When the only force on an object is gravity, it is in free fall — and its motion is wonderfully simple. Gravity adds a constant 9.81 m/s of speed every second, so the velocity climbs in a straight line while the distance fallen climbs with the square of the time. Two equations capture it all: h = ½gt² for how far it falls, and v = √(2gh) for how fast it lands. Famously, mass cancels out — in a vacuum a feather and a cannonball fall side by side.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: constant-acceleration kinematics (SUVAT).
The free-fall equations
These are the standard constant-acceleration (SUVAT) equations with the acceleration set to g. The square in h = ½gt² is why falls feel slow then sudden — in the first second the object drops about 4.9 m, but in the third second alone it covers over 24 m. Impact velocity depends only on the height and g, never on the mass, which is the counter-intuitive heart of free fall.
Worked example — a 20 m drop
Scenario: An object dropped from rest off a 20 m cliff (g = 9.81 m/s²).
It takes about 2 seconds and lands at nearly 20 m/s — roughly 71 km/h. A 20 kg rock and a 2 kg rock dropped together would land at the same moment and the same speed, because mass plays no part. On the Moon (g = 1.62) the same 20 m drop would take 4.97 s and land much more gently at 8.05 m/s, which is why astronauts could leap so high.
Frequently Asked Questions
h = ½gt², v = gt. Time to fall: t = √(2h/g); impact speed v = √(2gh). 20 m → ~2.0 s, ~19.8 m/s.
~9.81 m/s² on Earth — speed rises 9.81 m/s each second. Moon 1.62, Mars 3.71. Adjustable here.
t = √(2h/g). 5 m ≈ 1.0 s, 20 m ≈ 2.0 s, 45 m ≈ 3.0 s. Distance grows with time squared.
No — ideal vacuum free fall. Real objects reach a terminal velocity (~53 m/s skydiver). Good for dense objects, short drops.
Landing speed: v = √(2gh) from rest. Independent of mass — a feather and hammer hit at the same speed in vacuum.