Free fall: gravity, and nothing else
Free fall is the idealised case where the only force acting on an object is gravity — no air resistance, no wind, no terminal velocity. It is the version taught first in physics because it is the version with a clean closed-form answer, and it is a genuinely good approximation for dense, compact objects falling modest distances: a dropped tool, a stone off a bridge, the height of a fall in a physics problem. It stops being a good approximation for anything light and wide falling a long way, which is covered below.
The three equations
t = √(2h / g)v = g × th = ½ × g × t²Enter a height and get the fall time and impact velocity, or enter a time and get the height fallen and velocity reached — the same three equations rearranged for whichever variable you have. Standard gravity g = 9.80665 m/s² is used throughout, the internationally defined value for Earth's surface.
Worked examples
| Height | Fall time | Impact velocity |
|---|---|---|
| 1 m | 0.45 s | 4.4 m/s (16 km/h) |
| 10 m (a three-storey building) | 1.43 s | 14.0 m/s (50 km/h) |
| 100 m | 4.52 s | 44.3 m/s (159 km/h) |
| 1,000 m | 14.3 s | 140 m/s (505 km/h) — before accounting for air resistance |
Doubling the height does not double the fall time — time scales with the square root of height, which is why the fall time barely increases from 100 m to 1,000 m in relative terms while the impact speed grows much faster.
Where the idealised answer stops being realistic
Air resistance grows with the square of speed, so it matters very little for a short drop and increasingly for a long one. A coin dropped from a table experiences negligible air resistance and the formulas above are essentially exact. A skydiver falling for thousands of metres reaches terminal velocity — the speed at which air resistance exactly balances gravity, typically around 195 km/h (54 m/s) for a body in a stable belly-down position — well before hitting the ground, and the formulas above would badly overstate the actual impact speed for that case. As a rough guide, the free-fall equations are reliable up to perhaps a few hundred metres for a dense, compact object, and increasingly wrong beyond that or for anything with significant surface area relative to its weight.
Common physics-class checks
- Mass does not appear anywhere in the equations. In true free fall, a hammer and a feather fall at the same rate — famously demonstrated on the airless Moon during Apollo 15. On Earth, the feather's much larger surface area relative to its weight means air resistance dominates almost immediately, which is a statement about air resistance, not about gravity treating them differently.
- Initial velocity is assumed to be zero — an object simply released, not thrown. A thrown or launched object needs the fuller projectile motion equations, which this calculator does not cover.