 12 s)
Free fall: frequently asked questions
What is free fall?
Free fall is motion under gravity alone, with no air resistance. In free fall from rest at height h, the time to reach the ground is t = sqrt(2h/g) and the impact velocity is v = sqrt(2gh), where g is gravitational acceleration (9.81 m/s² on Earth).
Does the mass of the object affect free fall time?
No. In the absence of air resistance all objects fall at the same rate regardless of mass. This was famously demonstrated by Galileo and later proven by Apollo 15 astronaut David Scott who dropped a hammer and feather simultaneously on the Moon.
How fast is an object moving when it hits the ground?
The impact velocity is v = sqrt(2gh). For example, from h = 100 m with g = 9.81 m/s²: v = sqrt(2 x 9.81 x 100) = sqrt(1962) = 44.3 m/s (about 159 km/h or 99 mph). This is also the speed an object would need to reach height h if launched straight up.
How does altitude affect free fall time?
At high altitudes g is slightly lower: g = GM/(R+h)² where R is Earth's radius. At sea level g = 9.81 m/s²; at 10 km altitude g = 9.78 m/s². For most practical drop heights the variation in g is negligible.
What if the object has an initial velocity?
If the object starts with a downward velocity v0, the time to fall height h satisfies h = v0 t + (1/2)g t². Solving the quadratic: t = (-v0 + sqrt(v0² + 2gh)) / g. For zero initial velocity (v0 = 0) this reduces to t = sqrt(2h/g).
Official sources
- NIST Reference on Constants: Standard acceleration of gravity.
- OpenStax University Physics Volume 1: Free Fall.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.