Free Fall Calculator — Time and Impact Velocity
Free fall is the motion of an object under gravity alone — no air resistance. Drop anything from height h and it reaches the ground in t = √(2h/g) seconds, hitting at v = √(2gh) m/s. This calculator gives you both values instantly for any height and any gravity (Earth, Moon, Mars, etc.).
An object in free fall (no air resistance) takes t = √(2h/g) seconds to fall from height h. On Earth (g = 9.81 m/s²): falling 10 m takes 1.43 s and hits at 14.0 m/s (50 km/h); from 100 m it takes 4.52 s and hits at 44.3 m/s (159 km/h). Impact velocity formula: v = √(2gh).
When to use this calculator
- Solve free-fall kinematics homework problems.
- Calculate fall time from a building, cliff, or bridge.
- Estimate impact velocity of a dropped object.
- Compare falls on different planets (Moon, Mars, Jupiter).
- Verify physics experiment results in the lab.
- Estimate kinetic energy on impact for safety analysis.
Example: stone dropped 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: 17.15 × 3.6 = 61.7 km/h (38.3 mph).
- Kinetic energy on impact (1 kg stone): E = ½ × 1 × 17.15² ≈ 147 J.
How it works
1 min readFree Fall Formulas
Free fall = motion under gravity only, no air resistance. All three key equations:
On Earth, g = 9.81 m/s² (standard; varies ±0.05% by latitude).
Quick Reference Table — Fall on Earth (g = 9.81 m/s²)
| Height | Fall Time | Impact Velocity | Impact Speed |
|---|---|---|---|
| 1 m | 0.45 s | 4.4 m/s | 16 km/h |
| 5 m | 1.01 s | 9.9 m/s | 36 km/h |
| 10 m | 1.43 s | 14.0 m/s | 50 km/h |
| 20 m | 2.02 s | 19.8 m/s | 71 km/h |
| 50 m | 3.19 s | 31.3 m/s | 113 km/h |
| 100 m | 4.52 s | 44.3 m/s | 159 km/h |
| 200 m | 6.39 s | 62.6 m/s | 226 km/h |
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 (29 km/h) |
| Mars | 3.72 | 3.28 s | 12.2 m/s (44 km/h) |
| Jupiter | 24.79 | 1.27 s | 31.5 m/s (113 km/h) |
| Sun | 274 | 0.38 s | 105 m/s (378 km/h) |
Assumptions and Limits
Frequently asked questions
What is the free fall formula?
Two key equations: t = √(2h/g) for fall time, and v = √(2gh) for impact velocity. On Earth, g = 9.81 m/s². To find height from time: h = ½ × g × t². These assume zero air resistance and zero initial velocity.
How long does it take to fall 100 meters?
On Earth: t = √(2 × 100 / 9.81) = √20.39 = 4.52 seconds. Impact speed is √(2 × 9.81 × 100) = 44.3 m/s (159 km/h). Air resistance at real-world falls would reduce this slightly.
What is free fall in physics?
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. On Earth all objects in free fall share the same acceleration: g = 9.81 m/s².
Do all objects fall at the same speed?
In ideal free fall (no air), yes. Galileo proved it: a feather and a bowling ball fall identically in a vacuum. With air resistance, shape and mass matter — which is why a feather falls slowly on Earth.
What is terminal velocity?
The maximum speed reached when air drag equals gravity. For a spread-eagle skydiver it is ~55 m/s (~200 km/h). This calculator does not include air resistance — use it for short falls or vacuum conditions.
Does it work on the Moon or Mars?
Yes — change gravity to Moon: 1.62 m/s² or Mars: 3.72 m/s². On the Moon everything falls ~2.5× slower than on Earth from the same height. From 20 m on the Moon: t = 4.97 s vs 2.02 s on Earth.
From what height is a fall dangerous?
Falls from 6 meters (20 ft) and above are potentially life-threatening. At 6 m impact speed is ~11 m/s (39 km/h). At 10 m it is ~14 m/s (50 km/h). Medical literature cites 6–10 m as the zone where serious injury becomes very likely. This is educational only.
Does the formula work if the object is thrown downward?
No — t = √(2h/g) assumes initial velocity = 0 (object dropped, not thrown). If thrown downward at initial speed v₀, the full equation is h = v₀·t + ½·g·t². You must solve that quadratic for t.