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Free Fall Calculator

Find how long an object falls and how fast it hits from a given height.

How it is calculated

For an object dropped from rest with no air resistance, the fall time is t = √(2h ÷ g) and the speed on impact is v = g × t. h is the drop height in metres, g is the gravitational acceleration in m/s² (9.81 for Earth, about 1.62 for the Moon, about 3.71 for Mars) and v is given in m/s and in km/h (v × 3.6). If g is empty or not positive, 9.81 is used. Height must be above zero. Real objects meet air drag, so a light or wide object (a leaf, a parachute) falls slower than this ideal result, while for a dense compact object over a short distance the formula is close.

Worked example

An object is dropped from 20 m on Earth, with g = 9.81 m/s². Fall time: √(2 × 20 ÷ 9.81) = √4.0775 = 2.02 s. Impact speed: 9.81 × 2.0194 = 19.81 m/s, which is 71.31 km/h. The mass of the object does not appear anywhere: a heavy and a light compact object dropped together reach the ground at the same moment when drag is ignored.

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Common mistakes

  • Entering height in feet or centimetres. The formula expects metres.
  • Expecting a heavier object to fall faster. Mass cancels out; only height and g matter.
  • Ignoring air resistance for tall drops. Real impact speed from large heights is lower than this ideal figure.
  • Using this for objects thrown downward. The tool assumes the initial speed is zero.

About this calculator

This calculator finds the fall time and impact velocity of an object dropped from a given height under gravity alone (no air resistance), using the kinematic equations h = ½gt² and v = gt, where g is gravitational acceleration (9.81 m/s² on Earth).

Physics students and teachers use it to check homework and demonstrate that, in a vacuum, all objects fall at the same rate regardless of mass — a principle famously associated with Galileo. Gravity can be switched away from Earth's value to model a fall on the Moon or another planet.

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Comments (1)

  • Editorial team

    A feel for the numbers: a 20 m drop takes about 2.02 s and ends at 19.81 m/s, or 71.31 km/h. Mass does not appear in the formula, since without drag all objects fall alike. Change g to explore other worlds; on the Moon (1.62) the same drop lasts 4.97 s. For a compact, dense object over a short fall the ideal result is close, but not for a feather. Which height or planet are you curious about?

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