The two-parameter critical-power model
Critical Power comes from Monod and Scherrer's 1965 model of muscular work. Plot the total work done in a maximal effort against its duration and the points fall on a straight line: work = CP·t + W′. Rearranged, power against duration is a hyperbola whose asymptote is Critical Power, the highest power sustainable in theory without limit.
From two maximal efforts of different lengths, CP = (P1·t1 − P2·t2) ÷ (t1 − t2), and the anaerobic work capacity W′ = (P1 − CP)·t1. CP is reported in watts; W′ is a fixed amount of work in joules, usually shown as kilojoules.
What W′, the anaerobic battery, means
W′ (pronounced 'W-prime') is the finite work you can do above Critical Power before exhaustion, your anaerobic 'battery', typically 10–30 kJ in trained cyclists. Every second above CP drains it; recovery below CP recharges it. Two riders with the same CP but different W′ fare very differently in a sprint or a series of surges.
This is why the CP model is richer than a single FTP number: it separates your sustainable ceiling (CP) from your capacity to exceed it (W′). It explains why you can hold 120% of CP for a few minutes but not an hour, you're spending a fixed battery, not a renewable rate.
Testing it correctly
The model needs two genuinely maximal efforts of clearly different durations, a short, hard one (around 3 minutes) and a longer one (around 10–12 minutes), separated by full recovery or done on different days. Efforts too close in length give an unstable, sometimes nonsensical estimate.
Pace each effort evenly and go to true exhaustion. A conservatively paced short effort over-estimates CP and collapses W′; a fading long effort drops CP. Good, maximal pacing is what makes the two points define a meaningful line.
Critical Power vs FTP
CP and FTP describe nearly the same boundary and usually agree within a few percent. The difference: FTP is a single number from one test, while the CP model adds W′, modeling not just where your threshold sits but how long you can stay above it. For interval and race-pacing analysis, that extra parameter is valuable.
Worked example
Two maximal efforts, 300 W for 3 minutes (180 s) and 250 W for 10 minutes (600 s):
| Total work, effort 1 | 300 × 180 = 54,000 J |
| Total work, effort 2 | 250 × 600 = 150,000 J |
| Critical Power | (54,000 − 150,000) ÷ (180 − 600) ≈ 229 W |
| W′ anaerobic battery | (300 − 229) × 180 ≈ 12.9 kJ |
CP of ~229 W is the sustainable ceiling; the 12.9 kJ of W′ is what fuels efforts above it.
Frequently asked questions
What is the difference between critical power and FTP?
Both describe the boundary between sustainable and unsustainable effort and usually agree within a few percent. FTP is a single number from one test; critical power comes from two efforts and pairs with W′, the anaerobic work capacity. CP therefore models how long you can hold power above threshold, not just where it sits.
What is W′ (W-prime)?
W′ is the fixed work, in joules, you can perform above your critical power before exhaustion, your anaerobic battery, typically 10–30 kJ in trained cyclists. It drains above CP and recharges below it, which is why repeated surges eventually leave you unable to respond.
How do I test my critical power?
Do two maximal, evenly-paced efforts of clearly different durations, for example 3 minutes and 10–12 minutes, with full recovery between them or on separate days. The calculator solves CP = (P1·t1 − P2·t2) ÷ (t1 − t2) and W′ = (P1 − CP)·t1 from the two power-and-time pairs.
Why do the two efforts need different durations?
The two-parameter model fits a line through two points on the work–duration plot. If the efforts are too close in length the points nearly overlap and the slope (CP) and intercept (W′) become unstable. Spreading them, short versus long, gives a reliable estimate.
Can runners use critical power?
Yes. The critical-power concept applies to any maximal effort, and running power meters such as Stryd report a running critical power. The same math holds, though running power and cycling power aren't interchangeable, because running power includes the cost of vertical motion and form.
Sources
- Monod & Scherrer (1965). “The work capacity of a synergic muscular group.” Ergonomics 8(3):329–338, the critical-power / W′ two-parameter model.
- Jones, Vanhatalo et al. (2010). “Critical power: implications for determination of V̇O₂max and exercise tolerance.” Med Sci Sports Exerc 42(10):1876–1890.
- Allen, Coggan & McGregor, Training and Racing with a Power Meter. 3rd ed. (2019). Definition of Functional Threshold Power and the seven-zone power model.