DIY: How to Calculate Your Vertical Jump

I was at the Imaginarium Discovery Center in Anchorage, Alaska when I discovered a curious machine. You stand on a rubber pad and jump into the air. The machine measures your time in the air and video tapes it in ultra slow motion. This all got me to thinking... how high did I jump?

I've measured my vertical jump in fitness testing for high school P.E. and college track before. My best verticals have been in the range of 26-28 inches, which is decent but nothing like Michael Jordan's spectacular 43-48 inch vertical. Anything above 40 is considered outstanding. But at the museum, I got a chance to see my jump in slow motion and see how long I'd been in the air. The verdict on this attempt? 64 hundredths of a second. See for yourself:

I wondered, if I knew the amount of time I was in the air, couldn't I figure out how high I had jumped? After Googling physics formulas with no luck, I decided to consult my high school physics teacher. A quick refresher on basic physics helped me arrive at my answer: a measly 19 and three-quarter inches! I think I'm going to blame that on the fact that I was wearing Top-Siders at the time. Now for the part you've been waiting for:

How to calculate your vertical jump

The Jump

My jump was recored by a high-tec video camera and pressure-sensative pad. But you can get a pretty darn good measurement with a stopwatch. For more accurate results, have a friend help you out. Simply click the stopwatch when your feet leave the ground and click it again on impact.

Assumptions

1. There's no wind resistance
2. You're jumping straight up and down

The Math

I hate math. Skip this part.

Variables
To calculate your vertical, these are the variables you'll need calculate:
1. Time t (from ground to peak height — this is half of your total time in the air)
2. Acceleration a (how fast your body is accelerating through the air)
4. Ending velocity V (your velocity after you finished your jump)
3. Initial velocity V₀ (how much speed your legs generated as you left the launch pad)

1 - Time
What comes up must come down. When you jump in the air you're actually traveling twice the distance of your vertical. Since you really only care about your vertical for the physics calculations, take your total time and cut it in half.
(My time: .64 x .5 = .32 seconds)

2 - Acceleration
This is a constant equal to the force of gravity, approximately -9.81 m/s².

3 - Ending velocity
This is easy. You're interested in finding out the distance from the ground at the peak of your jump. The peak of your jump occurs exactly where you're no longer traveling upward but before you begin traveling downward, so your ending velocity is equal to 0. (If you didn't reach a velocity of zero at some point during your jump you'd be floating off somewhere in space.)

4 - Initial velocity
Your initial velocity represents the amount of speed your body generated when it left the ground. Using our variables so far, you can calculate your initial velocity:
V_(velocity) = V_{0 (initial velocity)} + a_{(acceleration)} * t_(time)
(My initial velocity: 3.136 m/s)

Factors that affect initial velocity
The more powerful your calves, quads, hamstrings, and core, the more force you will exert on the ground and more speed you will leave the ground with (P_avg=∆W/∆t). The heavier you are, the more force is required to accelerate your body to your initial velocity (F=ma).

The final equation
Here's the final equation to calculate distance traveled using the variables we've already calculated:
D_(distance) = (.5) * a_{(acceleration)} * t_(time)² + V_{0 (initial velocity)} * t_time
(My distance, d = (.5) * (-9.81) * (.32)² + 3.136 * (.32) = 0.5023 meters).

Converting to inches
Google says there are 39.3700787 inches in one meter. So in order to convert your vertical leap from meters to inches, just multiply by around 39.37 inches/meter. (That leaves me with 0.5023 meters x 39.37 inches/meter = 19.78 inches.

Google says there are 39.3700787 inches in one meter

Cheat sheet: look up your results

How do I stack up?

Total Time	Vertical Jump
Seconds	Meters	Inches
0.00	0.0000	0.00
0.01	0.0001	0.00
0.02	0.0005	0.02
0.03	0.0011	0.04
0.04	0.0020	0.08
0.05	0.0031	0.12
0.06	0.0044	0.17
0.07	0.0060	0.24
0.08	0.0078	0.31
0.09	0.0099	0.39
0.10	0.0123	0.48
0.11	0.0148	0.58
0.12	0.0177	0.70
0.13	0.0207	0.82
0.14	0.0240	0.95
0.15	0.0276	1.09
0.16	0.0314	1.24
0.17	0.0354	1.40
0.18	0.0397	1.56
0.19	0.0443	1.74
0.20	0.0491	1.93
0.21	0.0541	2.13
0.22	0.0594	2.34
0.23	0.0649	2.55
0.24	0.0706	2.78
0.25	0.0766	3.02
0.26	0.0829	3.26
0.27	0.0894	3.52
0.28	0.0961	3.78
0.29	0.1031	4.06
0.30	0.1104	4.34
0.31	0.1178	4.64
0.32	0.1256	4.94
0.33	0.1335	5.26
0.34	0.1418	5.58
0.35	0.1502	5.91
0.36	0.1589	6.26
0.37	0.1679	6.61
0.38	0.1771	6.97
0.39	0.1865	7.34
0.40	0.1962	7.72
0.41	0.2061	8.12
0.42	0.2163	8.52
0.43	0.2267	8.93
0.44	0.2374	9.35
0.45	0.2483	9.78
0.46	0.2595	10.22
0.47	0.2709	10.66
0.48	0.2825	11.12
0.49	0.2944	11.59
0.50	0.3066	12.07
0.51	0.3189	12.56
0.52	0.3316	13.05
0.53	0.3445	13.56
0.54	0.3576	14.08
0.55	0.3709	14.60
0.56	0.3846	15.14
0.57	0.3984	15.69
0.58	0.4125	16.24
0.59	0.4269	16.81
0.60	0.4415	17.38
0.61	0.4563	17.96
0.62	0.4714	18.56
0.63	0.4867	19.16
0.64	0.5023	19.77
0.65	0.5181	20.40
0.66	0.5342	21.03
0.67	0.5505	21.67
0.68	0.5670	22.32
0.69	0.5838	22.98
0.70	0.6009	23.66
0.71	0.6182	24.34
0.72	0.6357	25.03
0.73	0.6535	25.73
0.74	0.6715	26.44
0.75	0.6898	27.16
0.76	0.7083	27.89
0.77	0.7270	28.62
0.78	0.7461	29.37
0.79	0.7653	30.13
0.80	0.7848	30.90
0.81	0.8045	31.67
0.82	0.8245	32.46
0.83	0.8448	33.26
0.84	0.8652	34.06
0.85	0.8860	34.88
0.86	0.9069	35.71
0.87	0.9281	36.54
0.88	0.9496	37.39
0.89	0.9713	38.24
0.90	0.9933	39.10
0.91	1.0155	39.98
0.92	1.0379	40.86
0.93	1.0606	41.76
0.94	1.0835	42.66
0.95	1.1067	43.57
0.96	1.1301	44.49
0.97	1.1538	45.42
0.98	1.1777	46.37
0.99	1.2018	47.32
1.00	1.2263	48.28
1.01	1.2509	49.25
1.02	1.2758	50.23
1.03	1.3009	51.22
1.04	1.3263	52.22
1.05	1.3519	53.23
1.06	1.3778	54.24
1.07	1.4039	55.27
1.08	1.4303	56.31
1.09	1.4569	57.36
1.10	1.4838	58.42
1.11	1.5109	59.48
1.12	1.5382	60.56
1.13	1.5658	61.65
1.14	1.5936	62.74
1.15	1.6217	63.85

A graphical approach

A graphical look at vertical jump time versus height.

How good is my vertical jump?

For men and women age 18-29:

	Vertical Jump (in)
Percentile	Men	Women
90	24.4	16.6
80	23.2	15.8
70	22.0	14.9
60	20.7	14.0
50	19.5	13.2
40	18.3	12.3
30	17.1	11.4
20	15.9	10.6
10	14.6	9.7

Source: The University of Texas At Austin

Update: Andreas Rauh over at http://www.whatsmyvertical.com/ has taken the methodology here and built a cool tool that allows you to upload your video for a precise calculation of your vertical. Check it out!