Power

Critical power & W' calculator

Three maximal efforts. Two numbers that define your power profile.

Critical power (CP) is the threshold above which your finite energy reserve begins to deplete. It marks the boundary between intensity you can sustain and intensity that is always costing you. W' (pronounced "W prime") is the finite energy reserve you draw on above that ceiling. Together they predict what you can hold, for how long, and what it will cost you.

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Step 1 — Your test efforts

Enter the average power (mean maximal power) for three all-out efforts at different durations. The recommended combination is 3, 5, and 12 minutes, spread enough to resolve the model accurately.

Effort 1
Effort 2
Effort 3
kg
How to run the tests

Each test must be a true maximal effort for the full duration, not a hard tempo or a paced threshold attempt. The model only works if the efforts are genuine all-out bests.

  • Complete the three tests on separate days with full recovery between efforts.
  • Warm up thoroughly (at least 15 minutes at easy pace).
  • Use a consistent course; flat or on a turbo trainer is most accurate.
  • Record the average power from your head unit or cycling computer.
  • Spread the durations as widely as possible within the 3–20 minute range, as narrow spacing reduces model accuracy.

You can also use your personal best average power figures from recorded rides, provided they were genuine maximal efforts at those durations.

Step 2 — Your CP and W' results

Critical power (W)
Estimated FTP (W)
W' (work prime, kJ)
Critical power (W/kg)
Estimated FTP (W/kg)
W' (kJ/kg)

Model fit: . A value above 97% indicates the three efforts are consistent with the CP model. Estimated FTP is CP × 0.96.

Compared with test from

Power–duration curve

The shaded area between the curve and the CP line represents W', which is the finite energy reserve available above critical power. Each point on the curve is the maximum average power the model predicts for that duration. Your three test efforts are plotted as points.

What these numbers mean

CP is the power you can sustain indefinitely. W' is what you spend the moment you go above it.

Think of W' as a battery. Every second you ride above CP drains it at a rate proportional to how far above CP you are. Every second below CP recharges it. Once depleted, you cannot sustain power above CP until the battery recovers.

For ultra-distance riding, CP is the ceiling rather than the target. Any extended time at or above CP depletes glycogen at a rate you cannot replenish on the move, and the fatigue it generates compounds over distance. How far below CP to target depends on how long you will be on the bike. For half-day and all-day events most riders aim for 70 to 80% of CP. For true ultra-distance riding lasting many hours or multiple days, 55 to 70% is more appropriate, and sometimes lower on harder terrain. W' determines how much headroom you have for the surges you cannot avoid, such as short steep ramps, sudden changes in wind, or the cost of getting back up to pace, before you are forced below CP to recover.

Your W' reserve in practice

Your W' of kJ is the total above-CP energy available before you are forced back below critical power.

At W above CP
before W' is depleted
At W above CP
before W' is depleted

These are theoretical maxima assuming W' starts fully charged. In practice, repeated surges accumulate fatigue, so recovery below CP between efforts is essential.

How this was calculated

Model: The critical power model represents the power–duration relationship as P = CP + W'∕t, where P is power (W), t is duration (s), CP is critical power (W), and W' is the finite work capacity above CP (J). This is equivalent to a linear relationship between power and the reciprocal of duration.

Regression: CP and W' are estimated using ordinary least squares regression on the three (1∕t, P) data points. The slope of the regression line is W' (in joules) and the intercept is CP (in watts). Three points are the minimum required for this two-parameter model.

Model fit (R²): The Pearson correlation coefficient r is computed across the three points, then squared to give R². A value above 97% indicates the test data are consistent with the two-parameter CP model. Values below 97% suggest the efforts were not all maximal, or the durations were too narrowly spaced to resolve the model accurately.

Estimated FTP: Functional threshold power is defined operationally as mean maximal 60-minute power. CP is the theoretical asymptote of the power–duration curve and is consistently around 3–5% above a rider's 60-minute power in practice (Poole et al., 2016; Jones et al., 2010). The 0.96 multiplier reflects this empirical relationship.

Step 3 — Training zones and performance predictor

Your CP of W and W' of kJ. Here is how to put those numbers to work.

Power training zones

Zones are calculated from your estimated FTP of W. Choose the model that matches how you train; all three use the same underlying data.

Zone Name Power range Training purpose
Z1 Recovery Easy spinning. Active recovery between hard sessions.
Z2 Endurance The aerobic foundation. Most ultra-distance riding targets here.
Z3 Tempo Productive but sustainable. Longer intervals of 20–60 min.
Z4 Threshold Around FTP and CP. Classic 2×20 and sweet spot work.
Z5 VO2 max Short, hard intervals (3–8 min). Draws heavily on W'.
Z6 Anaerobic Above 120% FTP. Pure W' work: short, intense efforts.
Zone Name Power range Training purpose
Z1 Easy Below the first lactate threshold. Builds aerobic base without accumulating fatigue. The majority of training volume lives here.
Z2 Moderate Between the lactate thresholds, broadly equivalent to tempo or sweet spot in Coggan-based systems. Harder than Zone 1 but produces less adaptation per unit of fatigue than either Zone 1 volume or Zone 3 intervals. In a polarized approach, used sparingly as a deliberate target.
Z3 Hard Above CP, drawing directly on W'. High adaptation stimulus. Short, focused intervals (2–8 min) with full recovery between efforts.

Zone 3 starts at your CP of W, not an arbitrary FTP percentage. This is the precise physiological boundary your test data defines.

In the polarized model, most training volume (typically 75–80% of sessions) is in Zone 1 (easy, below LT1), with a small proportion of high-quality Zone 3 work (hard, above CP). Zone 2 in this model (tempo or sweet spot in Coggan terms) arises naturally on long rides and events but is not typically the deliberate target of a training session. The fatigue it generates is better invested in Zone 1 volume or Zone 3 quality.

Zone Name Power range Training purpose
Z1 Active Recovery Easy spinning. Recovery days and between hard efforts.
Z2 Endurance Aerobic base. Long steady riding. The bulk of ultra-distance training.
Z3 Tempo Sustained moderate-high effort. Longer steady-state intervals.
Z4 Lactate Threshold Classic threshold work. 2×20, sweet spot. Raises FTP over time.
Z5 VO2 max Hard short intervals (3–8 min). High cardiovascular demand, significant W' use.
Z6 Anaerobic Capacity Very short, very hard (30 s–2 min). Primarily W'-dependent.
Z7 Neuromuscular Power Maximal sprints (≤ 15 s). Peak power and neuromuscular recruitment.

Power predictor

Use your CP model to predict what you can hold for a given duration, or how long you can sustain a target power. The model is calibrated against 3–20 minute efforts, so predictions are most reliable within this range. Both assume full W' charge at the start of the effort. For applying CP to ultra-distance pacing, see the note below.

What power can I hold for…

Enter a duration to find the maximum average power predicted by your CP model.

Most reliable between 3 and 20 minutes.
Predicted max power

How long can I hold…

Enter a target power to find how long you can sustain it before W' is depleted.

Predicted max duration

CP and ultra-distance pacing

The predictor is built around W' depletion and is designed for efforts of 3–20 minutes. It does not extend to brevet, audax, or multi-hour pacing, but your CP is still the most important number for those events.

CP is your aerobic ceiling. Any power above it draws on W', and while W' does recover when you drop back below CP, it does so slowly. The further above CP you ride, and the more often you do it, the larger the cost becomes. How far below CP to target depends on how long you plan to be on the bike. For sustained efforts of an hour or two, 80–90% of CP is achievable for most trained riders. For half-day or all-day events, 70–80% is a more realistic ceiling. For true ultra-distance riding lasting many hours or multiple days, most experienced riders average somewhere between 55 and 70% of CP, and sometimes lower on harder terrain. Riding close to or repeatedly above CP on a long event accumulates a cost that compounds as the hours pass and becomes progressively harder to manage.

W' governs your surges. On a long ride, every climb, headwind, or acceleration above CP spends W'. Recovery below CP recharges it, but only slowly. A high W' gives you more margin to respond to the terrain and conditions before you are forced to back off. A lower W' means shorter, fewer surges with longer recovery needed between them.

When to retest

CP and W' are trainable. As your fitness develops, the model should be updated, typically every 6–10 weeks during a structured training block.

  • After a focused block of threshold or VO2 max training, CP typically rises and W' may increase or decrease depending on the training stimulus.
  • After an extended base period (high volume, low intensity), CP may hold steady while W' grows.
  • If your predicted powers feel noticeably easier or harder than expected during training, it is a signal the model needs updating.
FAQ

Critical power and W' — common questions

Critical power (CP) is the highest average power output you can sustain without depleting your finite energy reserve (W'). It marks the boundary between the intensity you can hold and the intensity that is always costing you. Below CP, you can ride indefinitely given adequate fuelling, but above it every second draws down W' until exhaustion forces you to slow. It is a more physiologically precise measure than FTP and forms the basis of the two-parameter CP model used by this calculator.

W' (pronounced W-prime) is the finite reserve of work capacity above critical power, measured in kilojoules. Think of it as a battery: every second above CP drains it proportional to how far above CP you are, while every second below CP slowly recharges it. A typical trained cyclist has a W' somewhere between 15 and 25 kJ. A higher W' gives you more capacity for surges, short climbs, and accelerations before you are forced to recover.

FTP is estimated by multiplying CP by 0.96. CP is the theoretical asymptote of the power-duration curve, and research consistently finds that 60-minute power sits around 3 to 5 percent below CP in trained cyclists (Poole et al., 2016; Jones et al., 2010). If you have a measured 60-minute power from a recent test, use that figure in preference to the estimate.

The recommended combination is 3, 5, and 12 minutes. The durations need to be spread widely enough to resolve both model parameters, CP and W', with confidence. Narrow spacing such as 5, 8, and 10 minutes makes the two parameters hard to separate and produces unreliable results. Each effort must be a true all-out maximum, completed on separate days with full recovery between tests.

The calculator reports model fit as R², which shows how well your three power values fit the CP model curve. A value above 97% indicates the three efforts are consistent with the two-parameter model. Values below 97% usually mean one effort was not genuinely maximal or the durations were too close together. The model is most accurate for efforts between 3 and 20 minutes. Beyond 20 minutes, fuelling and pacing strategy increasingly influence average power in ways the model does not capture.

CP is your aerobic ceiling rather than a power you should be targeting. Any power above it draws on W', and while W' does recover when you drop below CP, it does so slowly. How far below CP to target depends on how long you plan to be on the bike. For efforts of an hour or two, 80 to 90 percent of CP is achievable for most trained riders. For half-day or all-day events, 70 to 80 percent is more realistic. For true ultra-distance riding lasting many hours or multiple days, most experienced riders average somewhere between 55 and 70 percent of CP, and sometimes lower on harder terrain. Riding close to or repeatedly above CP on a long event accumulates a cost that compounds as the hours pass and becomes progressively harder to manage.
Free consultation

Want a coach to help you train to these numbers?

Knowing your CP is only useful if your training is structured around it.

In a free consultation we'll look at how your current CP and W' compare to the demands of your target events, discuss which training zones to prioritise, and work through how to structure work above and below CP to drive the adaptations you need. You'll leave with a clearer picture of what to focus on, even if we never work together.

Book a free coaching consultation Or email hey.boundary@gmail.com directly.