Critical Power and W': The Two-Parameter Model That Explains How Long You Can Hold On

The Two-Parameter Endurance Math

The Critical Power (CP) model condenses high-intensity endurance into two parameters: CP is the highest power theoretically maintainable for a long duration at metabolic steady state (physiologically close to, but often slightly above, maximal lactate steady state); W’ (read as “W prime”) is the finite “work capacity battery” above CP, measured in joules, representing the rapidly depletable anaerobic/non-steady-state energy reserve.

The relationship: sustainable time t = W’ ÷ (P − CP), where P is a constant output above CP. Once W’ is exhausted, output must drop back below CP, or failure ensues.

How to Estimate

Perform 3–5 all-out tests of varying durations (e.g., 3, 5, 12 minutes), fit the average power against time with a hyperbolic curve, and derive CP and W’. In practice, the average of the final 30 seconds of a 3-minute all-out test is also commonly used to approximate CP.

W’ Depletion and Recharge

The key practical value lies in the fact that W’ “recharges” when power is below CP. When a climb attack in a race depletes W’, returning to flats or descents and holding power below CP gradually refills W’, with the rate depending on how far below CP and for how long. This is the mathematical basis of intermittent pacing and race tactics: every surge spends battery, and those who know how to recharge in sheltered sections can attack more times.

Two Paths in Training

• Raise CP: Use threshold and sweet-spot training, plus a large aerobic base, to improve mitochondrial function and lactate steady state, pushing the sustainable ceiling higher.
• Expand W’: Use high-intensity intervals and sprint training to increase anaerobic reserve and tolerance. But W’ has limited room for improvement, and overemphasizing it can crowd out the aerobic base.

For long-distance athletes, the payoff from raising CP far exceeds expanding W’; for track and sprint-type athletes, W’ and its recharge rate are the keys to victory.

Model Limitations

The CP model is most accurate in the 2–20 minute range, with larger prediction errors for very long efforts (several hours, where CP drifts downward with fatigue) and very short efforts (<2 minutes). It assumes CP is constant, but over extended durations, due to glycogen depletion and rising core temperature, the “actual sustainable power” falls below the static CP. Treat it as a decision-making framework, not an iron law.

Real-Time Application

Some bike computers can display W’ balance (W’bal) in real time, letting athletes know how much battery remains during climbs or chases, avoiding blowing up too early. Planning W’ expenditure and recharge points in advance based on the course profile is an advanced tactic in modern time trials and off-road racing.

CP is your endurance chassis; W’ is your nitrous boost bottle. Racing isn’t about who has the bigger bottle—it’s about who calculates more clearly: releasing on the right climb, and quietly refilling the bottle on the right recovery stretch.

Related Reading

• Power Output Stability and Endurance Performance: Applied Research on the Critical Power Model
• The Complete Guide to CP and W’: A Hyperbolic Model That Understands Pacing Better Than FTP, from Wuling to Criterium Racing
• The W’ (W Prime) Model in Cycling: Training Implications of Anaerobic Work Capacity
• In-Depth Analysis: How Ultra-Slow Running and Aerobic Athletes Use Critical Power to Break Through Plateaus? Unpacking the Core Science of Anaerobic Work Capacity (W’) and Physiological Limits