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Power-duration model · CP & W′

You can push. But for how long?

Critical Power and W′ describe, with just two numbers, how hard you can go and for how long. Here is the essential theory, the test protocols, and a calculator that estimates CP, W′ and your zones.

Calculate CP and W′How to test
2 parameters
CP and W′ describe the whole curve
3 → 30 min
the window where the model holds
4 tests
maximal efforts for a sturdy estimate
Lone cyclist out of the saddle on a wet mountain road shrouded in fog
Handlebar head unit reading 312 watts and 168 beats per minute
W′your tank above threshold

What Critical Power is

Above a certain power, the relationship between power and time to exhaustion follows a well-defined hyperbolic curve. That curve is described by just two parameters: critical power (CP) and W′.

CP is the power you tend towards as effort duration increases indefinitely: in practice it is the boundary between the heavy and severe domains, and sits around the maximal lactate steady state. In the real world CP can be held for roughly 30 minutes.

W′ (“W prime”) is the amount of work, in kilojoules, you can produce above CP before stopping. It is a finite tank: you spend it above CP and refill it below.

CP · WATTS

The asymptotic power

Sustainable for a long time, driven by the aerobic system. Above it, the clock is running.

W′ · KILOJOULES

The anaerobic tank

Finite energy available above CP. It also tells you how close CP sits to your aerobic capacity.

3 → 30 MIN

The valid window

The model is reliable between 3 and 30 minutes. Outside that range predictions degrade fast.

W′, your tank above threshold

W′ depends on several physiological variables but is broadly read as anaerobic capacity. An alternative reading: it indicates how close your CP is to your aerobic capacity. Riders with a low CP relative to V̇O2max (low fractional utilisation) tend to have a larger W′.

There is no “right” W′: it depends on the discipline. A time triallist needs a high CP; a crit racer needs a bigger tank.

W′ reference values (kJ)

ProfileMenWomen
Endurance, moderately trained9 – 156 – 10
Punchy disciplines (crits, rolling races)15 – 1811 – 13
Sprinters / track25 – 30+18 – 25+

Indicative values for moderately trained athletes; they can be higher in well-trained riders with a high V̇O2max (Vanhatalo et al., 2011).

CP & W′ calculator

Enter 2 to 4 maximal efforts lasting between 3 and 20 minutes. The calculator runs a linear regression of P against 1/t: the slope is W′, the intercept is CP.

Your tests

01
02
03

Only used for per-kilogram values. Leave it empty if you prefer.

Your data stays saved locally in this browser.

Critical Power

275 W

3.93 W/kg

W′

15.6 kJ

222 J/kg

Fit quality

R² = 0.993

Excellent fit

Your tests describe a clean line: the estimate is trustworthy.

Estimated FTP for zones

259 W≈ 94% of CP

Power-duration curve

200250300350400510152025303540CP 275 W360WThe effort furthest from the line: that is the one to repeat.330W295WDURATION (MIN)

The curve shows predicted maximal power for each duration. The dashed line is CP: the asymptote the curve falls towards.

Predicted maximal power

3 min361 W5.16 W/kg
5 min327 W4.67 W/kg
8 min307 W4.39 W/kg
12 min297 W4.24 W/kg
20 min288 W4.11 W/kg
30 min284 W4.05 W/kg
5′ 46″

Training zones

calculated on estimated FTP, not on CP

  • Z1Active recovery< 142 W
  • Z2Endurance145 – 194 W
  • Z3Tempo197 – 233 W
  • Z4Threshold235 – 271 W
  • Z5V̇O2max274 – 310 W
  • Z6Anaerobic capacity313 – 388 W
  • Z7Neuromuscular> 390 W

How to run the tests

Two tests are enough in theory, but 3-4 efforts give a sturdier estimate and let you measure its reliability. Recommended durations: 3, 5 and 12 minutes, plus an optional 20-minute test.

Lone cyclist on a straight empty road running to the horizon under an overcast sky

  1. Pick the durations

    3, 5 and 12 minutes, plus an optional 20-minute test. Any duration between 3 and 20 minutes works, but at least one test over 10 minutes improves accuracy.

  2. One test per day

    Different tests on different days, well recovered. Two tests in one day under-estimate W′, because the tank has not refilled.

  3. Choose a method

    Self-paced time trial (fixed duration) or time to exhaustion at fixed power. Keep the same method: switching can shift CP by 7% and W′ by 12%.

  4. Even pacing

    Keep power as steady as you can: don’t start hard and fade. Bad pacing is the number one cause of nonsense estimates.

  5. Feed the model

    Enter duration and average power for each test in the calculator: you get CP, W′ and the R² that tells you how much to trust it.

  6. Repeat every 6-8 weeks

    Same durations, same method, same environment (indoor or outdoor). Only then are comparisons over time meaningful.

Warm-up template (Jones et al., 2003)

10-15′
Gradual ramp from 2/10 to 4/10 effort (about 45% → 75% of FTP/CP).
2-3 × 1′
Short efforts above expected CP: you should feel lactate building, without going all-out.
4-5′
Easy spinning at 2-3/10 (45-55% FTP) to let lactate come back down before the test.

Golden rules

  • Warm up properly: the model assumes the aerobic system kicks in instantly, and a good warm-up shrinks that lag.
  • It takes at least three testing sessions before results become reliable: treat the first two with caution.
  • Indoor and outdoor are not comparable: pick one context and stick to it.
  • If the numbers say you have a huge W′ but you know sprinting is your weakness, the data is wrong, not you.

CP, FTP, MLSS, lactate threshold

Close relatives, not interchangeable. They measure different things and are obtained in different ways.

MetricWhat it measuresHow you get it
CPBoundary between heavy and severe domains; maximal theoretically sustainable power, with W′ attached.3-4 maximal efforts between 3 and 20 minutes, regression of P on 1/t.
FTPPractical estimate of the power sustainable for about an hour; approximates lactate threshold.95% of 20-minute test power, or a ramp test.
MLSSHighest intensity at which blood lactate stays in steady state. CP sits very close to it.Series of 30-minute rides at different intensities with lactate sampling.
Lactate thresholdIntensity at which lactate starts rising above baseline. Tends to be lower than CP.Incremental lab test with capillary blood samples.

Common mistakes and model limits

  1. Using CP as FTP

    CP comes out higher than FTP: copying it into your zones means chronically training too hard. Apply the ~94% factor.

  2. Only two tests

    With two points the line always fits perfectly: zero information about reliability. With 3-4 points the R² actually means something.

  3. Mixing methods

    Time to exhaustion and fixed-duration trials give different results (CP -7%, W′ +12%). Don’t compare apples and pears.

  4. Tests too long or too short

    Under 3 minutes the anaerobic contribution dominates, over 20 the model frays. Stay inside the window.

  5. Testing tired or stressed

    Fatigue, motivation, heat, sleep: it all lands in the number. Always read results in the light of the day you had.

  6. Taking predictions literally

    Between 3 and 30 minutes they are a useful guide, not a guarantee. A 10-minute effort is predicted better than a 3-minute or a 20-minute one.

W′ balance: using it while racing

If W′ is a tank, W′ balance is the fuel gauge: it drains when you ride above CP, in proportion to how far above you are, and refills below CP, faster the easier you ride.

Many head units display it live. The point is not to empty the tank before the moment that decides the race: the last kick, the sprint, the final climb.

ABOVE CP
The tank drains faster the further above CP you ride.
BELOW CP
It refills exponentially: the easier you ride, the quicker you recover it.
RACING
Keep a reserve for the decisive move; at zero, your power collapses towards CP.

FAQ

How often should I retest?

Every 6-8 weeks, or at every change of training block. Always use the same durations and method, otherwise you are comparing different measurements.

Can I get CP and W′ from Strava or TrainingPeaks history?

Partly. Recorded power peaks can act as model points, but only if they were genuinely maximal, well paced, and close together in time. Dedicated tests remain far more reliable.

Can CP and W′ be trained separately?

Yes, and that is part of why the model is useful. Work around CP (threshold, sweet spot) and V̇O2max intervals raise CP; short repeated anaerobic efforts develop W′. Pushing one hard can compress the other.

Should I test indoors or outdoors?

Both are fine, but don’t mix them. Indoor is more repeatable (no wind, no traffic), outdoor is more race-specific. Choose and stay consistent.

What does a low R² mean?

That your points don’t sit on a line: almost always a pacing problem or insufficient recovery between tests. Find the point furthest from the line and repeat that effort.

Is CP my maximal lactate steady state?

It sits very close (Poole et al., 2016) but tends to come out slightly above lactate threshold and FTP. Treat it as an excellent approximation, not a lab measurement.

Do I really need a power meter?

Yes. The model is built on real watts; heart rate alone cannot give reliable CP and W′.

Glossary

CP
Critical power: the asymptote of the power-duration curve, in watts.
W′
Work available above CP, in kilojoules. Pronounced “W prime”.
W′ balance
The share of W′ still available at a given moment.
FTP
Functional Threshold Power: estimated power sustainable for about an hour.
MLSS
Maximal lactate steady state: highest intensity with stable lactate.
V̇O2max
Maximal oxygen uptake: the ceiling of the aerobic system.
Fractional utilisation
The percentage of V̇O2max you can sustain at threshold.
TTE
Time to exhaustion: how long a given power can be held.
R²
How well your tests sit on the model’s line (1 = perfect).
Erg mode
Trainer mode that holds a fixed power regardless of cadence.

References

  1. Karsten B, Petrigna L, Klose A, Bianco A, Townsend N, Triska C(2020) Relationship between the critical power test and a 20-min functional threshold power test in cyclingFrontiers in Physiology, 11, 613151
  2. Mattioni Maturana F, Fontana FY, Pogliaghi S, Passfield L, Murias JM(2018) Critical power: how different protocols and models affect its determinationJournal of Science and Medicine in Sport, 21(7), 742-747
  3. Simpson LP, Kordi M(2017) Comparison of critical power and W' derived from 2 or 3 maximal testsInternational Journal of Sports Physiology and Performance, 12(6), 825-830
  4. Poole DC, Burnley M, Vanhatalo A, Rossiter HB, Jones AM(2016) Critical power: an important fatigue threshold in exercise physiologyMedicine & Science in Sports & Exercise, 48(11), 2320-2334
  5. Vanhatalo A, Jones AM, Burnley M(2011) Application of critical power in sportInternational Journal of Sports Physiology and Performance, 6(1), 128-136
  6. Allen H, Coggan A(2010) Training and racing with a power meterVeloPress, 2a edizione
  7. Jones AM, Wilkerson DP, Burnley M, Koppo K(2003) Prior heavy exercise enhances performance during subsequent perimaximal exerciseMedicine & Science in Sports & Exercise, 35(12), 2085-2092

The content on this site is an original synthesis of the literature listed above. The calculator gives estimates: the model describes the power-duration relationship well, but it is not a substitute for physiological testing.

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