Free fall is motion under gravity alone: drop a phone, a stone or a raindrop in a vacuum and it gains the same amount of speed every second. This calculator answers the three questions people actually ask about a fall — how high, how long and how fast at the bottom. Give it any one of the three and it works out the others, for an object let go from rest or thrown straight down, on Earth or on another world.
How to use the free fall calculator
- Under I know the, pick Height, Fall time or Impact velocity, then enter that value with its unit.
- Leave Initial downward velocity (u) at 0 for a simple drop, or enter the speed of a downward throw.
- Choose Where? — Earth at standard gravity, the Moon, the planets from Mercury to Neptune, Pluto, the Sun, or a custom g.
- Pick units for the height and velocity results.
The result shows the fall time or height, the impact velocity (also in km/h and mph) and the average velocity. A fall profile table breaks the drop into ten equal time steps with the distance fallen, height left and speed at each.
Free fall formulas
The calculator takes downward as positive, so the height, the velocities and g are all positive numbers. For an object dropped from rest:
With an initial downward velocity u:
h = ut + ½gt² = (v² − u²) ÷ 2g
Earth’s preset is standard gravity, 9.80665 m/s². Real local values run from about 9.78 m/s² at the equator to 9.83 m/s² at the poles, which changes these answers by well under 1%.
Worked example: a 20 m drop
A ball is released from rest 20 m above the ground on Earth.
t = √(2 × 20 ÷ 9.80665) = √4.0789 = 2.020 s
v = √(2 × 9.80665 × 20) = 19.81 m/s (about 71.3 km/h or 44.3 mph)
Average velocity = 20 ÷ 2.020 = 9.90 m/s, exactly half the impact speed.
From the same height, the fall takes 4.969 s on the Moon (landing at 8.05 m/s) and 3.284 s on Mars (12.18 m/s).
Fall time grows with the square root of height
Because h = ½gt², quadrupling the height only doubles the time, and nine times the height triples it. Impact speed follows the same square-root rule.
| Height (Earth, from rest) | Fall time | Impact speed |
|---|---|---|
| 1 m | 0.452 s | 4.43 m/s (9.9 mph) |
| 5 m | 1.010 s | 9.90 m/s (22.2 mph) |
| 10 m | 1.428 s | 14.0 m/s (31.3 mph) |
| 20 m | 2.020 s | 19.8 m/s (44.3 mph) |
| 45 m | 3.029 s | 29.7 m/s (66.5 mph) |
| 100 m | 4.516 s | 44.3 m/s (99.1 mph) |
Compare 5 m, 20 m and 45 m: the times run 1 : 2 : 3.
Air resistance and terminal velocity
These are vacuum results. In air, drag grows roughly with the square of speed until it balances the weight, and the object stops speeding up at its terminal velocity. A skydiver falling belly-down settles near 55 m/s, roughly 120 mph. In a vacuum that speed would be reached after just 5.6 s and 154 m; with air it takes longer, and the speed never climbs past it. Light, broad objects such as feathers, leaves and paper reach terminal velocity almost at once, which is why they drift instead of dropping.
Use these figures for short drops of dense objects. Apollo 15 astronaut David Scott showed the vacuum case on the Moon in 1971 by dropping a hammer and a falcon feather, which landed together.
To throw something upward first or sideways, use the projectile motion calculator — a 90° launch angle gives a straight up-and-down flight. The gravitational potential energy calculator shows the energy released by the same drop.
Frequently asked questions
How long does it take to fall 20 meters?
Dropped from rest with no air resistance, t = √(2h ÷ g) = √(2 × 20 ÷ 9.80665) ≈ 2.02 seconds. The object hits the ground at about 19.81 m/s, roughly 44.3 mph.
Does a heavier object fall faster?
Not in a vacuum. Every mass gets the same acceleration g, which is why the mass is not an input. In air, a heavy, compact object is less affected by drag than a light, bulky one, so it pulls ahead — that is air resistance at work, not gravity.
What is terminal velocity?
The speed at which air drag balances weight, so the fall stops accelerating. A skydiver in the belly-down position levels off near 55 m/s, roughly 120 mph. This calculator ignores drag, so for long falls it overstates both the speed and how quickly the ground arrives.
Can I use the calculator for something thrown downward?
Yes. Enter the speed in the Initial downward velocity field. A stone thrown down at 5 m/s from 20 m lands after 1.573 s at 20.43 m/s, compared with 2.020 s and 19.81 m/s when simply dropped.
Why is my impact velocity rejected?
When you start from the impact velocity, it must be larger than the initial downward velocity, because a falling object only speeds up. Heights, times and gravity must also be greater than zero.