How to calculate free fall
Updated on June 30, 2026 · by Rafael Rossi
In free fall (no air), a body starts from rest and accelerates under gravity g ≈ 9.8 m/s².
Fall time
t = √(2h ÷ g). From 20 m: t = √(40/9.8) ≈ 2.0 s.
Impact speed
v = √(2·g·h) = g·t. From 20 m: v ≈ 19.8 m/s (~71 km/h).
Why mass doesn't matter
In a vacuum, all bodies fall with the same acceleration. The difference in air comes from resistance, not weight — that's why a feather falls slowly and a hammer fast. On the Moon (no air) they fall together, as astronaut David Scott showed on Apollo 15.
The formulas in short
- Fall height:
h = ½·g·t² - Time:
t = √(2h ÷ g) - Speed:
v = g·t = √(2·g·h)
FAQ
What about air resistance? In real falls, air slows a body to a "terminal velocity" (a skydiver reaches ~200 km/h belly-down). The formulas above hold for the ideal case or short falls.
Fall height from time? If something took 2 s to fall, it dropped h = ½ × 9.8 × 2² ≈ 19.6 m.