How free fall calculator works
Free fall is motion under gravity alone: no air resistance, no thrust, just a constant downward acceleration g. Starting from rest, the height fallen in time t is h = ½ g t² and the speed reached is v = g t. This calculator uses the agreed standard value g = 9.81 m/s² and states the no-drag assumption openly, because it is the model — the idealised textbook case where a hammer and a feather dropped together land together, as Apollo 15's David Scott demonstrated on the Moon in 1971.
The numbers grow fast, which is the whole physics story. Drop something 1 m and it lands after √(2 × 1 / 9.81) ≈ 0.45 s at 4.43 m/s. From 19.62 m — exactly ½ × 9.81 × 2² — the fall takes 2.00 s and the object hits at 19.62 m/s, about 70.6 km/h. From 44.145 m: 3.00 s and 29.43 m/s (106 km/h, approaching a skydiver's terminal speed). Notice the pattern: double the time and the distance quadruples, because distance grows with the square of time while speed grows linearly.
The calculator accepts either a height or a time — the other is the answer — and an optional initial downward velocity for objects thrown rather than dropped, which turns the equations into h = v₀t + ½gt² and v = v₀ + gt. Results include feet for the height and km/h and mph for the impact speed. The honesty clause: real falls above a few tens of metres diverge from this model as drag builds — a human's terminal velocity is roughly 55 m/s — and for real-world drop scenarios the idealised numbers are a lower bound on time and an upper bound on impact speed.