Free Fall Calculator
How long does it take to fall, and how fast is the landing? Solve from height, time or impact speed on any planet, then switch on air resistance to see what really happens.
By Manzoor Ahmad, pharmacist · Updated How do you calculate free fall time and speed?
Time to fall is t = √(2h ÷ g) and impact speed is v = √(2gh). Dropped from 100 m on Earth (g = 9.80665 m/s²), an object falls for 4.52 s and lands at 44.3 m/s (159 km/h) in a vacuum. With air resistance, a skydiver-sized object takes longer and tops out near 55 m/s.
With air resistance
Fall table
Free fall equations
Taking down as positive and ignoring air, free fall is just constant acceleration at g. These are the SUVAT equations with a = g.
| Find | Dropped from rest | With initial velocity u |
|---|---|---|
| Time to fall h | t = √(2h ÷ g) | t = (√(u² + 2gh) − u) ÷ g |
| Impact speed | v = √(2gh) = gt | v = √(u² + 2gh) |
| Distance after t | h = ½gt² | h = ut + ½gt² |
| Terminal velocity | vt = √(2mg ÷ ρCdA) | same |
| Fall time with drag | t = (vt ÷ g)·arcosh(egh/vt²) | numerical |
How long does it take to fall? Common heights
Vacuum values on Earth. Real falls of more than a few meters are slightly slower because of air resistance.
| Height | Fall time | Impact speed | In km/h |
|---|---|---|---|
| 0.75 m (table) | 0.39 s | 3.84 m/s | 13.8 |
| 2 m | 0.64 s | 6.26 m/s | 22.5 |
| 5 m | 1.01 s | 9.90 m/s | 35.7 |
| 10 m (3 floors) | 1.43 s | 14.0 m/s | 50.4 |
| 20 m | 2.02 s | 19.8 m/s | 71.3 |
| 56 m (Tower of Pisa) | 3.38 s | 33.1 m/s | 119 |
| 100 m | 4.52 s | 44.3 m/s | 159 |
| 828 m (Burj Khalifa) | 13.0 s | 127 m/s | 459 |
Worked example: 1,000 m with and without air
In a vacuum, t = √(2 × 1000 ÷ 9.807) = 14.3 s. A belly-to-earth skydiver (terminal velocity ≈ 55 m/s) takes about 22.0 s to fall the same 1,000 m and is already within 0.1% of terminal speed at the end.
Free fall FAQs
Dropped from rest with no air resistance, the distance fallen is h = ½gt², the speed is v = gt, and the time to fall a height h is t = √(2h ÷ g). On Earth g = 9.80665 m/s².
In a vacuum on Earth, t = √(2 × 100 ÷ 9.81) = 4.52 s, reaching 44.3 m/s (159 km/h). Air resistance makes a real fall slightly longer and slower.
Use v = √(2gh). From 10 m the impact speed is √(2 × 9.81 × 10) = 14.0 m/s, about 50 km/h, regardless of the object's mass.
Not in a vacuum: all objects fall with the same acceleration g. In air, a heavy, compact object falls faster than a light, broad one because drag affects it less relative to its weight.
Terminal velocity is the steady speed at which air drag equals weight, v = √(2mg ÷ ρCdA). A skydiver in a belly-to-earth position reaches about 55 m/s (200 km/h).
A falling object approaches terminal velocity gradually. It reaches about 76% of it after one 'characteristic time' vt ÷ g, and about 96% after two. For a skydiver that is roughly 6 and 11 seconds.
Standard gravity is defined as exactly 9.80665 m/s². Real values range from about 9.78 m/s² at the equator to 9.83 m/s² at the poles.
On Earth, 4.9 m in the first second. After 2 s it has fallen 19.6 m and after 3 s, 44.1 m, because distance grows with the square of time.
Yes. Enter a negative initial velocity (upward, since down is positive here). The calculator includes the time spent rising before the object comes back down.
The Moon's gravity is 1.62 m/s², about one-sixth of Earth's. A 10 m drop takes 3.5 s there versus 1.4 s on Earth, and lands at 5.7 m/s instead of 14 m/s.
Yes, in the physics sense. An object in free fall feels no support force, which is why astronauts in orbit, who are constantly falling around Earth, feel weightless.
It uses the standard quadratic drag equation with constant air density (1.225 kg/m³ at sea level) and a fixed drag coefficient. It is realistic for everyday drops, but air thins with altitude, so very high jumps fall faster than predicted.
Sources
For education and estimation. Real falls depend on air density, posture and wind. Never use these figures to judge whether a jump or drop is safe.