Free Fall Calculator (Time, Height and Impact Speed)
How far and how fast something falls in a given time, how long a drop takes, or the height behind an impact speed — no air resistance.
Inputs
| Drop | Time | Impact speed | |
|---|---|---|---|
| 1 m | 0.45 s | 4.43 m/s | 9.91 mph |
| 2 m | 0.64 s | 6.26 m/s | 14.01 mph |
| 5 m | 1.01 s | 9.90 m/s | 22.15 mph |
| 10 m | 1.43 s | 14.00 m/s | 31.33 mph |
| 20 m | 2.02 s | 19.81 m/s | 44.30 mph |
| 50 m | 3.19 s | 31.32 m/s | 70.05 mph |
| 100 m | 4.52 s | 44.29 m/s | 99.07 mph |
| 200 m | 6.39 s | 62.63 m/s | 140.10 mph |
| 500 m | 10.10 s | 99.03 m/s | 221.52 mph |
- Working
- s = ½ × 9.80665 × 3² = 44.1299 m; v = 9.80665 × 3 = 29.42 m/s
- Time
- 3 s
- Height
- 44.13 m (144.78 ft)
- Speed at the bottom
- 29.42 m/s = 105.9 km/h = 65.8 mph
- Average speed on the way down
- 14.71 m/s (half the final speed)
- No air resistance: real objects fall slower once drag matters, and a person reaches terminal velocity long before 1,000 m.
Use this calculator on your own site
Free embed
- Two lines of HTML, unlimited views
- Shows a small CalculateEveryday bar, with a credit link under the calculator
What each Free Fall input means
- I know the
- Start from the time of the fall, the height of the drop, or the speed at impact; the page finds the other two.
- Time
- Seconds since release, for the first mode.
- Height
- The drop height, for the second mode.
- Height unit
- Metres or feet, converted at exactly 0.3048 m a foot.
- Impact speed
- The speed in m/s, for the third mode: the page finds the drop that produces it.
- Gravity
- 9.80665 m/s² on Earth by default; 1.62 on the Moon, 3.72 on Mars.
Free Fall formula
From rest, no air: distance s = ½ g t² · speed v = g t · from a height: t = √(2s ÷ g), v = √(2 g s) · from a speed: t = v ÷ g, s = v² ÷ (2g)
An object dropped from rest speeds up by g — about 9.8 m/s — every second, so after t seconds it is moving at gt and has fallen ½gt², because its average speed over the fall was half its final speed. Turn the same two equations round and a known drop height gives the time, √(2s/g), and the impact speed, √(2gs); a known impact speed gives the height it must have fallen from, v²/2g. Those three questions are the three modes here, with heights in metres or feet and the speed shown in m/s, km/h and mph. The table under the result lists common drops so a '100 feet' or '50 metres' question is answered without retyping. All of it assumes no air resistance, which is accurate for a dense object over a few metres and increasingly wrong for long falls, where drag caps the speed.
Free Fall worked example
After 3 seconds of free fall from rest: distance = ½ × 9.80665 × 3² = 44.1 m, and speed = 9.80665 × 3 = 29.4 m/s, which is 106 km/h or 66 mph. Run the other way, a 100-foot drop (30.48 m) takes √(2 × 30.48 ÷ 9.80665) = 2.49 seconds and ends at 24.4 m/s (55 mph); a 10 m drop takes 1.43 s and ends at 14.0 m/s.
Where the Free Fall calculator can give the wrong answer
- No air resistance is the big assumption. Drag grows with speed until it balances weight, and from then on a falling body holds a terminal velocity instead of speeding up, so the table's 1,000 m row (140 m/s) is what a cannonball in a vacuum would do, not a skydiver.
- 'From rest' means the object was let go, not thrown. Something thrown downward starts with a speed and lands sooner and faster; something thrown upward first rises. OpenStax's full equations with v₀ cover those; this page sets v₀ = 0.
- g varies a little with latitude and altitude (9.78–9.83 m/s² on Earth) and a lot between worlds. 9.80665 is the standard figure; enter 1.62 for the Moon and 3.72 for Mars and the same fall takes far longer.
- The 'height that gives this speed' mode is the drop needed to reach a speed in a vacuum, not the height at which something would be going that fast in air, where drag caps the speed well below what the formula allows for long falls.
- Feet are converted at exactly 0.3048 m; mph at 2.2369 per m/s. Results are rounded to four decimals, which is more precision than g itself is known to at any particular spot.
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Free Fall FAQ
- About 2.5 seconds — 100 ft is 30.48 m, and √(2 × 30.48 ÷ 9.81) = 2.49 s — arriving at 24.4 m/s, about 55 mph, ignoring air. 200 ft takes 3.5 s; 50 ft takes 1.76 s. The table under the result lists the common heights.
- Its speed grows by 9.8 m/s (32 ft/s, about 22 mph) every second: 9.8 m/s after one second, 19.6 after two, 29.4 after three. The distance grows faster than that — 4.9 m in the first second, 19.6 m by the end of the second, 44.1 m by the end of the third — because the object is speeding up the whole time.
- Not in a vacuum: g is the same for everything, so a hammer and a feather dropped on the Moon land together, as the Apollo 15 astronauts showed. In air, drag matters more for light, wide objects, so the feather floats down and the hammer does not — the difference is air, not gravity.
- Distance fallen from rest is ½gt², and speed is gt, where g = 9.8 m/s² and t is the time in seconds. To get the time for a known height, t = √(2h/g). To get the impact speed from a height, v = √(2gh). All three are from the same constant-acceleration equations in OpenStax §2.7.
- 4.9 m (16 ft) in one second, 19.6 m (64 ft) in two, and 122.6 m (402 ft) in five, in a vacuum. Enter the time in the first mode and the page gives the distance and the speed at that moment.