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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).

How to use this calculator

  1. Enter the vertical drop height in your preferred unit.
  2. Leave initial speed blank for a drop from rest, or enter a non-negative downward speed.
  3. Leave gravity blank for 9.81 m/s² on Earth, or set another value.
  4. Calculate to see fall time, impact speed and a table of distance and speed during the fall.

Assumptions and limitations

This is a vertical fall with constant gravitational acceleration and no air resistance. It is suitable for idealized drops near a body’s surface. It does not model terminal velocity, changing gravity over large distances, or an initial upward throw.

Height and downward speed must be non-negative; gravity must be positive. Object mass does not affect the answer in this model. Surface gravity varies by location; the Moon and Mars examples use approximate values.

For air drag, see the terminal velocity calculator. For angled launches, use the projectile motion calculator.

Sources

OpenStax University Physics: Free Fall

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).

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