Free Fall Calculator
Calculate free fall time, distance fallen, and final velocity. Assumes no air resistance.
Free Fall Formulas
| Find | Formula | Given |
|---|---|---|
| Time (t) | t = √(2h / g) | Height h |
| Height (h) | h = ½ g t² | Time t |
| Final velocity (v) | v = g × t | Time t |
| Final velocity (v) | v = √(2gh) | Height h |
g = 9.81 m/s² (metric) or 32.174 ft/s² (imperial). Initial velocity = 0 (dropped from rest).
Free Fall Reference Table
| Height | Fall Time | Impact Speed |
|---|---|---|
| 1 m (3.3 ft) | 0.45 s | 4.4 m/s (10 mph) |
| 5 m (16 ft) | 1.01 s | 9.9 m/s (22 mph) |
| 10 m (33 ft) | 1.43 s | 14.0 m/s (31 mph) |
| 50 m (164 ft) | 3.19 s | 31.3 m/s (70 mph) |
| 100 m (328 ft) | 4.52 s | 44.3 m/s (99 mph) |
| 443 m (Empire State) | 9.51 s | 93.3 m/s (209 mph) |
Frequently Asked Questions
What is free fall?
Free fall is the motion of an object under the influence of gravity alone, with no air resistance. In free fall from rest, an object accelerates at g = 9.81 m/s² (32.174 ft/s²) on Earth. Real falls involve air resistance, which limits terminal velocity, but this calculator uses the idealised physics model useful for introductory physics problems.
How long does it take to fall 100 metres?
Using t = √(2h/g): t = √(2 × 100 / 9.81) = √20.39 ≈ 4.52 seconds. The final velocity at impact would be v = g × t = 9.81 × 4.52 ≈ 44.3 m/s (about 99 mph). This assumes free fall with no air resistance.
What is terminal velocity?
Terminal velocity is the maximum speed a falling object reaches when the drag force from air resistance equals gravity. At terminal velocity, acceleration stops. For a skydiver, terminal velocity is about 55 m/s (120 mph) face-down or 90 m/s (200 mph) in a head-down dive. This calculator does not model terminal velocity — it assumes no air resistance.
What is the acceleration due to gravity?
On Earth's surface, the standard acceleration due to gravity is g = 9.80665 m/s² (commonly approximated as 9.81 m/s² or 10 m/s² for quick estimates). It varies slightly by latitude and altitude — slightly less at the equator and at high altitudes, slightly more at the poles. This calculator uses g = 9.81 m/s² (metric) and 32.174 ft/s² (imperial).
How do I convert free fall time to impact speed?
Use v = g × t. If an object falls for 5 seconds (ignoring air resistance): v = 9.81 × 5 = 49.05 m/s ≈ 109 mph. Alternatively, if you know the drop height, use v = √(2gh): for a 50 m drop, v = √(2 × 9.81 × 50) = √981 ≈ 31.3 m/s.