What this calculator does
Free fall is the simplest case of motion under gravity: an object starts at rest and falls straight down with nothing but gravity acting on it, no launch angle and no sideways motion to track. Given any one of the fall height, the fall time or the impact velocity, the other two follow directly, because all three are tied together by the same constant acceleration.
Air resistance is ignored here, which is a reasonable approximation for a dense, compact object falling a modest distance, and a poor one for something light and wide like a leaf or a sheet of paper. For anything where drag matters, the fall will take longer and the impact speed will be lower than this calculator shows.
The formula
With an initial velocity of zero, three linked equations describe the fall: velocity builds up as v = g·t, the distance fallen is h = ½g·t², and eliminating time gives v² = 2g·h directly relating speed to distance. Enter whichever one of height, time or velocity you know, and the calculator solves the other two from it.
| Term | Meaning |
|---|---|
| h | The height or distance fallen, in metres. |
| t | The time spent falling, in seconds. |
| v | The velocity at the moment of impact, in metres per second. |
| g | Gravitational acceleration, 9.80665 m/s² on Earth at sea level by convention. |
The inputs explained
| Field | What to enter |
|---|---|
| Known value | Which quantity you already know: fall height, fall time or impact velocity. |
| Value | The value of that known quantity. |
| Gravitational acceleration (m/s²) | Gravitational acceleration to use; the Earth-surface standard value is filled in by default. |
When to use it
Dropping an object from a known height
Given the height of a building, cliff or bridge, the calculator gives the time it takes to hit the ground and the speed it will be travelling at on impact, both useful for a rough safety or physics-class estimate.
Timing a fall with a stopwatch
If the fall was timed rather than measured, entering the time instead gives the implied height and impact speed, a common approach for estimating the depth of a well or shaft by dropping something in and timing the splash.
Working from a known impact speed
If the impact velocity is known, perhaps from a speed trap or a stated terminal condition, the calculator works backwards to the height and time that would produce it, assuming free fall the whole way down.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How far does something fall in a given time?
Height fallen and impact velocity for a range of fall times, dropped from rest.
| Fall time | Fall height / distance | Impact velocity |
|---|---|---|
| 1 s | 4.903 m | 9.807 m/s |
| 2 s | 19.613 m | 19.613 m/s |
| 3 s | 44.130 m | 29.420 m/s |
| 4 s | 78.453 m | 39.227 m/s |
| 6 s | 176.520 m | 58.840 m/s |
| 10 s | 490.333 m | 98.066 m/s |
What is the impact speed from a given height?
Impact velocity and fall time for a range of drop heights.
| Fall height | Impact velocity | Fall time |
|---|---|---|
| 5 m | 9.903 m/s | 1.010 s |
| 10 m | 14.005 m/s | 1.428 s |
| 20 m | 19.806 m/s | 2.020 s |
| 50 m | 31.316 m/s | 3.193 s |
| 100 m | 44.287 m/s | 4.516 s |
Questions
What is the formula for free fall?
Starting from rest, velocity is v = g·t, distance fallen is h = ½g·t², and combining the two gives v² = 2g·h. Any one of height, time or velocity, together with g, determines the other two.
Does weight affect how fast something falls?
In free fall, ignoring air resistance, no: gravitational acceleration is the same for any mass, so a heavy object and a light one dropped from the same height land at the same time. Air resistance is what makes a feather fall slower than a stone in practice, not their difference in mass.
What value of g should I use?
The standard value, 9.80665 m/s², is the internationally agreed figure for Earth at sea level and is filled in by default. Actual local gravity varies slightly with latitude and altitude, but the difference is small enough to ignore for everyday estimates.
How is free fall different from projectile motion?
Free fall is the special case where the object starts at rest and moves in a straight vertical line under gravity alone. Projectile motion adds a horizontal launch component, so the object follows a curved path and the calculation needs a launch angle and launch speed as well.
For motion that includes a horizontal launch and an angle, see the projectile motion calculator. For the general set of motion equations, including cases with a non-zero starting velocity, use the SUVAT equations solver.