MotionLab

Free Fall Calculator

Drop something from any height — see exactly how long it falls and how fast it hits.

Height (m)

Gravity (m/s²)

Fall time (s)

4.515

d = ½gt², v = gt

Impact velocity (m/s): 44.295

What you entered

Height (m): 100Gravity (m/s²): 9.81

1
Time to fall: t = √(2h/g)
√(2 × 100 / 9.81)= 4.5152 s
2
Final velocity: v = g·t
9.81 × 4.5152= 44.2945 m/s
3
Distance check: d = ½gt²
0.5 × 9.81 × 4.5152²= 100 m

Result

Fall time (s): 4.515

An object dropped from 100 m takes 4.515 s to fall, hitting the ground at 44.29 m/s (159.5 km/h).

Free fall time and impact speed by drop height

Ignoring air resistance, the fall time is the square root of 2h/g and the impact velocity is g times that time. These use 9.81 m/s2.

Height (m)	Fall time (s)	Impact velocity (m/s)	Impact speed (km/h)
1	0.452	4.429	15.9
5	1.010	9.905	35.7
10	1.428	14.007	50.4
20	2.019	19.809	71.3
50	3.193	31.321	112.8
100	4.515	44.294	159.5

Height quadruples between the 5 m and 20 m rows while the time only doubles, because distance grows with the square of time - the object covers far more ground in its final second than its first. Impact speed grows with the square root of height, so a 100 m drop gives only about 3.2 times the speed of a 10 m drop, not ten times. Air resistance is ignored here, which is fine for dense objects over short drops but badly wrong beyond a few seconds: a human reaches terminal velocity near 55 m/s and stops accelerating, so the 100 m row is close to the limit of this model's usefulness.

Why mass doesn't matter

In a vacuum, all objects fall at the same rate regardless of mass — Galileo demonstrated this in the 1600s. The time to fall depends only on height and gravitational acceleration (9.81 m/s² on Earth). Air resistance complicates things for feathers and parachutes, but for dense objects the approximation is excellent.

The square-root relationship

Fall time goes as the square root of height — doubling the height doesn't double the fall time, it increases it by a factor of √2 (about 41%). This means the first few meters of a fall take proportionally longer than the last few, and impact speed grows faster than you'd intuitively expect.

Frequently asked questions

I drop my phone from a 4th-floor balcony (12 m high). How fast does it hit the ground?

v = √(2gh) = √(2 × 9.81 × 12) = 15.3 m/s (55 km/h). Fall time: t = √(2h/g) = √(24/9.81) = 1.56 seconds. Not much time to react, and 55 km/h is enough to shatter any phone screen.

Does a heavier object fall faster?

In a vacuum, no — Galileo proved this. In air, heavier objects fall slightly faster because they have a higher terminal velocity (air resistance matters less relative to their weight). But for dense objects dropped from normal heights, the difference is negligible. See the terminal velocity calculator for drag effects.

How high is a bridge if a stone takes 3 seconds to hit the water?

h = ½gt² = ½ × 9.81 × 9 = 44.1 m. Impact speed: v = gt = 9.81 × 3 = 29.4 m/s (106 km/h). This is why bridge falls are so dangerous — even a 2-second fall (19.6 m) reaches 71 km/h.

How does free fall relate to potential and kinetic energy?

As an object falls, potential energy (mgh) converts to kinetic energy (½mv²). At any point: mgh₀ = ½mv² + mgh (conservation of energy). The velocity formula v = √(2gh) comes directly from setting PE = KE. See the potential energy and kinetic energy calculators.