Free fall calculator
Enter a height, get the fall time and speed.
How long does it take to fall from a height?
t = √(2h ÷ g). From 100 meters, √(200 ÷ 9.80665) = 4.52 seconds, ignoring air resistance.
How fast is an object going when it lands?
v = g × t, or √(2gh): after falling 100 m it reaches 44.3 m/s (99 mph) — without air resistance.
Does a heavier object fall faster?
Not without air: all objects fall with the same acceleration, as Galileo showed. In air, drag slows light or broad objects much more.
What value of g does it use?
Standard gravity, 9.80665 m/s² (32.174 ft/s²). Real gravity varies slightly with latitude and altitude.
What about air resistance?
It is ignored here, so results are upper limits for speed. A falling person, for example, stops speeding up at a terminal velocity.
How far does an object fall in a given time?
Distance = ½gt², starting from rest. In 2 s it falls 19.6 m (64.3 ft), in 3 s 44.1 m (145 ft) and in 5 s 122.6 m (402 ft), while its speed grows by 9.80665 m/s every second: 29.4 m/s (65.8 mph) after 3 s. Valid only while air resistance stays negligible.
How deep is a well if I hear the splash after 3 seconds?
Not ½g × 3² = 44.1 m, because part of the 3 s is the sound coming back up. With sound at 343 m/s (20 °C, OpenStax University Physics, section 17.2), the stone falls for 2.88 s and the sound takes the rest, so the depth is ½g × 2.88² = 40.7 m. Ignoring the sound overstates the depth by 8%.
The formula and what it assumes
An object released from rest and falling only under gravity has constant acceleration g, so the fall time from height h is t = √(2h ÷ g) and the speed at the bottom is v = g·t = √(2gh) (OpenStax University Physics, Volume 1, section 3.5, with the constant-acceleration equations of section 3.4). OpenStax neglects air resistance and takes g as constant over the fall; it varies from about 9.78 to 9.83 m/s² with latitude and altitude, and the calculator uses the standard value, 9.80665 m/s². The mass of the object does not appear: without air, every object falls with the same acceleration.
Worked example: a 50 ft drop
Enter 50 ft, which is 50 × 0.3048 = 15.24 m. Then t = √(2 × 15.24 ÷ 9.80665) = 1.76 s and v = 9.80665 × 1.76 = 17.29 m/s, which is 56.7 ft/s or 38.7 mph. For comparison, a ball thrown downward at 4.9 m/s from a 98 m building lands after 4.0 s (OpenStax Example 3.14); simply dropped from rest it would take 4.47 s. This calculator is for objects released from rest; use the kinematics calculator when there is a starting speed.
Common mistakes
Treating the answer as exact for any object is the biggest one. Drag grows with speed and with the area facing the air, so a leaf, a sheet of paper or a parachute falls far slower than the result, and even a person is limited after a long drop: OpenStax Example 6.17 gives about 44 m/s as the terminal speed of an 85 kg skydiver in a spread-eagle position; the 44.3 m/s the calculator gives for a 100 m fall is already above that limit, so a person would arrive slower. Another is the unit of height: 50 read as meters instead of feet makes the drop 3.28 times higher and the time and speed about 1.8 times larger. Last, the fall time is not proportional to the height: four times the height takes only twice as long.
Sources: OpenStax University Physics, Volume 1, section 3.5 (free fall; Example 3.14), section 3.4 (constant acceleration), section 6.4 (drag force and terminal speed; Example 6.17) and section 17.2 (speed of sound); standard gravity 9.80665 m/s² is exact (NIST SP 811, Appendix B.8). Related: terminal velocity calculator, kinematics calculator, projectile motion calculator and speed of sound calculator.