Free fall calculator

The formula

$$t = \sqrt{\frac{2h}{g}}$$ $$v = g\,t = \sqrt{2gh}$$

$h$ is the drop height, $g$ the acceleration due to gravity (9.80665 m/s² on Earth), $t$ the time to fall and $v$ the speed on impact.

Where it comes from

A dropped object starts at rest and gains speed at a constant rate $g$, so after time $t$ its speed is $v = g t$.

Because speed rises steadily from 0 to $gt$, the average speed during the fall is half the final speed, $\tfrac{1}{2}gt$. Distance is average speed times time:

$$h = \tfrac{1}{2}g t \cdot t = \tfrac{1}{2} g t^2$$

Solve for $t$ to get the fall time, then substitute into $v = gt$:

$$v = g\sqrt{\frac{2h}{g}} = \sqrt{2gh}$$

The same result comes from energy. Potential energy $mgh$ turns into kinetic energy $\tfrac{1}{2}mv^2$. The mass cancels, which is why a hammer and a feather fall together on the Moon.

Worked example

A ball dropped from 20 m:

$$t = \sqrt{\frac{2 \times 20}{9.81}} = 2.02\ \text{s}$$ $$v = \sqrt{2 \times 9.81 \times 20} = 19.8\ \text{m/s}$$

That’s about 71 km/h, or 44 mph.

Watch out for

• Air resistance. This is a vacuum result. A falling person reaches a terminal speed of about 55 m/s and stops speeding up. Light or flat objects, like paper, are slowed much sooner.
• Height quadruples for double the speed. Because $v \propto \sqrt{h}$, a fall from 4 times higher hits only twice as fast.

Sources

• OpenStax, University Physics Volume 1, section 3.5 "Free Fall"
• BIPM, standard acceleration of gravity g₀ = 9.80665 m/s² (3rd CGPM, 1901)

Last checked November 11, 2026