Physics · Mechanics
Free fall calculator.
Find how long an object takes to fall and how fast it is going when it lands, from the drop height, or find the height from a measured fall time.
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Free fall formulas
An object dropped from rest with no air resistance falls for t = √(2h ÷ g) and lands at v = √(2gh). Standard gravity is exactly 9.80665 m/s² (NIST CODATA); OpenStax notes that g varies between about 9.78 and 9.83 m/s² with latitude and altitude. With an initial downward speed u the calculator uses h = ut + ½gt² and v² = u² + 2gh.
Worked example. Drop from 100 m on Earth: t = 4.516 s and v = 44.29 m/s (159.4 km/h). The same 100 m on the Moon (g = 1.62 m/s²) takes 11.11 s and ends at 18 m/s. From a fall time of 3 s on Earth the height is 44.13 m and the speed 29.42 m/s.
Real falls are slowed by air drag, and a person or a light object reaches a terminal speed far below these figures. The calculator is a physics-class idealisation, not a safety estimate for falls or drops.
Frequently asked questions
How long does it take to fall 100 metres?
4.516 seconds on Earth with no air resistance, landing at 44.29 m/s.
What value of g does the calculator use?
Earth uses the NIST standard gravity of 9.80665 m/s². Other bodies use NASA surface gravity values, rounded as published.
Does mass affect free fall?
Not without air resistance. Every object falls with the same acceleration g, whatever its mass.
How do I get the height from a stopwatch time?
Choose Fall time. h = ½gt², so 3 s gives 44.13 m on Earth.
Why is real fall speed lower?
Air drag grows with speed until it balances weight, giving a terminal speed. This calculator ignores drag.
Sources
Checked
- OpenStax University Physics Volume 1, 3.5 Free Fall
- NIST CODATA: standard acceleration of gravity (9.806 65 m/s2, exact)
- NASA NSSDC Planetary Fact Sheet (surface gravity row)
- NASA NSSDC Moon Fact Sheet
- NASA NSSDC Mars Fact Sheet
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Scope
Idealised textbook model with no air drag. Not a safety estimate for falls, drops or equipment. Results are arithmetic from the formulas shown, for study and general interest, and not professional or engineering advice.