Calculate Anaerobic Power Using the Regression Equation
Accurately estimate your Peak Anaerobic Power (PAP) using the Sayers regression equation based on body mass and vertical jump height.
PAP (Watts) = (60.7 × Jump Height [cm]) + (45.3 × Body Mass [kg]) – 2055
Power Output Comparison
Chart: Your calculated Peak Power vs. Typical standards for Rec. Athletes and Elite Power Athletes.
Projected Power at Various Jump Heights
| Jump Height (cm) | Peak Power (Watts) | Relative Power (W/kg) | Difference |
|---|
What is the Calculation of Anaerobic Power Using the Regression Equation?
To calculate anaerobic power using the regression equation is a method used by sports scientists and coaches to estimate an athlete’s explosive power output without needing expensive laboratory equipment like force plates. Anaerobic power represents the maximal amount of work a person can perform in a short duration (typically seconds) using energy systems that do not rely on oxygen.
The “regression equation” refers to mathematical formulas derived from statistical analysis of large groups of athletes. These formulas correlate simple field tests—most commonly the Vertical Jump (VJ) and body mass—with actual power measurements taken in a lab. The most widely accepted regression equation for Peak Anaerobic Power (PAP) from a Countermovement Jump is the Sayers Equation.
This calculation is essential for:
- Strength and Conditioning Coaches: To monitor training progress.
- Athletes: To benchmark explosive capabilities against peers.
- Rehabilitation Specialists: To assess return-to-sport readiness.
Anaerobic Power Formula and Mathematical Explanation
When you calculate anaerobic power using the regression equation, specifically the Sayers Equation, you are using a linear formula that weights jump height slightly more heavily than body mass. This derivation comes from the study “Cross-validation of three jump power equations” (Sayers et al., 1999).
The formula for Peak Anaerobic Power (PAP) is:
Variable Definitions
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| PAP | Peak Anaerobic Power | Watts (W) | 2,500 – 7,000+ W |
| Jump Height | Vertical displacement of center of mass | Centimeters (cm) | 30 – 90 cm |
| Body Mass | Total weight of the athlete | Kilograms (kg) | 50 – 120 kg |
Practical Examples (Real-World Use Cases)
Understanding how the numbers interact is crucial when you calculate anaerobic power using the regression equation.
Example 1: The Heavy Power Athlete
Consider a rugby player weighing 105 kg with a vertical jump of 55 cm.
- Calculation: (60.7 × 55) + (45.3 × 105) – 2055
- Step 1: 3338.5 + 4756.5 – 2055
- Result: 6,040 Watts
Interpretation: This athlete generates massive absolute power due to high body mass, making them effective in contact situations like scrums or tackles.
Example 2: The Lightweight Sprinter
Consider a sprinter weighing 65 kg with a high vertical jump of 75 cm.
- Calculation: (60.7 × 75) + (45.3 × 65) – 2055
- Step 1: 4552.5 + 2944.5 – 2055
- Result: 5,442 Watts
Interpretation: Although the absolute power is lower than the rugby player, this athlete’s Relative Power (Watts/kg) is likely higher (83.7 W/kg vs 57.5 W/kg), indicating superior speed and acceleration capabilities.
How to Use This Anaerobic Power Calculator
- Measure Body Mass: Weigh yourself wearing standard athletic clothing. Enter this value in the “Body Mass (kg)” field.
- Test Vertical Jump: Perform a standard Countermovement Jump (CMJ) using a jump mat, Vertec, or wall reach test. Enter the result in centimeters.
- Review Results: The calculator will instantly calculate anaerobic power using the regression equation.
- Analyze Metrics: Look at both the Absolute Power (Watts) and Relative Power (W/kg). Use the chart to see where you stand compared to baselines.
Key Factors That Affect Anaerobic Power Results
Several physiological and external factors influence the outcome when you calculate anaerobic power using the regression equation.
- Muscle Fiber Composition: Athletes with a higher percentage of Type II (fast-twitch) fibers generate significantly more force per unit of time, leading to higher PAP scores.
- Neuromuscular Coordination: The efficiency with which the nervous system recruits muscle motor units affects jump height and, consequently, the power calculation.
- Body Composition: Lean muscle mass contributes to power production, whereas excess adipose tissue adds to body mass (increasing the “Mass” variable in the equation) but reduces jump height, often yielding a misleading or lower relative power score.
- Fatigue Levels: Testing in a fatigued state (e.g., post-workout) will reduce vertical jump height, leading to an underestimation of true anaerobic potential.
- Warm-up Protocol: A proper dynamic warm-up can utilize the post-activation potentiation (PAP) effect, potentially increasing jump height by 2-5% and improving the calculation result.
- Test Accuracy: The regression equation assumes accurate input. Using a wall-reach test (less accurate) versus a jump mat (more accurate) introduces measurement error into the power estimation.
Frequently Asked Questions (FAQ)
No. Other formulas exist, such as the Lewis Formula (estimates average power) or the Harman Formula. However, the Sayers equation is generally preferred for estimating Peak Power from a countermovement jump because it aligns closely with force plate data.
Absolute power tells you how much force you can put into an external object (like a barbell or opponent). Relative power tells you how well you can move your own body. For sprinters and jumpers, relative power is the more critical metric.
Strictly speaking, no. This specific regression equation was validated using the Countermovement Jump (CMJ), which utilizes the stretch-shortening cycle. A static Squat Jump typically results in lower heights and requires a different equation.
For males, elite power athletes often exceed 65-70 W/kg. For females, elite athletes often exceed 55-60 W/kg. Recreational athletes will typically score significantly lower.
Yes. Anaerobic power typically peaks in the mid-20s and gradually declines with age due to the loss of fast-twitch muscle fibers (sarcopenia) unless counteracted by specific power training.
The Sayers equation has a high correlation coefficient with actual lab data, but standard error estimates exist. It provides a very strong estimation for field testing but is not identical to direct laboratory measurement.
The Sayers equation does not factor in limb length directly, only mass and jump height. However, biomechanically, limb length affects leverage and jump mechanics, which indirectly influences the jump height input.
To improve relative power (speed/agility), focus on increasing jump height while maintaining or slowly increasing lean mass. Gaining non-functional weight will increase the “Mass” part of the equation but likely decrease jump height, often neutralizing gains.
Related Tools and Internal Resources
Explore more tools to optimize your athletic performance:
- VO2 Max Calculator – Estimate your aerobic capacity alongside your anaerobic power.
- One Rep Max (1RM) Calculator – Calculate your maximum strength potential for lifting.
- Advanced BMI Calculator – Assess body composition metrics.
- TDEE Calculator – Determine caloric needs to support power training.
- Running Pace Calculator – Plan your interval training speeds.
- Wilks Score Calculator – Compare strength levels across different body weights.