By Zencalcy Editorial TeamLast reviewed About us
Critical power is the highest power you can hold for a long time without fading, and W prime is the fixed amount of work you can do above it before you must ease off. Two hard efforts of different lengths are enough to estimate both.
Find critical power and W prime from two hard efforts.
CP = (W1 × t1 − W2 × t2) / (t1 − t2) W' = (W1 − CP) × t1
The two efforts must be genuinely maximal and the second clearly longer than the first, or the estimate becomes unstable. Typical tests use something near a three minute and a twelve minute effort.
| Symbol | Meaning |
|---|---|
| W1 | Average power of the shorter maximal effort, in watts. |
| t1 | Duration of the shorter effort, in seconds. |
| W2 | Average power of the longer maximal effort, in watts. |
| t2 | Duration of the longer effort, in seconds. |
A five minute effort at 300 W and a twenty minute effort at 250 W give CP = (300 × 300 − 250 × 1200) / (300 − 1200) ≈ 233 W and W' = (300 − 233) × 300 ≈ 20,000 J, or about 20 kJ.
Critical power is the highest power output you can hold without fatigue climbing without limit, and it is estimated from the two effort model. You perform two hard tests to exhaustion at different power outputs, note the time each lasted, then fit the relationship where power equals a constant work capacity divided by time plus your critical power.
In arithmetic terms, plotting power against one over time gives a straight line whose slope is the finite work capacity, often called W prime, and whose intercept is critical power. Below critical power you can hold the effort for a long time; above it, you are spending the W prime and will fatigue as it drains.
A straight line needs only two points, so two carefully executed tests can define the model, though more tests improve the fit. The catch is that the tests must be genuine maximal efforts of different lengths, such as around three and twelve minutes, or the line is unreliable. The model treats the body as a fixed store of work above the sustainable line, which is a simplification but a useful one.
Continue with the Heart Rate Recovery Calculator, Heart Rate Reserve Calculator, or the Heart Rate Zones Calculator — or browse more heart rate & performance tools and all sports calculators.
It is close to the hardest pace you can hold for a long effort, roughly half an hour to an hour. Training just below it builds endurance, and short bursts above it draw on W prime.
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Content updated: September 2026