Free Fall Calculator: Velocity, Distance & Time

Free Fall Calculator: Velocity, Distance, and Time

A free fall calculator finds the speed, distance fallen, and final height of an object dropped or thrown under gravity, with no other forces acting on it. Enter a starting height, a starting velocity, and a time, and it returns the object's final velocity, the distance it fell, and how far it still is above the ground.

What Is Free Fall?

Free fall is motion caused by gravity alone. Air resistance is ignored. Near Earth's surface, every falling object speeds up at the same rate, no matter its mass. A coin and a hammer dropped together hit the ground at the same instant, as long as air drag is small enough to ignore.

Galileo Galilei reached this conclusion centuries ago, overturning the older idea that heavier objects fall faster. In 1971, Apollo 15 astronaut David Scott dropped a hammer and a feather on the Moon, where there is no air to slow the feather. Both landed together, on camera.

The rate of that acceleration is called standard gravity, written g. Its defined value is exactly 9.80665 meters per second squared (m/s²). The General Conference on Weights and Measures adopted 980.665 cm/s² in 1901. In imperial units this is 32.17405 feet per second squared (ft/s²), because one ft/s² equals exactly 0.3048 m/s². The calculator uses these exact values. Textbooks often round to 9.81 m/s².

Free Fall Formula

Three equations cover every free fall problem. Downward is treated as the positive direction.

Velocity formula

$v = v_0 + gt$

• $v$ = final velocity
• $v_0$ = initial velocity (0 if dropped from rest; negative if thrown upward)
• $g$ = standard gravity, 9.80665 m/s² (or 32.17405 ft/s²)
• $t$ = time elapsed, in seconds

Distance formula

$d = v_0t + \frac{1}{2}gt^2$

For an object dropped from rest ($v_0 = 0$), this simplifies to $d = \frac{1}{2}gt^2$.

Velocity-distance formula

When time is unknown, this equation connects velocity and distance directly:

$v^2 = v_0^2 + 2gd$

For an object dropped from rest, this simplifies to $v = \sqrt{2gd}$. It is the formula used to find impact speed from a known drop height, or drop height from a known impact speed.

How to Calculate Free Fall With This Calculator

The calculator takes three inputs and computes three results.

1. Choose a unit system. Metric uses meters and meters per second. Imperial uses feet and feet per second.
2. Enter the initial height, the height the object starts at above the ground. It cannot be negative.
3. Enter the initial velocity. Use 0 for an object dropped from rest, a positive number for an object thrown downward, or a negative number for an object thrown upward.
4. Enter the time elapsed since the object was released. It must be greater than zero.

The calculator then returns the final velocity, the distance traveled, and the final height (the initial height minus the distance fallen). If the entered time is long enough that the object would already have hit the ground, the calculator reports that instead of a negative height.

Example: Time and Velocity From a Known Height

A wrench is dropped from a scaffold 20 meters high. How long does it take to hit the ground, and how fast is it moving on impact?

Using $d = \frac{1}{2}gt^2$ with $d = 20$ m and $g = 9.80665$ m/s²:

$t = \sqrt{\frac{2 \times 20}{9.80665}} \approx 2.02 \text{ seconds}$

$v = gt = 9.80665 \times 2.02 \approx 19.8 \text{ m/s (about 71 km/h)}$

Example: Height From Impact Velocity

An object hits the ground at 25 m/s after being dropped from rest. From what height did it fall?

Using $v^2 = 2gd$:

$d = \frac{v^2}{2g} = \frac{25^2}{2 \times 9.80665} = \frac{625}{19.6133} \approx 31.9 \text{ meters}$

That is roughly the height of a ten-story building.

How Gravity Changes

Standard gravity, 9.80665 m/s², is an average reference value. Actual gravity varies slightly across Earth's surface. It is weaker at the equator (about 9.78 m/s²) than at the poles (about 9.83 m/s²), because Earth bulges outward at the equator and spins fastest there. Gravity also weakens slightly with altitude.

Other worlds have very different gravity, so the same formulas give very different results. NASA lists these equatorial surface gravity values (for Jupiter, at the 1-bar level of its atmosphere):

On the Moon, a dropped object gains speed about six times more slowly than on Earth. The same drop takes about 2.5 times as long, since time grows with $\sqrt{1/g}$.

Free Fall and Air Resistance

These formulas assume a vacuum, with no air pushing back on the object. Real air resistance grows with the square of speed, so it matters more at higher velocities. It has little effect on a dense, compact object like a wrench or a stone falling a short distance. It has a large effect on light or wide objects, such as a feather, a sheet of paper, or a parachute.

When air resistance grows large enough to match the pull of gravity, the object stops accelerating and falls at a constant speed, called terminal velocity. A skydiver reaches terminal velocity long before opening a parachute.

Frequently Asked Questions

What is free fall in physics?

Free fall is the motion of an object acted on by gravity alone, with air resistance ignored. All falling objects near Earth's surface accelerate downward at the same rate, about 9.81 m/s², regardless of their mass.

Why do all objects fall at the same rate?

Gravity pulls harder on a heavier object, but a heavier object also resists a change in motion more (it has more inertia). These two effects cancel exactly, so mass does not affect the rate of acceleration in free fall.

What is the formula for free fall velocity?

$v = v_0 + gt$, where $v_0$ is the starting velocity, $g$ is gravitational acceleration, and $t$ is time. For an object dropped from rest, this is simply $v = gt$.

What is the formula for free fall distance?

$d = v_0t + \frac{1}{2}gt^2$. For an object dropped from rest, this simplifies to $d = \frac{1}{2}gt^2$.

How long does it take an object to fall a given height?

Solving the distance formula for time gives $t = \sqrt{2d/g}$, for an object dropped from rest. A 20-meter drop takes about 2.02 seconds.

Why does this calculator use 9.80665 m/s² instead of 9.8?

9.80665 m/s² is the exact internationally defined value of standard gravity. Rounding it to 9.8 or 9.81 is common in textbooks and is accurate enough for most purposes, but the calculator uses the exact defined value, in both metric and imperial units, so results match precisely regardless of which unit system is selected.

Does this calculator account for air resistance?

No. It assumes idealized free fall in a vacuum. This gives accurate results for dense, compact objects falling moderate distances, but overestimates speed and distance for light or wide objects, or for very long falls where air resistance becomes significant.

References

1. National Institute of Standards and Technology. The International System of Units (SI), NIST SP 330 (2019). NIST SP 330 — 3rd CGPM (1901) declaration: standard acceleration due to gravity is 980.665 cm/s².
2. National Institute of Standards and Technology. NIST Guide to the SI, Appendix B.8: Factors for units listed alphabetically. NIST SP 811 Appendix B.8 — standard free-fall acceleration 9.806 65 m/s²; 1 ft/s² = 0.3048 m/s².
3. NASA Space Science Data Coordinated Archive. The Apollo 15 Hammer-Feather Drop. Apollo 15 hammer-feather drop — David Scott dropped a hammer and a feather on the Moon; they fell at the same rate.
4. NASA Space Science Data Coordinated Archive. Earth Fact Sheet. Earth fact sheet — surface acceleration 9.780 m/s² at the equator and 9.832 m/s² at the poles.
5. NASA Space Science Data Coordinated Archive. Planetary Fact Sheet - Metric. Planetary fact sheet — equatorial gravity: Moon 1.6, Mars 3.7, Venus 8.9, Jupiter 23.1 m/s² (1-bar level).