Last updated: 2026-06-14

Free Fall

Free fall describes the motion of an object acted on by gravity alone, with no air resistance. Dropped from rest, the object falls a distance $h = \tfrac{1}{2} g t^2$ in time $t$ and reaches a speed $v = g t$, where $g$ is the gravitational acceleration — about 9.81 m/s² near Earth's surface. Combining the two gives the impact speed directly from the height: $v = \sqrt{2 g h}$. Because every object accelerates at the same rate regardless of its mass, a feather and a hammer dropped in a vacuum land together, as demonstrated on the Moon during Apollo 15.

This calculator solves for the distance fallen, the time to fall, and the impact speed, starting from either a known fall time or a known height.

Equations of free fall

Because distance depends on $t^2$, an object falls four times as far in twice the time. These are the constant-acceleration equations of motion applied to the special case of an object released from rest.

Worked example

A stone is dropped from a 45 m cliff. The time to reach the ground is:

and its speed on impact is:

That is roughly 107 km/h. Choosing "From fall height" and entering 45 m reproduces both values.

How height and time relate

Because distance grows with $t^2$ while speed grows only linearly with $t$, a fall that lasts twice as long covers four times the distance but ends at only twice the speed. This is why the last moments of a long drop add so much height: a stone falling for 3 seconds covers about 44 m, but one falling for 4 seconds covers 78 m. The calculator works in both directions, returning the impact speed and distance from a fall time, or the time and speed from a fall height. The default gravity is Earth's 9.81 m/s²; presets for the Moon and Mars are tucked into the constants if you need them.

The role of air resistance

These equations assume gravity is the only force, which is a good approximation for dense, compact objects over short distances. In real air, drag grows with speed until it balances gravity and the object stops accelerating, reaching its terminal velocity — about 53 m/s for a skydiver in a spread-eagle position, but far less for a feather or sheet of paper. For light objects or very long falls, the free-fall model overestimates the true speed, and a drag model is needed for accurate results.