Free fall in a nutshell
An object in free fall moves under gravity alone. Near the Earth’s surface it accelerates at g = 9.81 m/s² (32.2 ft/s²): every second, its speed increases by about 22 mph. Without air resistance, a feather and a hammer fall at the same rate, as the Apollo 15 astronauts showed on the Moon. The calculator ignores air resistance, which is accurate for dense objects over short drops.
The formulas
Starting from rest, from a height h:
- Fall time t = √(2h ÷ g)
- Impact speed v = √(2gh) = g × t
- With an initial downward speed v₀: t = (√(v₀² + 2gh) − v₀) ÷ g, and v = v₀ + g × t
- Distance fallen after t seconds: d = ½ g t²
The distance grows with the square of the time: in 1 second an object falls 16 feet, in 2 seconds 64 feet, in 3 seconds 145 feet.
Worked example: a 100 ft drop
- 100 ft = 30.48 m.
- Time: √(2 × 30.48 ÷ 9.81) = 2.49 s.
- Impact speed: 9.81 × 2.49 = 24.5 m/s, which is 54.7 mph.
- Average speed over the fall: 30.48 ÷ 2.49 = 12.2 m/s (27.3 mph), half the final speed.
Fall time and speed from other heights
| Height | Time | Impact speed |
|---|---|---|
| 3 ft | 0.43 s | 9.4 mph |
| 10 ft | 0.79 s | 17.3 mph |
| 30 ft | 1.37 s | 30 mph |
| 100 ft | 2.49 s | 54.7 mph |
| 300 ft | 4.32 s | 94.7 mph |
| 1,000 ft | 7.88 s | 173 mph |
On other worlds
Gravity on the Moon is about one-sixth of Earth’s (1.62 m/s²), on Mars about 38% (3.71 m/s²) and on Jupiter 2.5 times (24.79 m/s²). A 100 ft drop takes 6.1 seconds on the Moon, and ends at 22 mph instead of 55.
When air resistance matters
In real air, drag grows with the square of the speed until it balances the weight: the object then stops accelerating at its terminal velocity. A skydiver in a belly-to-earth position reaches about 120 mph after roughly 12 seconds, a raindrop only about 20 mph. For drops above about 100 feet, or for light and flat objects, the real fall is slower than the calculator shows.
Practical uses
- Estimating a height: drop a stone into a well and time the splash. 2 seconds means about 64 feet (ignoring the time the sound takes to come back).
- Safety: a fall of 10 feet already ends at 17 mph. OSHA requires fall protection from 6 feet in construction.
- Physics homework: the same formulas give the time and speed for any drop, as long as the air can be neglected.