Cycling Critical Power & W′ Calculator
Enter three recent maximal cycling efforts to fit critical power and W′ from the work-time model. The results include fit diagnostics plus a predicted power for a chosen duration or modeled time above critical power.
Critical power260
- W′ anaerobic work capacity
- 19.18
- Relative critical power
- 3.46
- Predicted power for target duration
- 276
- Modeled time at target power
- 5 min 18 sec
- Work-time model fit (R²)
- 99.94%
- Inverse-time CP cross-check
- 264
- CP model disagreement
- 1.72%
- Trial residuals
- Short: -6.1 W; Medium: 4.7 W; Long: -1.2 W
Power-duration estimates
| Duration | Modeled power |
|---|---|
| 3 min | 366 |
| 5 min | 324 |
| 10 min | 292 |
| 12 min | 286 |
| 20 min | 276 |
| 30 min | 270 |
| 60 min | 265 |
Fit uses the work-time model W = critical power × time + W′.
How to use this calculator
- Enter three complete, maximal efforts that span short, medium, and longer durations.
- Use average power for each full effort and keep the testing conditions as comparable as possible.
- Enter body weight to see critical power relative to mass.
- Choose a target duration and a target power to reverse the fitted model in either direction.
How cycling critical power and W′ are calculated
Critical power (CP) is the slope of the relationship between total work and time across hard efforts. W′, spoken as “W prime,” is the intercept of that line and is expressed as work. In this two-parameter model, CP is the sustainable component and W′ is a finite modeled work capacity available above CP. They are fitted estimates, not direct measurements of a fixed physiological boundary.
For each trial, the calculator converts minutes to seconds and multiplies average power by duration:
W_i = P_i × t_i
It fits the least-squares line W_i = CP × t_i + W′. The slope is CP = sum((t_i − mean t)(W_i − mean W)) / sum((t_i − mean t)^2), and the intercept is W′ = mean W − CP × mean t. Once fitted, modeled power at a duration is P(t) = CP + W′ / t. For a target power above CP, the reverse calculation is t = W′ / (P − CP).
What the fit checks mean
The work-time R² shows how closely the three work values lie on the fitted line. Residuals show each measured power minus its modeled power, which makes an unusually strong or weak trial easier to spot. The calculator also fits power against inverse time as a cross-check. The two methods are mathematically related but can give different CP estimates when real efforts do not follow the model exactly.
Choose trials with a useful spread, commonly somewhere within about two to 30 minutes. Similar durations make the slope sensitive to small pacing or meter errors. A longer effort that produces equal or higher average power than a shorter one is worth checking, but it is not automatically an error: wind, terrain, cooling, fatigue, and pacing can all matter.
What this calculator leaves out
The model treats W′ as one pool and does not describe how it is restored during recovery, how it changes across repeated intervals, or how aerobic power drifts during a long ride. It also does not account for grade, drafting, temperature, altitude, equipment, calibration, cadence, or day-to-day readiness. Predictions become less dependable when pushed far outside the durations used to fit the line, especially beyond the usual two- to 30-minute testing range.
Worked example
Suppose three maximal efforts are 300 W for 3 minutes, 272 W for 5 minutes, and 260 W for 7 minutes. Their work values are 54,000 J, 81,600 J, and 109,200 J. Those points lie exactly on W = 230 × t + 12,600, so CP is 230 W and W′ is 12.6 kJ.
At 10 minutes, the model gives 230 + 12,600 / 600, or 251 W. At 300 W, it gives 12,600 / (300 − 230), or 180 seconds: 3 min 0 sec. With a 75 kg body weight, relative CP is 3.07 W/kg.
Common questions
What are critical power and W′?
Critical power is the slope of the fitted work-time line, expressed in watts. W′ is the positive intercept, expressed in joules or kilojoules, and represents a finite modeled work capacity above critical power. Both are estimates based on the efforts supplied to the model.
How should I choose the three test durations?
Use maximal, evenly paced efforts that are meaningfully separated in duration, often spanning a short, middle, and longer effort in roughly the two- to 30-minute range. Keep terrain, power measurement, temperature, recovery, and pacing conditions as consistent as practical. Very similar durations make the fitted slope more sensitive to small errors.
Is critical power the same as FTP?
No. FTP and critical power are both training benchmarks expressed in watts, but they are obtained and interpreted differently. Critical power comes from a power-duration model fitted across efforts, while FTP is typically estimated from a single protocol or steady-performance concept.
Why must target power be above critical power for time to exhaustion?
The two-parameter equation divides W′ by the amount that target power exceeds CP. At or below CP, that difference is zero or negative, so the model does not predict a finite time to exhaustion. This does not mean a rider can actually hold that power forever; it only marks the boundary of this calculation.
What is a good R² for a critical-power test?
An R² near 1.00 means the three work values sit close to one fitted line. This calculator flags a value below 0.95 as a reason to review trial quality and conditions. A high R² improves internal consistency but cannot prove the test predicts every ride or interval.
Can I use outdoor ride best powers instead of formal tests?
Yes, if the efforts were genuinely maximal and their conditions are reasonably comparable. Outdoor best powers can be distorted by terrain, wind, drafting, stops, and different levels of accumulated fatigue. Check residuals and the two CP estimates before treating a mixed set of rides as a clean test.