Critical Power (CP)

Critical Power (CP) is a model-based threshold used in endurance physiology to describe the boundary between heavy and severe intensity domains.

In simple terms, CP estimates the highest power at which a physiological steady state may still be possible. Above CP, fatigue develops quickly and the finite work capacity above CP, called W', begins to matter.

In 1965, Monod and Scherrer proposed the Critical Power model. They described CP as the maximal rate of work that can be sustained without progressive fatigue, and introduced a finite “energy reserve” available above CP (later referred to as W').

Core Model: The Two-Parameter Model

The theoretical foundation of CP is often called the two-parameter model, describing your performance as the combination of two components:

1. Critical Power (CP):

   • Nature: a model threshold for high sustainable power.
   • Interpretation: staying below CP usually allows much longer work than staying above CP, though duration is still limited by glycogen, heat, motivation, fueling, and other factors.
   • Unit: Watts (W).

2. W' (W Prime)：

   • Nature: Anaerobic Work Capacity.
   • Interpretation: a finite amount of work available above CP. Once your power exceeds CP, this reserve is depleted.
   • Unit: Joules (J) or kilojoules (kJ).

Power–Duration relationship

These two parameters form the well-known hyperbolic relationship:

P = CP + W' / t

Or, rearranged to predict time to exhaustion:

t = W' / (P - CP)

This means:

• When P > CP: the time you can hold it depends on how large your W' is and how far above CP you are. The higher above CP, the faster W' is depleted.
• When P ≤ CP: the simple model no longer predicts a finite exhaustion time, but real performance is still limited by other fatigue mechanisms.

Physiological Meaning: A Boundary Between Intensity Domains

In exercise physiology, CP is often treated as the boundary between the Heavy and Severe intensity domains:

• Below CP:

  • You can reach a physiological steady state.
  • Blood lactate may rise but can stabilize.
  • VO2 can stabilize at a submaximal level.

• Above CP:

  • No steady state.
  • Blood lactate keeps rising until you stop.
  • VO2 often shows a slow component and rises toward VO2max.
  • Once W' is depleted, you generally need to reduce power toward CP or below.

CP vs. FTP

Although CP and Functional Threshold Power (FTP) are often used interchangeably, they differ slightly in definition and typical value:

1. Different definitions:

   • FTP: commonly defined as the maximum average power you can sustain for about 60 minutes; a performance-based, practical concept.
   • CP: a model parameter representing the fatigue threshold in the CP model.

2. Typical values:

   • CP is often slightly higher than FTP.
   • In many athletes, riding at CP lasts less than an hour, often closer to ~30–40 minutes, but this varies with model fit and testing data.
   • In Trainingload.ai, we often treat FTP ≈ 95%–96% of CP.

3. Use cases:

   • FTP is commonly used as the basis for training zones (Zone 1–Zone 7).
   • The CP + W' model is useful for predicting time-to-exhaustion for short, high-intensity efforts (intervals, attacks, sprints).

W' Depletion and Recovery

W' is often modeled as a finite reserve that depletes above CP and recovers below CP:

• Depletion: when P > CP, W' depletes at a rate proportional to (P - CP).
• Recovery: when P < CP, W' begins to recover. The recovery rate depends on how far below CP you are.
  • Full rest (0 W) recovers fastest.
  • Riding just below CP (e.g., 90% CP) recovers very slowly.

This is why recovery intensity matters so much in interval workouts.

How Trainingload.ai estimates CP

Trainingload.ai can estimate CP from historical MMP (Max Mean Power) data rather than requiring one fixed protocol.

1. Data selection: best average power for key durations over the last ~90 days (e.g., 1 min, 3 min, 5 min, 10 min, 20 min…).
2. Model fitting: fit CP and W' from these time–power points.
3. FTP estimate: derive FTP from CP (default 0.95 × CP).

If you have a test file, you can also upload it for a one-off estimate: see estimate FTP and CP training load from an activity file.

For manual model fitting, use the fit Critical Power for training load planning.

Tips to improve estimate quality

To make the estimated CP more useful, ensure your power–duration curve contains enough hard, representative efforts:

• Short durations: include 3–5 minute maximal efforts (important for W').
• Medium/long durations: include 10–20 minute or longer maximal efforts (important for CP).

If you only do low-intensity riding for a long time, the system may underestimate your CP and W'.

How Trainingload.ai uses CP

Trainingload.ai uses CP to understand the power-duration profile behind threshold and above-threshold work. CP helps estimate FTP, but it is also useful for reviewing whether intervals, climbs, or race-like surges are targeting the intended intensity.

CP is most useful when paired with W':

• CP describes the sustainable side of the model.
• W' describes the finite work available above CP.
• The power-duration curve shows whether your data has enough maximal efforts to support the estimate.

Related tools and docs

• Fit Critical Power for training load planning
• Estimate FTP training load from an activity file
• W' (Anaerobic Work Capacity)
• Power Duration Curve