Free Fall: formula
Enter the drop height in meters and the gravitational acceleration, 9.81 meters per second squared on Earth. The fall time is the square root of twice the height divided by gravity, and the impact speed is the square root of twice gravity times height. The formulas ignore air resistance, which matters for high drops and light objects.
Height is measured from release to the ground.
Free Fall: worked example
| Drop height (m) | 50 |
|---|---|
| Gravity (m/s²) | 9.8 |
| Fall time (s) | 3.2 |
| Impact speed (m/s) | 31.3 |
| Impact speed (km/h) | 112.8 |
Air drag limits real falls to a terminal velocity: a skydiver reaches about 55 meters per second, and a feather far less. Over long drops the ideal result is much too high. Objects thrown down or up need the uniform acceleration equations.
Gravity varies slightly with latitude and altitude.
Free Fall: changing Drop height (m)
| Drop height (m) | Fall time (s) | Impact speed (m/s) | Impact speed (km/h) |
|---|---|---|---|
| 40 | 2.9 | 28 | 100.9 |
| 45 | 3 | 29.7 | 107 |
| 50 (example) | 3.2 | 31.3 | 112.8 |
| 55 | 3.3 | 32.8 | 118.3 |
| 60 | 3.5 | 34.3 | 123.5 |
Free Fall: compare input ranges
| Input | Tested from | To | Fall time (s): low input | Fall time (s): high input | Swing |
|---|---|---|---|---|---|
| Gravity (m/s²) | 9 | 11 | 3.3 | 3 | 0.318 (10.0%) |
| Drop height (m) | 45 | 55 | 3 | 3.3 | 0.32 (10%) |
Free Fall: individual input comparisons
| Input | Value | Fall time (s) | Impact speed (m/s) | Impact speed (km/h) |
|---|---|---|---|---|
| Drop height (m) | 40 | 2.9 | 28 | 100.9 |
| 45 | 3 | 29.7 | 107 | |
| 50 | 3.2 | 31.3 | 112.8 | |
| 55 | 3.3 | 32.8 | 118.3 | |
| 60 | 3.5 | 34.3 | 123.5 | |
| Gravity (m/s²) | 8 | 3.5 | 28.3 | 101.8 |
| 9 | 3.3 | 30 | 108 | |
| 10 | 3.2 | 31.6 | 113.8 | |
| 11 | 3 | 33.2 | 119.4 | |
| 12 | 2.9 | 34.6 | 124.7 |
Free Fall: combined input changes
| Drop height (m) / Gravity (m/s²) | 8 | 10 | 12 |
|---|---|---|---|
| 40 | 3.2 | 2.8 | 2.6 |
| 45 | 3.4 | 3 | 2.7 |
| 50 | 3.5 | 3.2 | 2.9 |
| 55 | 3.7 | 3.3 | 3 |
| 60 | 3.9 | 3.5 | 3.2 |
Free Fall: which assumptions move the result?
Free Fall: values and definitions
| Quantity and definition | Value used |
|---|---|
| Drop height (m) | 50 |
| Gravity (m/s²) | 9.8 |
| Fall time (s) | 3.2 |
| Impact speed (m/s) | 31.3 |
| Impact speed (km/h) | 112.8 |
Free Fall: half and double Gravity (m/s²)
| Gravity (m/s²) | Fall time (s) |
|---|---|
| 4.9 | 4.5 |
| 9.8 | 3.2 |
| 19.6 | 2.3 |
Common error: Assuming a heavier object lands first. Without air resistance, mass does not change the fall time, and a hammer and a feather land together.
Physics & Mechanics calculators: Centripetal Force Calculator, Pendulum Period Calculator, Horsepower Calculator, Speed, Distance and Time Calculator, Kinetic Energy Calculator, Newton's Second Law Force Calculator.
Without air resistance, an object dropped from rest falls a distance that grows with the square of the time. From 50 meters it lands after about 3.2 seconds at about 31 meters per second, roughly 113 kilometers an hour. Doubling the height does not double the time; it multiplies it by about 1.4.
Real objects fall slower than this, and a light one with a large area falls much slower.
Use the drop only where air is a minor effect. A feather or a parachute falls in a very different way from a stone.
See the speed relations on the uniform acceleration calculator, the projectile arc on the projectile motion calculator and the energy on the potential and kinetic energy calculators. The force and pendulum period pages cover related mechanics, and the speed converter changes units.
Do heavier objects fall faster?
Not in a vacuum. In air, drag matters more for light or wide objects, so they fall slower than heavy compact ones.
What is terminal velocity?
The constant speed a falling object reaches when air drag equals its weight, about 55 meters per second for a skydiver.
How long does it take an object to fall 50 meters?
About 3.2 seconds in free fall, ignoring air resistance.