About the Free Fall Calculator
This free fall calculator works out how an object moves when gravity is the only force acting on it. Enter the drop height to get the time it takes to hit the ground and the impact speed, or enter a fall time to find how far the object dropped and how fast it was going. You can also give it an initial downward speed, for example a ball thrown straight down.
It is useful for physics coursework, estimating the height of a cliff or well by timing a dropped stone, safety discussions about falling objects on building sites, and comparing gravity on the Moon, Mars and Jupiter. Speeds are shown in m/s, km/h and mph, and the chart traces height and speed over the fall.
The calculation ignores air resistance, so it is accurate for dense objects over short drops. Over long falls real objects approach a terminal velocity (roughly 55 m/s for a skydiver belly-down) and never reach the speeds predicted here.
With the default inputs, the impact velocity is 19.81 m/s. Change any value above to recalculate instantly.
How to use the free fall calculator
- 1Choose whether you know the drop height or the fall time.
- 2Enter the height in metres or the time in seconds.
- 3Add an initial downward speed if the object is thrown, not dropped.
- 4Pick the gravity (Earth by default) and read the fall time and impact velocity.
Formula and method
An object in free fall accelerates downward at a constant g — 9.80665 m/s² is the standard value on Earth. Starting with downward speed v₀, the distance fallen after t seconds is v₀t + ½gt² and its speed is v₀ + gt.
Given a height, the calculator solves the quadratic for the positive fall time, then finds the impact speed; for a simple drop (v₀ = 0) this reduces to t = √(2d/g) and v = √(2gd). Air resistance, buoyancy and the tiny change of g with altitude are ignored, which is accurate for compact objects over drops of tens of metres.
- d
- Distance fallen (m)
- t
- Fall time (s)
- v₀
- Initial downward speed (m/s)
- v
- Speed at impact (m/s)
- g
- Gravitational acceleration (m/s²)
Worked examples
Dropping a stone from 20 m
t = √(2 × 20 ÷ 9.80665) ≈ 2.02 s and v = √(2 × 9.80665 × 20) ≈ 19.81 m/s, about 71 km/h at impact.
Timing a stone down a well
A stone that takes 3 s to hit the water has fallen ½ × 9.80665 × 3² ≈ 44.1 m and is moving at 29.4 m/s. (Sound travel time adds a small error in practice.)
Ball thrown down at 5 m/s from 30 m
Solving 30 = 5t + 4.903t² gives t ≈ 2.02 s, and the impact speed is √(5² + 2 × 9.80665 × 30) ≈ 24.77 m/s.
Frequently asked questions
How long does it take an object to fall?+
For an object dropped from rest with no air resistance, t = √(2h / g). On Earth a 5 m drop takes about 1.01 s, a 20 m drop about 2.02 s and a 100 m drop about 4.52 s.
Do heavier objects fall faster?+
Not in a vacuum — all objects accelerate at the same rate g regardless of mass, as Apollo 15 astronaut David Scott showed with a hammer and feather on the Moon. In air, drag slows light or broad objects more.
What is the formula for impact velocity?+
Impact speed after falling height h from rest is v = √(2gh). With an initial downward speed v₀ it becomes √(v₀² + 2gh). Air resistance lowers the real value.
What is terminal velocity?+
Terminal velocity is the constant speed reached when air drag balances weight. For a skydiver in a belly-to-earth position it is roughly 55 m/s (about 200 km/h); this calculator ignores drag, so it has no terminal velocity.
What value of g should I use?+
The standard gravity defined for calculations is 9.80665 m/s². Actual surface gravity varies from about 9.78 m/s² at the equator to 9.83 m/s² at the poles; many textbooks round to 9.8 or 9.81.