An object dropped from rest speeds up by g every second, so the height it falls grows with the square of the time. From 20 m it hits the ground after t = √(2 × 20 ÷ 9.80665) = 2.02 s, at 19.8 m/s: 71 km/h or 44 mph. Type the height, or the time if you timed a fall, pick the planet and the calculator gives the time or the height, the impact speed in three units and how far the object falls in the first and the last second, with the steps.
Falls on Earth, without air resistance
| Height | Time | Speed at impact | km/h | mph |
|---|---|---|---|---|
| 1 m (3.3 ft) | 0.45 s | 4.4 m/s | 16 | 10 |
| 2 m (6.6 ft) | 0.64 s | 6.3 m/s | 23 | 14 |
| 5 m (16.4 ft) | 1.01 s | 9.9 m/s | 36 | 22 |
| 10 m (32.8 ft) | 1.43 s | 14.0 m/s | 50 | 31 |
| 20 m (65.6 ft) | 2.02 s | 19.8 m/s | 71 | 44 |
| 50 m (164 ft) | 3.19 s | 31.3 m/s | 113 | 70 |
| 100 m (328 ft) | 4.52 s | 44.3 m/s | 159 | 99 |
Four times the height only doubles the time and the speed: 5 m takes about 1 s, 20 m about 2 s. A fall from 10 m ends at about the speed of a car in town.
The same 10 m drop elsewhere
| Where | g | Time | Impact speed |
|---|---|---|---|
| Earth | 9.80665 m/s² | 1.43 s | 14.0 m/s |
| Mars | 3.71 m/s² | 2.32 s | 8.6 m/s |
| Moon | 1.62 m/s² | 3.51 s | 5.7 m/s |
| Jupiter (at its cloud tops) | 24.79 m/s² | 0.90 s | 22.3 m/s |
Timing a fall to measure a height
Drop a stone into a well and time it: if it takes 2 seconds, the well is about ½ × 9.81 × 2² = 19.6 m deep. Sound takes another 0.06 s to come back up, so for deep drops your measurement runs slightly long. Choose “The time” in the calculator to do this.
Where the simple formula stops
Air resistance grows with speed until it balances the weight. A falling person stops speeding up at roughly 190–200 km/h (about 120 mph); a raindrop, much sooner. For short drops of dense objects the answers here are very close; for long falls, parachutes or paper, they are an upper limit.
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Frequently asked questions
How long does it take to fall 10 meters?
1.43 seconds, without air resistance: t = √(2h ÷ g) = √(20 ÷ 9.80665). The object lands at 14 m/s, about 50 km/h or 31 mph.
What is the formula for free fall?
From rest: h = ½ g t², v = g t and v = √(2 g h). With g = 9.80665 m/s², a 2-second fall covers 19.6 m and ends at 19.6 m/s.
Do heavy objects fall faster than light ones?
Not in a vacuum: every object speeds up at the same g. In air, drag slows light, broad objects (a feather, a sheet of paper) much more than dense, compact ones (a stone, a ball bearing).
What value of g should I use?
Standard gravity is exactly 9.80665 m/s²; real gravity varies from about 9.78 at the equator to 9.83 at the poles. Textbooks often use 9.8 or 9.81, and some use 10 for quick estimates: type whichever your class uses.
How long would the same fall take on the Moon?
About 2.5 times longer. With g = 1.62 m/s², a 10 m drop takes 3.51 s and ends at only 5.7 m/s.
Sources
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