Free Fall

Calculating Free-Fall Time and Impact Velocity

Free fall is the motion of an object falling under gravity alone, ignoring air resistance — the standard simplification used for a quick estimate. Enter either the height it falls from or the time it falls for, and this calculator finds the other, plus its impact velocity.

The Formula

$$\vB{\text{Height}} = \frac{1}{2} \times g \times \vA{\text{Time}}^2$$ $$\vA{\text{Time}} = \sqrt{\frac{2 \times \vB{\text{Height}}}{g}}$$ $$\vC{\text{Velocity}} = g \times \vA{\text{Time}}$$

where $g$ is gravitational acceleration, defaulted to Earth’s standard gravity (9.80665 m/s²).

Worked Example

An object falling from a height of 20 m:

1. Find fall time: $\vA{\text{Time}} = \sqrt{\frac{2 \times \vB{20}}{9.80665}} \approx \vA{2.02}$ seconds.
2. Find impact velocity: $\vC{\text{Velocity}} = 9.80665 \times 2.02 \approx \vC{19.81}$ m/s (about 71.3 km/h, or 44.3 mph — roughly as fast as a car on a city street).

Key Factors to Consider

• Air resistance becomes significant at higher speeds and for lighter, larger-surface-area objects. A dense, compact object (like a rock) falling a short distance closely matches this idealized calculation, while a light, spread-out object (like a sheet of paper) diverges from it quickly, since air resistance grows with speed and eventually balances gravity at an object’s “terminal velocity” — a real-world limit this simplified free-fall model doesn’t include.
• Gravitational acceleration varies slightly by location on Earth, not just by planet. Standard gravity (9.80665 m/s²) is an internationally agreed reference value — actual local gravity varies very slightly with altitude and latitude, though the difference is small enough to ignore for virtually all everyday calculations.
• This calculator assumes a straight vertical drop starting from rest. An object thrown downward, launched at an angle, or already moving when it starts falling needs a fuller projectile-motion treatment (accounting for initial velocity and, for angled motion, horizontal distance) rather than this pure free-fall model.
• The same formulas work in reverse for a rising object under gravity alone, with sign flipped. An object thrown straight up decelerates under the same gravitational constant, reaches a peak, then falls — the free-fall equations describe the falling half of that motion directly.

Common Mistakes

• Assuming a heavier object falls faster than a lighter one. As covered above, this calculator’s idealized free-fall model has no dependence on mass at all — in the absence of air resistance, a bowling ball and a marble dropped from the same height hit the ground at the same instant, a result famously demonstrated on the Moon during Apollo 15’s hammer-and-feather drop.
• Mixing unit systems between height and gravitational acceleration. As covered above, the formulas here use SI units (meters, seconds, and Earth’s standard gravity of 9.80665 m/s²) internally — entering a height in feet without converting first produces a fall time and impact velocity that look plausible but are actually wrong.
• Treating this calculator’s result as accurate for a light, wide object like a leaf or a sheet of paper. As covered above, air resistance becomes significant for objects with a large surface area relative to their mass, and this model doesn’t account for it — the calculated fall time and velocity only closely match reality for a dense, compact object.
• Assuming the object already had some downward speed before it started falling. As covered above, this calculator’s formulas assume the object starts from rest (zero initial velocity) — an object thrown or launched downward reaches the ground sooner and faster than this calculator predicts.

Useful to Know

• Free fall’s independence from mass is one of the most famous results in physics, first argued by Galileo and later demonstrated literally on the Moon, where there’s no air resistance to complicate the comparison.
• Impact velocity from this calculator can be converted to more familiar everyday units — the worked example above reports a fall’s impact speed in km/h and mph for exactly this reason.
• This calculator pairs naturally with the Force Calculator (for finding the force behind a fall using Newton’s second law) and the Kinetic & Potential Energy Calculator (for the energy an object carries at impact).