Free Fall Calculator (t = √(2h/g))
Free fall is the motion of an object under gravity alone (no air resistance). The time to fall from height h is t = √(2h/g) and impact velocity is v = √(2gh). This calculator gives both values for any height and gravity.
When to use this calculator
- Solve free-fall kinematics problems.
- Calculate fall time from a building or cliff.
- Estimate impact velocity of a falling object.
- Compare falls on different planets (different gravity).
- Verify physics experiment results.
Example: dropping a stone from a 15 m bridge
- Data: h = 15 m, g = 9.81 m/s², initial velocity = 0.
- Fall time: t = √(2 × 15 / 9.81) = √3.058 = 1.75 s.
- Impact velocity: v = √(2 × 9.81 × 15) = √294.3 = 17.15 m/s.
- Conversion to km/h: 17.15 × 3.6 = 61.7 km/h (38.3 mph).
- Kinetic energy on impact (if 1 kg): E = ½·m·v² = ½·1·17.15² ≈ 147 J.
How it works
1 min readWhat Is Free Fall
Free fall is motion of a body subject only to gravity, without air resistance. Galileo demonstrated this with the famous Tower of Pisa experiment: all objects fall with the same acceleration regardless of mass. On Earth: g ≈ 9.81 m/s².
Equations:
Gravity on Different Celestial Bodies
| Body | g (m/s²) | Time from 20 m | Impact velocity |
|---|---|---|---|
| Earth | 9.81 | 2.02 s | 19.8 m/s (71 km/h) |
| Moon | 1.62 | 4.97 s | 8.05 m/s |
| Mars | 3.72 | 3.28 s | 12.2 m/s |
| Jupiter | 24.79 | 1.27 s | 31.5 m/s |
| Sun | 274 | 0.38 s | 105 m/s |
When to Use / Common Mistakes
Frequently asked questions
What is free fall?
Motion of a body under gravity alone, without friction or air resistance. In practice, air slows objects, but for short distances the approximation is good.
Do all objects fall at the same speed?
In free fall (without air), yes. Galileo proved it: a feather and a bowling ball fall alike in a vacuum. With air, shape and mass matter.
What is terminal velocity?
The maximum speed an object reaches falling with air resistance. For a human it's ~55 m/s (~125 mph). This calculator does NOT include air resistance.
Does it work on the Moon?
Yes, change gravity to 1.62 m/s². On the Moon everything falls 6 times slower than on Earth.
From what height is a fall lethal?
Falls from over 6 meters (20 ft) are potentially lethal (impact at ~24 mph). At 10 m (33 ft) impact is ~31 mph. Information is educational only.
Can I calculate height knowing the time?
Yes: h = ½gt². If an object takes 3 seconds to fall: h = ½ × 9.81 × 9 = 44.1 m.
Does the formula include initial velocity?
No, it assumes initial velocity = 0 (object dropped, not thrown). With initial velocity v₀: h = v₀t + ½gt².