About the Free Fall Calculator
Free fall is motion under gravity alone. Drop a stone from a bridge and, until air resistance becomes important, it falls with a steady acceleration of about 9.81 metres per second squared, gaining nearly 10 m/s of speed every second. That simple rule lets you work out how long any fall takes and how fast the object is moving when it lands.
This free fall calculator works in two directions. From a height, it finds the time to fall and the landing speed; from a time, it finds the distance fallen and the speed reached. It uses Earth's standard gravity by default and can switch to the Moon, Mars, Venus or Jupiter. It also shows how far and how fast an object falls in each of the first five seconds.
How to Use the Free Fall Calculator
Choose From height or From time.
Enter the height and its unit, or the fall time in seconds.
Choose the gravity if the fall is not on Earth.
The calculator assumes the object starts from rest and ignores air resistance.
The Formulas
from a height h: t = √(2h ÷ g) v = √(2 g h) = g t
from a time t: h = ½ g t² v = g t
g on Earth = 9.80665 m/s²Step-by-Step Examples
A 20 m drop.
t = √(2 × 20 ÷ 9.80665) = 2.0196 s
v = 9.80665 × 2.0196 = 19.806 m/s ≈ 71.3 km/hA 100 m drop: t = 4.516 s, v = 44.287 m/s (about 159.4 km/h).
Falling for 5 seconds.
h = ½ × 9.80665 × 5² = 122.58 m
v = 9.80665 × 5 = 49.033 m/sA 20 m drop on the Moon (g = 1.62 m/s²) takes 4.969 s and ends at about 8.05 m/s.
Distance Grows with the Square of Time
A falling object does not cover the same distance each second. In the first second it falls about 4.9 m; by the end of two seconds it has fallen 19.6 m; after three, 44.1 m; after four, 78.5 m; after five, 122.6 m. The distance grows with the square of the time, so doubling the fall time quadruples the distance. The speed, by contrast, grows steadily, by about 9.8 m/s each second. That is why a short fall can be harmless but a fall only a little longer is dangerous: the speed at impact rises with the square root of the height.
Galileo and Falling Bodies
For nearly two thousand years people followed Aristotle's idea that heavy objects fall faster than light ones. In the early 1600s Galileo Galilei showed by experiment and argument that, apart from air resistance, all objects fall with the same acceleration. He timed balls rolling down gentle ramps to slow the motion enough to measure. In 1971, on the Apollo 15 mission, astronaut David Scott dropped a hammer and a feather together on the airless Moon, and they landed at the same moment, a vivid confirmation broadcast live.
Air Resistance and Terminal Velocity
In air, a falling object pushes air out of the way, and the drag force grows with speed. Eventually drag balances weight and the object stops accelerating, falling at a steady terminal velocity. A skydiver lying flat reaches about 55 m/s, around 200 km/h, after roughly 12 seconds and several hundred metres; diving head-first raises it considerably. A raindrop falls at only a few metres per second, and a feather far more slowly. Opening a parachute greatly increases drag, lowering the terminal velocity to a safe landing speed of around 5 m/s. The free-fall formulas are therefore accurate for dense objects over short drops, and increasingly overestimate speed for longer falls or lighter objects.
Using Free Fall to Measure Height
You can estimate the height of a cliff, bridge or well by dropping a stone and timing how long it takes to hit the bottom. A fall of 2 seconds means about 19.6 m; 3 seconds about 44 m. For deep drops, remember that the sound of the splash or impact also takes time to come back up — about a third of a second for every 100 metres — so the measured time is a little too long and the calculated height a little too high.
Gravity on Other Worlds
Surface gravity differs across the Solar System. On the Moon it is about 1.62 m/s², a sixth of Earth's, so falls take about two and a half times as long and end at much lower speeds. Mars has about 3.71 m/s², Venus 8.87 m/s², and Jupiter a crushing 24.79 m/s² at its cloud tops. The calculator's gravity setting lets you compare the same drop in each place.
Free Fall and Weightlessness
Astronauts in orbit float not because gravity has vanished — at the height of the International Space Station it is still about 90 percent of its strength on the ground — but because they and their spacecraft are falling together. Everything aboard accelerates at the same rate, so nothing presses on the floor. Short periods of the same weightless feeling come on drop towers, in aircraft flying parabolic arcs, and briefly at the top of a roller coaster hill.
Understanding Your Result
The headline is the fall time or the distance fallen.
The landing speed line gives the final speed in m/s, km/h and mph.
The detail line restates the height, time, gravity and average speed.
The first five seconds line shows distance and speed after each second.
When Should You Use This Calculator?
Use it for physics homework on kinematics.
Use it to estimate heights by timing a dropped object.
Use it to compare falls on Earth and other worlds.
Common Mistakes
Assuming distance grows linearly with time. It grows with the square of time.
Ignoring air resistance for long falls. Real objects reach a terminal velocity.
Forgetting sound travel time. It adds to timed measurements of deep drops.
Throwing instead of dropping. The formulas assume the object starts from rest.