Functional Reserve Capacity Calculator

Two all-out efforts give you your critical power and the size of your anaerobic battery.

How it is calculated

The tool solves the two-parameter critical power model from two all-out efforts. Times are entered in minutes and converted to seconds (s1 = t1 × 60, s2 = t2 × 60). Then W′ = (P1 − P2) × s1 × s2 ÷ (s2 − s1) in joules and CP = (P2 × s2 − P1 × s1) ÷ (s2 − s1) in watts. The first effort must be the shorter and stronger one: if t2 is not longer than t1, or P1 is not above P2, there is no result. W′ is shown in kJ and J, CP and W′ are also divided by body weight (70 kg when empty). If a target power above CP is entered, time to exhaustion is W′ ÷ (target − CP) in mm:ss; otherwise a dash is shown.

Worked example

Suppose a rider holds 400 W for 3 minutes and 300 W for 12 minutes, weighs 70 kg and wants to know about 350 W. In seconds that is 180 and 720. W′ = 100 × 180 × 720 ÷ 540 = 24,000 J, which the tool shows as 24.0 kJ (343 J/kg). CP = (300 × 720 − 400 × 180) ÷ 540 = 266.7, shown as 267 W or 3.81 W/kg. At 350 W the surplus over CP is about 83 W, so exhaustion comes after 24,000 ÷ 83.3 = 288 s, or 4:48.

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Common mistakes

  • Entering the efforts in the wrong order. The short, harder effort goes in P1/t1 and the longer, easier one in P2/t2, otherwise there is no result.
  • Using times in seconds. The fields are minutes, so a 3 minute test is 3, not 180.
  • Feeding in efforts that were not maximal. A pacing test that left something in the tank understates both CP and W′, and the two-point fit amplifies even small errors in the power values.
  • Choosing two efforts that are too close in duration, such as 5 and 6 minutes: the subtraction in the formulas then magnifies noise, so CP and W′ swing wildly.
  • Reading a dash for time to exhaustion as an error. It simply means the target is empty or at or below CP, a power that the model says could be held without draining W′.

Sources

About this calculator

Critical power (CP) and W′ (pronounced "W prime," also called functional reserve capacity or the anaerobic work capacity) come from the two-parameter critical power model: CP is the highest power you could theoretically sustain indefinitely without fatigue accumulating, and W′ is a fixed, finite store of work — measured in kilojoules — above CP that gets depleted during hard efforts and slowly refills during easy ones. The model is fit from two maximal, all-out time-to-exhaustion tests at different durations (commonly 3 and 12 minutes), plotting power against time to solve for both parameters.

Cyclists and runners training with power meters use CP and W′ to pace efforts precisely: CP functions like a more physiologically grounded version of functional threshold power (FTP), while W′ tells you exactly how many kilojoules of "anaerobic battery" you have left for surges, attacks or a finishing sprint, and how long you can hold any power above CP before it runs out.

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