Vertical Jump Calculator

A standing jump is over almost before it starts. The feet leave the floor, the body rises, hangs and falls, and about half a second later the test is finished. Measuring the jump means measuring that half second.

The traditional test avoids the clock altogether. The jump and reach, also called the Sargent jump, needs a flat wall and some chalk on the fingertips: reach up flat-footed and touch the wall, jump and touch it again at the top, and measure between the two marks. Its weakness is timing. A review of jump measurement notes that a touch made anywhere but the peak of the jump reads low, and that hitting the peak takes practiced coordination of arms and legs.

Coaches and clinicians jump people because the test is quick and says something about the legs. Researchers who study the method call it one of the simplest and most common tests of muscular fitness, used to follow training, to judge readiness to return after injury, and to check function in the young and the old. What it measures directly is modest: how far the body’s center of mass rises.

Power is an inference from that height. One regression, built from 108 college-age men and women jumping on a force platform, estimates peak power in watts as 60.7 times the jump height in centimeters, plus 45.3 times body mass in kilograms, minus 2055. Its authors put the standard error at 355 watts, and the height they fed it was a jump-and-reach score, a detail that matters later.

Half a second, one line of physics

The other way to measure a jump is to time it. In 1983 Bosco, Luhtanen and Komi described a jumping test that needed little more than a digital timer reading to a thousandth of a second, and the reasoning behind it is first-year mechanics. Once the feet are off the floor nothing acts on the jumper except gravity, since air resistance is negligible, so the body is a projectile. If it comes down at the height it left from, the trip up and the trip down take equal time. A body that falls from rest for half the flight time t drops g times the square of t / 2, divided by 2.

That fall is the height of the jump, and it is the whole method: h = g t^2 / 8. The speed at takeoff is g t / 2.

Take a flight of 0.5 s. Standard gravity is 9.80665 meters per second squared, so the height is 9.80665 times 0.25, divided by 8: 0.306 m, which is 30.6 cm, a little over 12 inches. The takeoff speed is 2.45 meters per second. Type 0.5 into the tool as a flight time and those are the numbers it returns. The same arithmetic runs backwards. One published group of 52 men averaged 40.2 cm by flight time, which works out to 0.573 s in the air and a takeoff speed of 2.81 meters per second.

Notice the square. Double the time and the height is four times as large. The authors of the first study to validate an iPhone app for this test drew the consequence themselves: because the time is squared, the error grows with longer flights.

The gap between two frames

A phone camera turns the timer into something everyone owns. The app validated in 2015 ran on an iPhone filming at 120 frames per second, held near the floor about 1.5 m in front of the jumper and zoomed in on the feet. The user picks two frames: the first with both feet off the ground, and the first with a foot touching down again. Across 100 jumps by 20 men, heights from the app and from a force platform timing the same flights differed by 1.1 cm on average, with a correlation of 0.995. The same authors named the weakness. At 120 frames per second the instant of takeoff or landing may simply not be on film.

That is the limit of the whole approach, and it can be stated exactly. A camera samples the jump. Somewhere between the last frame with the feet on the floor and the next one, the toes left; somewhere between the last airborne frame and the first one back down, they returned. Each end is unknown by up to one frame interval, so the flight time is known only to within one interval either way.

At 30 frames per second an interval is 33.3 ms. For the 0.5 s jump above, the height could lie anywhere from 26.7 to 34.9 cm, which is 4.1 cm either way. At 60 frames per second the doubt is 2.0 cm, at 120 it is 1.0 cm, and at 240 it is 0.5 cm.

Those are worst cases, and measured error is smaller. A 2023 study filmed jumps at 1000 frames per second, cut the footage down to 120, 240 and 480, and had three observers mark every clip. The typical error in flight time was 3.4 ms at 120 frames per second, 1.8 ms at 240, 1.2 ms at 480 and 0.8 ms at 1000, which for jump height comes to 1.4, 0.7, 0.5 and 0.3 percent. The authors concluded that going beyond 240 buys little, and that the remedy for a noisy test is to average several jumps.

One jump, though, cannot say where in its range it fell. A single result is honest only when the range is quoted beside it.

A clock that runs eight times slow

The frame rate that matters is the one the camera filmed at, and a file does not always say what that was. Phones now film at 120 and 240 frames per second, the two rates at which the best-known jump app has been validated, and a slow-motion mode saves such footage to play back slowly. Wikipedia’s account of slow motion names two ways of storing it: one keeps real time, so the file’s frame rate is the sensor’s, and the other stretches the clip, so the file lasts longer than the event did.

Android’s source code spells out the idea behind every such clip: when the capture rate differs from the frame rate, the video was acquired at a different rate than it plays, which is what produces slow motion. A player, for its part, reports only each frame’s timestamp on the file’s own timeline.

So the file’s clock can run slow. Film at 240, save to play at 30, and it runs 8 times slow: the half-second flight now fills four seconds of file time. Put four seconds into the formula and the jump is 19.6 m high. That one is easy to catch. A clip slowed by a factor of two is harder, because it merely quadruples the height. The cure is to stop trusting the clock: count the frames between the two marks and give each one its real interval, 1/240 of a second.

One more trap hides in a dim room. Android’s camera interface lets the auto-exposure routine adjust the capture frame rate to maintain good exposure, within a range the app sets. An ordinary recording made in poor light may therefore not hold the rate its settings promised.

Filming a jump so it can be measured

The published protocols agree on the setup. Put the camera low and square to the front of the jumper: one study had the researcher lie on the ground with the phone, another used a tripod 30 cm high, and both worked from about 1.5 m with the picture framed on the feet. The feet are the whole subject. Nothing above the ankles helps decide whether a toe is still on the floor. Keep the hands on the hips, as the jumpers in both studies did, because arm position is a known source of error in flight-time heights: in one study of jumps with an arm swing it shifted the center of mass by 1.7 cm.

Then give the camera light. Very high frame rates go with very short exposures, and short exposures need light: the 2023 study shot at 1/32000 of a second and added two lamps to make up the loss. Its authors traced the scatter between earlier phone studies to how well the two frames can be picked, which they said depends on the placement of the phone, the subject and the lighting.

What flight time flatters, and what it leaves out

The formula rests on one assumption: the body lands in the position it took off in. People do not. Ankles and knees are almost straight at takeoff and usually less so at landing, so the center of mass is lower when the feet touch down, the flight lasts longer than the formula supposes, and the height comes out too large. Earlier experiments that set flight-time heights against criterion methods found them too high by up to about 4 cm, which suggests the jumpers came down with some part of the body bent. Those 52 men are a case in point: 40.2 cm by flight time against 36.1 cm from the impulse of the same jumps on a force plate.

A 2024 simulation, the source of that summary, pushed on the ankle alone. The studies it draws on report ankles 10 to 20 degrees more bent at landing than at takeoff, and a change of about 10 degrees is hard to see by eye. Letting the foot come down flat inflated a 30 cm jump by 18 percent for a person of average height, and a 10 cm jump by a tall person by as much as 60 percent. The smaller the jump, the larger the share of it that is landing posture.

Borrowed numbers deserve the same suspicion. In one comparison a jump mat reported flights of 0.629 s on average for jumps that a force plate timed at 0.524 s, and heights of 50 cm against 34 cm. A flight time typed in from another device carries that device’s errors with it.

Even a perfect flight time answers a narrower question than the chalk does. It gives the rise after the feet leave the floor, and by then the jumper is already up on the toes. In one study the same jumps averaged 27.6 cm by flight time and 37.9 cm by motion capture, which follows the body from flat-footed standing. Corrective equations have since been published for takeoff and landing position and for foot size.

Reach tests include that rise, and more: against force plate methods the Vertec, a reach-and-touch device, overestimated how far the center of mass moved, by an amount that depended on how the standing reach was taken.

The gap is not small. Among 440 adolescent handball players measured by both at once, the Vertec read 11.2 cm higher than the Optojump, a system that works from flight time, a difference of 31 percent. The authors concluded that the two cannot be used interchangeably. Neither number is wrong. They measure different things, which is why a flight-time height and a reach height should never share a column, and why a power formula fitted to one should not be fed the other without saying so.

What the method cannot do is quick to list. It cannot see how you landed. It cannot recover the rise before takeoff. It cannot time anything more finely than the gap between two frames, and it cannot know by itself whether the clip was slowed. Inside those limits it is a good test, and practitioners live with its bias on the assumption that the error stays about the same for the same jumper using the same technique. A review that found gaps of 1 to 2 cm between methods and equipment asks for the same equipment, method and instructions at every session. Same camera, same frame rate, hands on hips, several jumps, and the range written beside the number.