Physics · Classical Mechanics · Dynamics & Forces
Vertical Jump Power Calculator
Calculate the peak mechanical power output of a vertical jump using body mass and jump height via the Lewis or Sayers formula.
Calculator
Formula
Sayers formula: P_peak is peak power in Watts, h_cm is jump height in centimetres, m is body mass in kilograms. The Lewis (1974) formula is the square-root approximation: P = \sqrt{4.9 \cdot m} \cdot \sqrt{h_{m}} \cdot 9.81, where h_m is jump height in metres.
Source: Sayers S.P. et al. (1999) 'Cross-validation of three jump power equations', Medicine & Science in Sports & Exercise 31(4):572-577; Lewis D.A. (1974) as cited in Fox & Mathews, The Physiological Basis of Physical Education and Athletics.
How it works
The Sayers formula (1999) is the most commonly recommended equation: P = 60.7 × hcm + 45.3 × m − 2055, where hcm is jump height in centimetres and m is body mass in kilograms. It was validated against force-plate measurements across a large sample and consistently outperforms earlier equations in cross-validation studies.
The older Lewis formula (1974) uses a square-root model derived from mechanical energy principles: P = √(4.9 × m) × √(hm) × g, where hm is jump height in metres and g = 9.81 m/s². While intuitive and historically significant, it tends to underestimate power compared to force-plate criterion values, especially at higher jump heights.
Takeoff velocity is derived from projectile kinematics: v = √(2gh), the speed a body must leave the ground to reach height h under gravity alone. This metric is useful for ballistic training prescription and sprint/jump correlations.
Worked example
Suppose an athlete has a body mass of 80 kg and achieves a vertical jump height of 55 cm.
Sayers formula:
P = 60.7 × 55 + 45.3 × 80 − 2055
P = 3338.5 + 3624 − 2055 = 4907.5 W
Relative power = 4907.5 / 80 = 61.3 W/kg
Lewis formula (comparison):
P = √(4.9 × 80) × √(0.55) × 9.81
P = √392 × √0.55 × 9.81 = 19.80 × 0.7416 × 9.81 ≈ 4460 W
Takeoff velocity:
v = √(2 × 9.81 × 0.55) = √(10.791) ≈ 3.28 m/s
The Sayers equation gives the higher, more accurate estimate consistent with force-plate validation data.
Limitations & notes
Both formulas estimate peak power from a single kinematic variable (jump height) and body mass. They do not account for differences in jump technique, arm swing contribution, depth of countermovement, or individual body proportions, all of which affect actual force-plate measured power. The Sayers equation was derived from a specific population of college-aged adults; its accuracy may be reduced in children, elderly individuals, or elite athletes at the extreme ends of power output. The Lewis formula systematically underestimates peak power and is retained here for historical comparison only. Jump height should be measured consistently — preferably using a Vertec, jump mat, or video analysis — since small errors in height measurement propagate directly into power estimates. These equations should not replace force-plate testing in high-stakes clinical or research contexts.
Frequently asked questions
Which formula should I use — Sayers or Lewis?
Use the Sayers (1999) formula for most applications. It was cross-validated against force-plate data and is significantly more accurate than the Lewis equation. The Lewis formula is included for historical context and comparison with older literature.
How do I measure vertical jump height accurately?
The most common methods are the Vertec reach device (standing reach vs. jump reach), a jump mat that measures airtime (h = g × t² / 8), or video analysis with frame-by-frame tracking. Avoid self-reported estimates — even a 2 cm error in height can change calculated power by over 100 W.
What is a good peak power output for a vertical jump?
For adult males, power outputs of 4000–5500 W (roughly 50–70 W/kg) are typical for recreational athletes. Elite male basketball or volleyball players often exceed 6000–8000 W. Female athletes typically produce 3000–5000 W. These are rough benchmarks; compare within age, sex, and sport-specific norms.
Why does heavier body mass increase calculated power even at the same jump height?
Power is force times velocity. A heavier athlete must generate more force to achieve the same jump height (overcoming greater gravitational pull), implying higher impulse and thus higher peak power. This is why relative power (W/kg) is often more meaningful for comparing athletes of different sizes.
Can I use this calculator for squat jump or drop jump as well?
Yes, provided you measure the net jump height (centre-of-mass displacement from takeoff to peak). The Sayers formula was validated primarily on countermovement jumps, but the physics of ballistic height and power estimation apply to any vertical jump variant where you can measure jump height and body mass.
What does takeoff velocity represent physically?
Takeoff velocity is the minimum vertical speed at which the athlete's centre of mass must leave the ground to reach the measured jump height, calculated from energy conservation: v = √(2gh). It reflects the explosive impulse the legs deliver in the final phase of ground contact and correlates well with sprint acceleration ability.
Last updated: 2025-01-30 · Formula verified against primary sources.