How to use it
- Type one value in its box, for example Height of the fall h 20. Leave the other two boxes empty.
- Read Impact speed, which is in km/h, and Time of the fall. The other results are shown below it.
- Check Speed and distance during the fall to see how the speed and the distance grow second by second, then open How it is worked out.
The equations
A body that starts from rest with no air resistance falls with a constant acceleration g. The standard value of g is 9.80665 m/s², which is exact by definition (standard gravity). Near the surface of the Earth the acceleration of free fall is close to that value and does not depend on the mass of the body.
v = gt
h = ½gt²
v² = 2gh
average speed = v ÷ 2- From the height h, the time is t = √(2h ÷ g) and the impact speed is v = √(2gh).
- From the time t, the speed is v = gt and the height is h = ½gt².
- From the impact speed v, the time is t = v ÷ g and the height is h = v² ÷ (2g).
What the calculator does not cover
- Air resistance. A skydiver reaches a terminal speed of about 53 m/s, when drag balances weight, so the real speed never reaches the figure this calculator gives for a long fall.
- A body thrown up or down: the calculator assumes it starts from rest.
- Falls on the Moon or another planet: g is different there, and the calculator uses the value for the Earth's surface.
Worked example: a fall from 20 m
With h = 20 m, the time is t = √(2 × 20 ÷ 9.80665) = 2.02 s. The impact speed is v = √(2 × 9.80665 × 20) = 19.81 m/s, which is 19.81 × 3.6 = 71.3 km/h.
The average speed over the fall is half of the impact speed, 19.81 ÷ 2 = 9.903 m/s, because the speed grows steadily from zero.
| Quantity | Value |
|---|---|
| Distance fallen | 20 m |
| Time of the fall | 2.02 s |
| Impact speed | 19.81 m/s |
| Impact speed in km/h | 71.3 km/h |
| Average speed | 9.903 m/s |
Frequently asked questions
Does the mass of the body change the fall?
Not without air resistance: every body falls with the same acceleration, whatever its mass, as Galileo showed. A feather falls slowly only because the air holds it back.
How do I convert the impact speed to km/h?
Multiply metres per second by 3.6, because one metre per second is 3.6 kilometres per hour. A speed of 19.81 m/s is 71.3 km/h. You can also type the speed in km/h and the calculator converts it.
Why is the average speed half the impact speed?
The speed grows at a steady rate from zero to the impact speed, so its average over the fall is half the final value. The distance is that average multiplied by the time.
Why does a long fall on Earth not reach the speed this calculator gives?
Air drag grows with the square of the speed and balances the weight at a terminal speed, about 53 m/s for a human skydiver. A fall from a great height cannot go faster than that, so this calculator is accurate only for short falls and for falls in a vacuum.
Can I use the height of a building or a cliff?
Yes, if the body is dropped from rest. Type the height in metres. A cliff of 20 m gives the same figures as the example, as long as the air drag is small over that distance.
What if the time is in minutes?
Type it with min or h, for example 2 min. The calculator converts the time to seconds before it works out the height and the speed.
Sources
- Wikipedia: Free fall (acceleration near the Earth's surface and terminal velocity)
- Wikipedia: Standard gravity (9.80665 m/s², exact by definition)
Figures and text last checked on Tuesday, November 10, 2026.