Health & Fitness
Cycling Critical Power & W′ Calculator
Updated Aug 27, 2026 Reviewed Aug 27, 2026
Fit critical power and W prime from two to five maximal cycling efforts, compare two linearized models, inspect fit error, and predict power or duration.
Two-parameter power-duration model
Enter maximal efforts with distinct durations
Result
Calculation summary
Enter values to see the result
Your result, breakdown, assumptions, and warnings will appear here.
Live power-duration curve
Power approaches a critical asymptote
Power = CP + W′ ÷ duration
- Critical power
- 264 W
- W′
- 25.4 kJ
- Power-fit R²
- 0.995
How to use this calculator
- 1Enter two to five maximal, constant-power efforts with distinct durations.
- 2Choose work versus time or power versus inverse time.
- 3Inspect CP, W′, R², RMSE and residuals before using either prediction field.
Formula
P = CP + W′ ÷ t
The work-time form fits P×t against t; the inverse-time form fits P against 1/t. Both are two-parameter models.
Calculation steps
- Fit a straight line in the selected transformed coordinate system.
- Recover CP from the slope or intercept and W′ from the remaining coefficient.
- Recalculate predicted power for every trial and report residual fit quality.
Worked example
Three maximal efforts at 3, 8 and 20 minutes produce a CP asymptote, a finite W′ work capacity and power predictions above CP.
Assumptions
- Trials are maximal, accurately timed and measured with comparable equipment.
- The two-parameter model describes constant severe-intensity efforts and does not model recovery.
- Model choice and trial-duration selection can materially change CP and W′.
- Predictions at or below CP are not given a finite exhaustion time.
Sources
Frequently asked questions
Is CP the same as FTP?
No. They are related threshold concepts obtained from different models and should not be treated as interchangeable.
Why are two fitting models included?
Linearized forms weight errors differently, so comparing them exposes model sensitivity instead of hiding it.
Why does the calculator warn about trial span?
A narrow set of only short efforts can overestimate CP and underestimate W′.
What does W′ represent?
It is the curvature constant in joules for work performed above CP, not a literal single energy tank or a recovery model.
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