Critical Power and W′ calculator
Critical Power (CP) is the highest power at which your body can still stay in a metabolic steady state: the boundary between heavy and severe exercise. W′ is the amount of work you can deliver above CP before you blow up. This calculator works out both, using the two time trials from my CP test: 3 and 12 minutes.
Work out your CP and W′
Ride two time trials, of 3 and of 12 minutes, both evenly paced and maximal: no sprint start and no final sprint. Enter your average power for each. The calculation runs in your browser; I see nothing of what you enter.
How I work it out
In every time trial you do work: power × time. Plot that work against time and your time trials sit on a straight line. The slope of that line is your CP: what you can add every second without running empty. Where the line crosses the vertical axis is your W′: the work you have on top of that. Monod and Scherrer described this linear relationship between work and time in 1965; Moritani and colleagues applied it to the bike in 1981.
With two time trials, exactly one line runs through them. That gives these two formulas, with 180 and 720 seconds as the length of your time trials:
CP = (P12 × 720 − P3 × 180) ÷ 540
W′ = (P3 − CP) × 180
P3 and P12 = average power over the 3-minute and 12-minute time trial (W) · CP in watts · W′ in joules (÷ 1000 = kJ)
| 3-minute time trial | 400 W × 180 s = 72,000 J |
|---|---|
| 12-minute time trial | 320 W × 720 s = 230,400 J |
| CP | (230,400 − 72,000) ÷ 540 = 293.3 W |
| W′ | (400 − 293.3) × 180 = 19,200 J = 19.2 kJ |
| At 75 kg | 293.3 ÷ 75 = 3.91 W/kg |
How long can you then hold 350 W? Time = W′ ÷ (power − CP) = 19,200 ÷ 56.7 = 339 seconds, well over five and a half minutes.
What your result means
Your CP is a boundary, not a training zone. It separates two of the four intensity domains I also use in the essentials on CP and W′:
- Severeabove your CP
No steady state: your oxygen uptake climbs to its maximum and your W′ drains. How long you last is set by W′ and CP together.
- Heavybelow your CP
Hard, but your body still finds a balance. This is where your W′ recharges.
- Moderate and lightwell below your CP
Your endurance pace and your recovery rides. Where exactly these domains begin does not follow from these two time trials.
That is why this page gives no zone table in percentages of CP. Blocks above CP should be based on how much W′ you use, not on a fixed percentage; more on that in what CP is and what determines it. I set your zones when I analyse your CP test.
What to keep in mind
- The model assumes maximal, evenly paced time trials. Start too hard or fade, and your average is off, and so is the result. If your 3-minute power is only just above your 12-minute power, one of the two was probably not maximal.
- Two points always make a line. So there is no check on a failed time trial. In trained riders, two maximal tests give a reliable CP and W′ (Parker Simpson & Kordi, 2017); a third time trial, for example of 7 minutes, makes the estimate more robust.
- The 2-parameter model slightly overestimates CP. Compared with a model with three parameters, CP comes out a little higher and W′ a little lower, especially when the shortest test is short (Gaesser et al., 1995). Treat your result as a good estimate, not a lab value.
- The model holds between roughly 2 and 15 minutes. That is the range of the tests used to determine CP (Goulding & Marwood, 2023). For a 20-second sprint or a one-hour ride it predicts far less well.
- Conditions matter. Fatigue from earlier exercise and riding at altitude lower your CP (Goulding & Marwood, 2023). To see progress, repeat on the same course, rested, with the same power meter recording every second.
Sources
- Monod H, Scherrer J. The work capacity of a synergic muscular group. Ergonomics. 1965;8(3):329–38. doi:10.1080/00140136508930810
- Moritani T, Nagata A, deVries HA, Muro M. Critical power as a measure of physical work capacity and anaerobic threshold. Ergonomics. 1981;24(5):339–50. doi:10.1080/00140138108924856
- Gaesser GA, Carnevale TJ, Garfinkel A, Walter DO, Womack CJ. Estimation of critical power with nonlinear and linear models. Med Sci Sports Exerc. 1995;27(10):1430–8. doi:10.1249/00005768-199510000-00012
- Parker Simpson L, Kordi M. Comparison of Critical Power and W′ Derived From 2 or 3 Maximal Tests. Int J Sports Physiol Perform. 2017;12(6):825–30. doi:10.1123/ijspp.2016-0371
- Goulding RP, Marwood S. Interaction of Factors Determining Critical Power. Sports Med. 2023;53:595–613. doi:10.1007/s40279-022-01805-w
Want to know whether your numbers are right?
This calculator works with what you enter. With the CP test you get the protocol, I check your ride file for pacing, and I send you your CP, your W′ and what it means for your training.