Critical Power (CP) Calculator — Find Your CP and W' 🌎

The Critical Power Model Explained

Critical Power (CP) is the highest power output at which oxygen delivery fully meets metabolic demand — a true physiological ceiling, not an estimate. Below CP, lactate and oxygen consumption reach steady state and you can theoretically sustain the effort indefinitely. Cross that threshold and you begin consuming W′ (W-prime), a finite anaerobic work capacity that depletes continuously until exhaustion or you drop back below CP to allow partial reconstitution.

The model was formalized by Monod & Scherrer (1965) for isometric muscle contractions and extended to cycling by Whipp et al. (1982), then rigorously validated in peer-reviewed trials by Poole et al. (1988) and later Vanhatalo et al. (2011) using "all-out" 3-minute protocols.

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How CP and W′ Are Calculated

The 2-parameter hyperbolic model assumes total work above CP is a fixed constant:

> W_total = CP × t + W′

Rearranged: P = W′/t + CP — a hyperbola where power is a function of time.

Performing two maximal efforts at different durations generates two equations and two unknowns:

CP = (P1·t1 − P2·t2) / (t1 − t2)
W' = (P1 − CP) × t1

Where P1, P2 are mean powers and t1, t2 are durations (in seconds). The accuracy of both estimates depends heavily on choosing test durations that bracket the physiologically relevant range — typically 3–7 minutes and 10–15 minutes. Using durations shorter than 2 minutes over-estimates CP; durations beyond 20 minutes under-estimate W′.

More robust 3-point or multi-point fits (using least-squares regression across 3+ efforts) significantly reduce individual test error — single-pair estimates carry ±10–15% error in W′ under lab conditions (Jones & Vanhatalo, 2017).

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Typical CP and W′ Reference Values

Absolute watts. For w/kg comparisons divide by body weight. W′ values do not scale proportionally with CP — a rider with high CP can have modest W′ and vice versa.

Notably, W′ is relatively independent of aerobic fitness. Sprint specialists often show W′ > 30 kJ with moderate CP; climbers may show W′ < 15 kJ with very high CP. This matters for race tactics: W′ determines how many hard accelerations or attacks you can survive before collapse, not just how long you can hold a given power.

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CP vs FTP — Key Differences

CP is typically 5–15 W higher than FTP because FTP is empirically derived and implicitly includes real-world glycogen depletion, neuromuscular fatigue, and psychological factors that the mathematical model ignores. Neither metric is superior — they answer different questions.

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How to Perform the Test Protocol

1. Complete 2–3 maximal efforts on separate days (or same day with ≥30 min full recovery between).
2. Recommended durations: ~3 min, ~8 min, and ~12 min for a 3-point fit.
3. Each effort must be a genuine all-out, constant-pace maximal effort — not a ramp or variable-pace ride.
4. Use a calibrated power meter or smart trainer (±2% accuracy minimum).
5. Input mean power and exact duration in seconds into the calculator.

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What the Model Does NOT Include

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Common Errors That Corrupt Results

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CP and W′ are training-state dependent — retest every 8–12 weeks during a structured training block to track meaningful changes.