Critical Power Cycling Calculator
Critical power (CP) is the highest cycling power output that can in theory be sustained without continuously drawing on a finite anaerobic reserve. The two-parameter model describes the relationship between power and time-to-exhaustion using CP and the anaerobic work capacity, W prime. From two maximal efforts of different durations you can solve for both. This tool applies the linear work-versus-time form of the model.
Two-test critical power model
Work done in an effort: W1 = P1 * t1, W2 = P2 * t2
Linear model: W = W' + CP * t
CP = (W2 - W1) / (t2 - t1)
W' = W1 - CP * t1
Power is in watts, time in seconds, and work in joules (watts times seconds). The model treats total work as a straight line against time, with slope equal to critical power and intercept equal to the anaerobic work capacity W prime. The two efforts must have different durations.
Worked example
For effort 1 of 300 W for 180 s and effort 2 of 250 W for 600 s: W1 = 300 * 180 = 54,000 J, W2 = 250 * 600 = 150,000 J. CP = (150,000 - 54,000) / (600 - 180) = 96,000 / 420 = 228.57 W. W prime = 54,000 - 228.57 * 180 = 54,000 - 41,142.86 = 12,857.14 J.
Frequently asked questions
How long should the two test efforts be?
The efforts should be maximal and of clearly different durations, typically one shorter (for example 3 minutes) and one longer (for example 10 to 12 minutes), with full recovery between. Using durations that are too close together makes the estimate unstable.
What is W prime?
W prime is the fixed amount of work, in joules, that can be done above critical power before exhaustion. It represents a finite anaerobic energy store that depletes during efforts above CP and recovers below it.
Is critical power the same as FTP?
They are related but not identical. Functional threshold power (FTP) is usually estimated from a single sustained effort, while critical power comes from the power-duration relationship across multiple efforts. CP is often close to, but not exactly, FTP.
Why must the two durations differ?
The model finds the slope of work against time. If both efforts last the same time, the denominator (t2 minus t1) is zero and the slope is undefined, so the calculator returns no answer.
Sources
- Monod and Scherrer critical power model, indexed at the U.S. National Library of Medicine: PubMed.
- U.S. National Institutes of Health, exercise and physical activity resources: NIH Health Information.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. Educational tool for training estimates. See our methodology.