The Physics of the Universe
HomeCalculators › Free Fall

Free Fall Calculator

Enter a drop height to find the fall time and impact speed of an object in free fall (ignoring air resistance), using h = v₀t + ½gt². Optionally set an initial downward speed or a different gravity.

 

Formula

$$ h = v_0 t + \tfrac{1}{2} g t^{2} \qquad t = \frac{-v_0 + \sqrt{v_0^{2} + 2gh}}{g} \qquad v = \sqrt{v_0^{2} + 2gh} $$

Worked example

Dropping an object from 30.5 m (about 100 ft) from rest on Earth takes \( t=\sqrt{2h/g}=\sqrt{2(30.5)/9.81}\approx 2.49\ \text{s} \) and it hits the ground at \( v=\sqrt{2gh}\approx 24.5\ \text{m/s} \) (about 55 mph).

How it works

In free fall an object accelerates downward at g under gravity alone, with air resistance ignored. From a drop height h and initial downward speed v₀, the fall time is t = (−v₀ + √(v₀²+2gh))/g and the impact speed is v = √(v₀²+2gh).

Because acceleration is constant, all objects fall at the same rate regardless of mass in a vacuum — a hammer and a feather land together on the airless Moon. On other worlds simply change g (Moon 1.62, Mars 3.72 m/s²).

Frequently asked questions

How long does it take to free fall 100 feet?

About 2.5 seconds. 100 ft is 30.5 m, so t = √(2·30.5/9.81) ≈ 2.49 s, ignoring air resistance, reaching roughly 24.5 m/s (55 mph) at the bottom.

How do you calculate the speed of a falling object?

For a drop from rest, v = √(2gh); with an initial speed, v = √(v₀²+2gh). It depends only on height and gravity, not on mass.

Do heavier objects fall faster?

No. Ignoring air resistance, all objects fall at the same rate because gravitational acceleration is independent of mass. Differences on Earth come only from air drag.

What is the acceleration of free fall on Earth?

About 9.81 m/s² at the surface (often rounded to 9.8 or 10). It varies slightly with latitude and altitude, and is much lower on the Moon (1.62 m/s²).

Related calculators