Free Fall Calculator — fall time & impact speed

How it works

Free fall is motion under gravity with no other forces. An object released from rest accelerates downward at a constant g (9.81 m/s² near Earth's surface), so its fall is described by the kinematics h = ½ × g × t² (OpenStax University Physics). Rearranging gives the two quantities people usually want:

• Time to fall — t = √(2h ÷ g)
• Impact speed — v = √(2 × g × h), equivalently v = g × t

Height is in metres, giving time in seconds and speed in metres per second. A striking feature is that mass does not appear — in the absence of air resistance a feather and a hammer dropped from the same height land at the same instant, as famously demonstrated on the Moon. Real drops through air differ because drag grows with speed until it caps the fall at a terminal velocity, which this ideal model ignores.

Worked example

Dropped from 45 m with g = 9.81 m/s²:

• Time to fall: t = √(2 × 45 ÷ 9.81) = √9.174 ≈ 3.03 s
• Impact speed: v = √(2 × 9.81 × 45) = √882.9 ≈ 29.71 m/s

As a check, v = g × t = 9.81 × 3.03 ≈ 29.71 m/s — the two formulas agree.

Frequently asked questions

How long does it take to fall a given height?

Use t = √(2h ÷ g). For a 45 m drop with g = 9.81 m/s², that is √(90 ÷ 9.81) ≈ 3.03 seconds. Doubling the height increases the time by a factor of √2, not 2.

How fast is an object going when it lands?

Its impact speed is v = √(2 × g × h), or equivalently g times the fall time. From 45 m that works out to about 29.71 m/s.

Do heavier objects fall faster?

No. In free fall the acceleration is g regardless of mass, so all objects speed up at the same rate and hit the ground together — provided air resistance is negligible.

Does this account for air resistance?

No. These formulas assume ideal free fall under gravity only. In air, drag slows the fall and limits it to a terminal velocity, so real impact speeds from large heights are lower than the formula predicts.

What is g?

g is the acceleration due to gravity, about 9.81 m/s² near Earth's surface. It is smaller elsewhere — roughly 1.62 m/s² on the Moon — which you can enter to model a fall on another body.

What is terminal velocity?

Terminal velocity is the steady speed a falling object reaches when air resistance grows to balance gravity, after which it stops accelerating. This calculator models ideal free fall without drag, so it does not cap the speed — real objects falling far through air level off at their terminal velocity.