Vertical Jump to Power: What the Conversion Assumes

The physics half: h = v² ÷ (2g), and there is nothing to argue about

The instant your feet leave the ground, the only force on you worth counting is gravity. Air resistance on a human body moving at walking speed is negligible, and nothing you do in the air changes the path of your centre of mass. So the rise of your centre of mass is fixed by the velocity you left the ground with, through h = v² ÷ (2g), which rearranges to v = √(2gh). Using the standard value g = 32.174 ft/s², a 24 in rise means v = √(2 × 32.174 × 2.0) = 11.34 ft/s. A 16 in rise means 9.26 ft/s; a 28 in rise means 12.25 ft/s.

The square in that relationship is the part people underestimate. Height goes with the square of velocity, so a 10% gain in take-off speed buys a 21% gain in height, and conversely the differences in height between good and great jumpers correspond to much smaller differences in velocity than the height numbers suggest. It also means the useful physical quantity produced by the legs is the velocity, not the height — height is the consequence, and the whole of it is decided before you are airborne.

Flight time is the same equation, rearranged

If the take-off and landing positions are identical, the flight is symmetric: you spend as long going up as coming down, so t = 2v ÷ g, and substituting gives h = g × t² ÷ 8. That is how every contact mat, optical timing gate and phone app works — it never measures your height at all, it measures how long you were off the ground and then applies this equation. A 24 in jump corresponds to 0.705 seconds of flight; 16 in to 0.576 s; 28 in to 0.762 s. The whole useful range of human jumping is squeezed into about a fifth of a second, which tells you immediately how much timing precision the method demands.

Ten milliseconds of timing error — a plausible amount for a phone camera at 100 frames per second — moves a 24 in reading by 0.69 in and a 16 in reading by 0.56 in. That is tolerable. The far larger problem is the symmetry assumption itself, which the next-to-last section takes apart.

The power half is not physics

Power is work divided by time, and the work that matters here was done during the push-off, while your feet were still on the ground — a phase the jump height tells you nothing directly about. Two athletes can reach the same height with completely different force-time curves: one with a long, moderate push, one with a short, violent one. Only a force platform, which records force against time throughout the contact, can resolve that. Everything else is inference.

The three equations you will meet are all regressions built to make that inference. Sayers peak power (W) = 60.7 × jump height in cm + 45.3 × body mass in kg − 2,055. Harman peak power (W) = 61.9 × height in cm + 36.0 × mass in kg + 1,822, with a companion average-power equation, 21.2 × height + 23.0 × mass − 1,393. The Lewis formula gives average power as √4.9 × mass in kg × √(height in metres) × 9.81. Note that all three are metric by construction: an imperial jump has to be converted before it goes in — 180 lb is 81.65 kg and 24 in is 60.96 cm — which is a small thing but a real source of copied errors.

Three formulas, one athlete, a 3,200 W gap

Take a 180 lb athlete with a 24 in jump — 81.65 kg and 60.96 cm once converted. Sayers returns 5,344 W. Harman's peak-power equation returns 8,535 W. That is 3,191 W of disagreement, or 60% of the smaller figure, for two equations that claim to estimate the same physical quantity in the same units. The gap is roughly constant in absolute terms across the whole table — about 3,200 W at every jump height — because the two lines have nearly the same slope in height and differ mostly in their intercepts and mass coefficients. As a percentage it therefore shrinks as the jump gets bigger: 77% at 16 in, 60% at 24 in, 54% at 28 in.

The Lewis figure — 1,384 W for the same athlete — is not a third opinion on peak power. Lewis estimates average power over the push-off, which is a genuinely different quantity, typically a small fraction of the instantaneous peak. Comparing it to Sayers is a category error, and it is made constantly on the web, usually by tables that list all three under one heading called simply power. Harman's own average-power equation returns 1,777 W for the same jump, which is the number Lewis should be compared against, and those two are within about 30% of each other rather than a factor of four.

Sayers and colleagues built their equation precisely because the existing ones were not agreeing with force-platform measurements, and they cross-validated it on 108 college-age athletes and non-athletes. Their equation underestimated measured peak power by less than 1% — but with a standard error of estimate of 355 W. On the 5,344 W figure above, that is 6.6%. So even the best-validated of the three carries a routine individual error of several hundred watts, before any of the measurement problems below are taken into account.

The measurement problem that dominates everything

Three common methods do not measure the same quantity. A jump-and-reach device records the difference between a standing reach and the highest vane displaced in the air — that is hand displacement, and it includes shoulder-girdle elevation and trunk lean that have nothing to do with how high your centre of mass went. A contact mat or timing gate records flight time and infers the centre-of-mass rise from it. A force platform integrates the vertical force record to get take-off velocity directly, and computes the rise from that. These are three different physical questions and they return three different answers.

The size of the discrepancy is not a rounding detail. In one published comparison, jump height read about 27% higher on a jump-and-reach device than on a force platform for the same athletes, and reported differences across the literature span roughly 8% to 36% depending on protocol. Put that 27% on a 24 in jump and you get 30.5 in — 6.5 in of pure method. Feed that inflated height into Sayers, at 154 W per inch, and the power estimate rises from 5,344 W to 6,343 W. That single methodological choice moves the answer by more than the standard error of the equation and more than most training interventions will in a year.

Tucking the legs, quantified

Every flight-time method assumes your body is in the same configuration at take-off and at landing. Tuck your knees in the air, or land with your ankles plantarflexed and your hips lower than they were at take-off, and you fall further than you rose. The extra fall adds time, and the equation reads that time as height it never happened at. The maths gives a rule of thumb that is almost exact for small drops: the reading is inflated by about half the drop.

Worked exactly: a true 24 in jump followed by a landing 2 in lower than take-off produces a flight time of 0.7196 s, which the equation reads as 25.0 in — a 4.1% overestimate. The same 2 in tuck on a true 16 in jump reads 17.0 in, a 6.2% overestimate, because the same absolute error is a bigger share of a smaller jump. A sloppy 4 in tuck on a 16 in jump reads 17.9 in, 12.2% high. Note that the inflation is 1.0 in for a 2 in drop and about 1.9 in for a 4 in drop — half the drop, as promised, with the approximation loosening slightly as the drop grows.

This is why testing protocols insist on landing in the same posture you took off from, with legs extended, and why an athlete who has learned to tuck will appear to improve without training. If you are comparing your own jumps over time, the protocol matters more than the device: the same mat, the same instruction, the same landing, every time.

What to actually do with the number

Report the jump height, the method and the body mass, and let the watts be a derived convenience rather than the headline. Height and take-off velocity are the honest measurements; the power figure adds no information the first two did not already contain, since the formulas are linear functions of exactly those two inputs. If you do want watts, pick Sayers — it is the most recently cross-validated of the three — and then never switch, because a change of equation will move your number by thousands of watts and a year of training probably will not.

Frequently asked questions

How do I convert vertical jump height into take-off velocity?

Take the square root of twice gravity times the height: v = √(2gh). With g = 32.174 ft/s² and the height expressed in feet, a 24 in jump is 2.0 ft, so v = √(2 × 32.174 × 2.0) = 11.34 ft/s. A 16 in jump gives 9.26 ft/s and a 28 in jump 12.25 ft/s. The relationship is exact — no population, no regression, no error bar — because once you are airborne, gravity is the only force acting. The same equation run the other way gives flight time, t = 2v ÷ g, which is 0.705 s for that 24 in jump. Note the square: height scales with the square of velocity, so a 10% faster take-off produces a 21% higher jump.

Which power formula should I use — Sayers, Harman or Lewis?

For peak power, Sayers is the reasonable default: it was developed specifically because the earlier equations did not match force-platform measurements, and it was cross-validated on 108 college-age athletes and non-athletes, underestimating measured peak power by under 1% with a standard error of estimate of 355 W. Harman's peak-power equation returns much larger numbers — 8,535 W against 5,344 W for a 180 lb athlete with a 24 in jump, a 60% difference — so the two are not interchangeable and mixing them across a season will fabricate a change. Lewis is a different question entirely: it estimates average power, not peak, so it is not a competitor to either. Whichever you pick, keep it, and always report which one you used.

Why does my jump measure higher on a jump-and-reach device than on a mat?

Because the two devices are measuring different things. A jump-and-reach device records how far your hand travelled above your standing reach, which includes shoulder-girdle elevation and trunk lean; a mat records flight time and infers how far your centre of mass rose. One published comparison found jump-and-reach readings about 27% higher than a force platform for the same athletes, with reported differences elsewhere ranging from roughly 8% to 36% depending on protocol. On a 24 in jump, 27% is 6.5 in — and fed into the Sayers equation at 154 W per inch, that pushes the power estimate from 5,344 W to 6,343 W. Neither device is wrong; they answer different questions. Pick one, use it for every test, and never compare a number from one against a number from the other.

Does tucking my legs make my jump measure higher?

On a flight-time device, yes, and by a predictable amount. The method assumes you land in the same body position you took off from. Tuck, or land with your hips lower than at take-off, and you fall further than you rose; the extra fall adds flight time, and the equation converts that time into height you never reached. The rule of thumb is that the reading inflates by about half the drop. Worked exactly: a true 24 in jump with a landing 2 in lower reads 25.0 in, 4.1% high; the same 2 in tuck on a true 16 in jump reads 17.0 in, 6.2% high; a 4 in tuck on a 16 in jump reads 17.9 in, 12.2% high. A force platform is immune, since it derives take-off velocity from the ground-contact phase and never uses the landing.

Is peak power or average power the number I want?

It depends what you are comparing, and the two are not close to each other. Peak power is the highest instantaneous value reached during the push-off; average power is the mean across the whole push. For a 180 lb athlete with a 24 in jump, Harman's peak equation gives 8,535 W while Harman's own average equation gives 1,777 W for the same jump — the same author, the same data, a factor of nearly five apart, because they describe different moments. Lewis, at 1,384 W, sits close to Harman's average value, which is where it belongs. The common error on the web is to list Sayers, Harman peak and Lewis side by side under one heading, which makes an apples-to-oranges comparison look like a disagreement. Decide which quantity you want first, then pick a formula that estimates it.