Free Fall Calculator
Fall Time3.029 s
Impact Velocity29.714 m/s
Distance Fallen45.000 m
The Free Fall Calculator works out how long an object takes to drop from a given height and how fast it is moving when it lands, assuming it starts from rest and air resistance is ignored. Enter the drop height in metres and the tool inverts the distance equation to find the fall time, then multiplies by gravity to get the impact speed. Gravity is fixed at the Earth surface value of 9.81 m/s².
Formula
t = √(2h/g) ; v = g·t ; h = ½·g·t²
- h
- Drop height (m)
- t
- Time to fall (s)
- v
- Velocity at impact (m/s)
- g
- Gravitational acceleration, 9.81 m/s²
How it works
- Enter the height in metres from which the object is released; the object is assumed to start at rest with zero initial velocity.
- The calculator solves t = √(2h/g) for the fall time, then computes the impact velocity as v = g·t and confirms the distance fallen with ½·g·t².
- Doubling the drop height increases the fall time by only about 41 percent, because distance grows with the square of time.
Worked example
A stone is dropped from a 45 metre cliff.
- Fall time = √(2 × 45 ÷ 9.81) = √9.174 = 3.029 s.
- Impact velocity = 9.81 × 3.029 = 29.713 m/s.
- Distance check = ½ × 9.81 × 3.029² = 45 m.
It falls for 3.029 s and hits the ground at 29.713 m/s.
Frequently asked questions
- Does a heavier object fall faster?
- No. Ignoring air resistance, all objects accelerate at the same rate g and reach the ground at the same time regardless of mass. This is why a feather and a hammer fall together in a vacuum.
- Is air resistance included in these results?
- No. The calculator assumes ideal free fall in a vacuum. In real air, drag slows light or large objects and they may approach a terminal velocity, so actual fall times are longer.
- What is the initial velocity assumed by this tool?
- It assumes the object is released from rest, so the initial velocity is zero. If an object is thrown downward or upward, the equations need an extra initial-velocity term.
- Can I use this on the Moon or another planet?
- This version fixes gravity at Earth value 9.81 m/s². On the Moon, where g is about 1.62 m/s², the same drop would take roughly 2.5 times longer to land.