Gravity / Free Fall Calculator

This calculator answers the free-fall question: drop something from a height and find out how long it falls and how fast it is going when it lands, or start from a fall time and work back to the height.

Free-fall formulas (near Earth’s surface): d = ½ × g × t² v = g × t v = √(2 × g × d)

What each variable means:

• g: gravitational acceleration on Earth’s surface = 9.81 m/s² (32.185 ft/s²)
• d: distance fallen (meters or feet)
• t: time of free fall (seconds)
• v: velocity at time t

Worked example, free fall: An object is dropped from a 50-meter building. How long does it take to hit the ground, and how fast is it moving at impact?

d = ½ × g × t² → 50 = ½ × 9.81 × t² → t² = 10.19 → t = 3.19 seconds v = g × t = 9.81 × 3.19 = 31.3 m/s (≈ 113 km/h)

Notice how little of that fall happens early. In the first second the object drops 4.9 m; in the last second before impact it covers 26.6 m. Distance goes as t², so a fall twice as long is four times as far, which is why the difference between a two-storey and a four-storey fall is much worse than “twice as bad”.

Where the free-fall formula comes from

Gravity near the surface is a special case of Newton’s law of universal gravitation, F = G × m₁ × m₂ / r², published in 1687. Set m₁ to the Earth’s mass and r to its radius and the whole clump of constants collapses into a single number, g, that no longer depends on the falling object at all. That is the reason a hammer and a feather land together in a vacuum: the heavier object feels more force, but it also has more inertia, and the two cancel exactly.

For the force between two arbitrary masses, use the Gravitational Force calculator linked below. This page assumes you are near the surface of a planet, where g is effectively constant.

Reference values by planet (surface g):

• Moon: 1.62 m/s² | Mars: 3.72 m/s² | Earth: 9.81 m/s² | Jupiter: 24.8 m/s²

Drop something from 50 m on the Moon and it takes 7.86 seconds instead of 3.19, landing at 12.7 m/s rather than 31.3. That is a survivable landing speed, which is why the Apollo crews could hop around in bulky suits without much worry.

Air resistance is ignored here, and that matters more than people expect. A real object reaches terminal velocity when drag balances weight, around 195 km/h for a skydiver in a stable belly-down position and roughly 25 km/h for a table-tennis ball. Below about 10 m of fall the difference is small for dense objects, but the formula will badly overstate the impact speed of anything light or fluffy.