Free Fall Calculator — Distance, Time, and Velocity
Calculate free fall distance, velocity, and time under gravity. Covers kinematic equations, terminal velocity limits, and examples from cliff drops to skydiving.
Drop something from a height and gravity does exactly what the equations predict — at least in vacuum. Free fall is one of the cleanest physical demonstrations of kinematics because there's only one force acting: gravity. Real objects have air resistance too, but for many situations the pure free-fall equations are close enough.
The CalcHub free fall calculator solves for any combination of distance, time, initial velocity, and final velocity under constant gravitational acceleration.
The Equations
Starting from rest (v₀ = 0):
| What you want | Formula |
|---|---|
| Velocity after time t | v = g × t |
| Distance fallen in time t | d = ½ × g × t² |
| Velocity after falling distance d | v = √(2gd) |
| Time to fall distance d | t = √(2d/g) |
- v = v₀ + gt
- d = v₀t + ½gt²
How Long Does It Take to Fall?
| Height | Fall Time | Impact Speed |
|---|---|---|
| 1 m | 0.45 s | 4.4 m/s |
| 5 m | 1.01 s | 9.9 m/s |
| 10 m | 1.43 s | 14.0 m/s |
| 100 m | 4.52 s | 44.3 m/s |
| 1000 m | 14.3 s | 140 m/s |
Worked Example
A construction worker accidentally drops a wrench from a 45 m scaffold. How long until it hits the ground, and how fast is it moving on impact?
t = √(2 × 45 / 9.81) = √(9.17) ≈ 3.03 s
v = 9.81 × 3.03 ≈ 29.7 m/s (≈ 107 km/h)
This is why hard hat zones exist — tools falling from height carry lethal impact energy.
What's terminal velocity?
As an object falls, air resistance increases with speed. When air resistance equals gravitational force, acceleration stops and speed becomes constant — terminal velocity. For a human skydiver in belly-down position, it's about 55 m/s (200 km/h). In head-first dive, around 90 m/s.
Does mass affect free fall?
Not in vacuum — all objects fall at the same rate. Galileo famously demonstrated this (and it was later confirmed on the Moon by an Apollo astronaut dropping a hammer and feather simultaneously). In air, shape and size affect drag, which is why a feather falls slower than a coin.
How accurate is the 9.81 m/s² value?
Standard gravity is defined as exactly 9.80665 m/s². Actual surface gravity varies from 9.764 m/s² at the equator/high altitude to 9.833 m/s² at the poles. For most problems, 9.81 or even 10 m/s² is perfectly fine.