Free Fall Calculator
Solve for fall time, distance fallen or impact speed from any one of them, using the exactly defined standard gravity of 9.80665 m/s².
d = ½·g·t² v = g·t (dropped from rest, no air resistance)
Distance fallen
Formula used for this direction
d = ½·g·t²
Your values
t = 3, g = 9.807 m/s²
How Free Fall Works
An object dropped from rest with no air resistance accelerates at a constant g. Two formulas follow: the distance fallen grows as d = ½·g·t², and the speed grows as v = g·t. Because distance depends on the square of time, a falling object covers far more ground in its third second than in its first.
Rearranging gives the directions this calculator solves: t = √(2·d ÷ g) for the time to fall a known height, and v = √(2·g·d) for the speed on arrival. That last form is the useful one in practice, because you usually know how high something was, not how long it was in the air.
Worked example — dropped from a first-floor window
A 10 metre drop, starting from rest.
t = √(2 × 10 ÷ 9.80665) = 1.428 seconds
v = √(2 × 9.80665 × 10) = 14 m/s, which is 31.33 mph — fast enough that the difference between a 10 m and a 2 m fall is the difference between a serious injury and a sprain.
A second example, ten times higher. A 100 metre drop takes 4.516 seconds — only about 3.2 times as long as the 10 m drop, not ten times. Squared relationships compress like that.
Going the other way: after falling for 3 seconds an object has dropped 44.13 m.
Fall Time and Impact Speed by Height
Every row below is computed by this page's own functions at standard gravity, ignoring air resistance.
| Drop height | Fall time | Impact speed | Impact speed (mph) |
|---|---|---|---|
| 1 m | 0.452 s | 4.43 m/s | 9.91 mph |
| 2 m | 0.639 s | 6.26 m/s | 14 mph |
| 5 m | 1.01 s | 9.9 m/s | 22.2 mph |
| 10 m | 1.43 s | 14 m/s | 31.3 mph |
| 20 m | 2.02 s | 19.8 m/s | 44.3 mph |
| 50 m | 3.19 s | 31.3 m/s | 70.1 mph |
| 100 m | 4.52 s | 44.3 m/s | 99.1 mph |
The Same 10 m Drop on Other Worlds
| Body | Gravity | Time to fall 10 m |
|---|---|---|
| Mercury | 3.7 m/s² | 2.32 s |
| Venus | 8.9 m/s² | 1.5 s |
| Earth | 9.8 m/s² | 1.43 s |
| Moon | 1.6 m/s² | 3.54 s |
| Mars | 3.7 m/s² | 2.32 s |
| Jupiter | 23.1 m/s² | 0.93 s |
| Saturn | 9 m/s² | 1.49 s |
| Uranus | 8.7 m/s² | 1.52 s |
| Neptune | 11 m/s² | 1.35 s |
| Pluto | 0.7 m/s² | 5.35 s |
Gravity figures from the NASA NSSDC Planetary Fact Sheet, fetched 2026-09-19. Atmospheric drag is ignored throughout, which matters a great deal on Venus and not at all on the Moon.
Keep going
- An object about to fall holds gravitational potential energy equal to mgh, and free fall converts exactly that into kinetic energy; the potential energy calculator gives the starting figure. Potential Energy Calculator
- Free fall is projectile motion with no horizontal component; the projectile calculator adds a launch angle and solves the full two-dimensional path. Projectile Motion Calculator
Frequently Asked Questions
How long does it take to fall a given distance?
t = √(2·d ÷ g). Falling 10 metres from rest takes about 1.43 seconds; falling 100 metres takes about 4.52 seconds — ten times the height, but only about three times the time, because distance grows with the square of time.
Do heavier objects fall faster?
No, not in a vacuum. Gravity pulls harder on a heavier object, but that heavier object also resists acceleration proportionally more, and the two effects cancel exactly. A hammer and a feather dropped together on the Moon land together — famously demonstrated by Apollo 15. On Earth the feather loses only because of air resistance, which these formulas ignore.
What speed does something hit the ground at?
v = √(2·g·d) if dropped from rest. From 10 metres that is about 14 m/s, roughly 31 mph. Note it grows with the square root of height, so doubling the drop height multiplies the impact speed by only about 1.41, not 2.
Does this account for air resistance?
No. These are the standard vacuum formulas, which is the usual textbook treatment. Real falls reach a terminal velocity where drag balances gravity — roughly 53 m/s for a skydiver in a belly-down position — after which speed stops increasing entirely. For short drops of a few metres the difference is small; for long falls these figures overestimate badly.
Why use 9.80665 rather than 9.8 or 9.81?
9.80665 m/s² is the standard acceleration of gravity, defined exactly by international agreement and published by NIST. It is a defined constant, not a measurement. Actual local gravity varies with latitude and altitude by a few tenths of a percent, so for most problems 9.8 is perfectly adequate — but this calculator uses the exact defined value so results are reproducible.
Related Calculators
- Acceleration Calculator — Motion & Kinematics
- Velocity Calculator — Motion & Kinematics
- Projectile Motion Calculator — Motion & Kinematics
- Force Calculator — Forces & Rotation