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DIY: How to Calculate Your Vertical Jump

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) = V0 (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 (Pavg=∆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 + V0 (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
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
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

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Comments

Anonymous's picture

Whoa this is super neat

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