How to use the critical power model calculator
- List two or more maximal efforts, each with its average power in watts and its duration as minutes and seconds (3:00). Use all-out efforts of different lengths, ideally between 2 and 20 minutes.
- Optionally enter a power to test in the advanced options.
- Read the critical power (CP), the work capacity above CP (W prime) and the R squared of the fit.
- Use the tables to see how long you could hold several powers and what power you could hold for several durations.
Formula
work = power x time
work = CP x time + W prime
least-squares line through (time, work) gives CP as the slope and W prime as the intercept
time to exhaustion at power P = W prime / (P - CP), for P above CP
power held for time t = CP + W prime / t
With exactly two efforts the line passes through both points. With more, R squared shows how well one line fits.
Three efforts
Efforts of 400 W for 3:00, 330 W for 6:00 and 300 W for 12:00 do 72,000, 118,800 and 216,000 joules of work. A line through these gives CP = 267.1 W and W prime = 23.40 kJ, with an R squared of 0.9999.
At 350 W the predicted time to exhaustion is 23,400 / (350 - 267.14) = 282 seconds, or 4:42. A power of 5 percent above CP could be held for about 29:12. For two efforts of 450 W for 3:00 and 300 W for 12:00 the line gives exactly CP = 250 W and W prime = 36 kJ.
What CP and W prime mean
In this model, critical power is the highest power that can in theory be held for a long time, and W prime is a fixed amount of work you can do above that power before you must stop. Riding above CP spends W prime, and riding below it does not. Real bodies are more complicated, but the two-number model describes many efforts well.
The model is usually trusted between about 2 and 20 minutes. Very short efforts depend on other energy systems and very long efforts are limited by other things, so the page warns you when an effort falls outside that range.
Using it
Use efforts that are truly maximal, ideally on different days, and with the same equipment. A few watts of error in a short test shifts W prime a lot. To turn power into training zones, see the cycling power zones calculator; for power relative to body mass, see the power-to-weight ratio calculator; for running, try the VDOT training paces calculator. This is general fitness information, not medical or coaching advice.
Assumptions and limits
- The linear work-time model holds for the efforts you give, with constant power during each effort.
- Each effort is a maximal effort, and the efforts have different durations.
- A fit with a zero or negative CP or W prime is refused, since it means a longer effort had more power than a shorter one.
- Between 2 and 8 efforts are accepted, each between 30 seconds and 2 hours.
Frequently asked questions
Can I use two efforts?
Yes. Two efforts fix the line exactly. More efforts let the tool show R squared, which tells you whether a single line describes them well.
Why does the page say a power can be held at or below CP?
In the model, below CP the time to exhaustion is unlimited. In life, other limits such as fuel and fatigue apply, so treat that as a very long effort, not a promise.
Is CP the same as functional threshold power?
They are related but not equal. Functional threshold power is usually defined from a test of about an hour or a shorter test with a correction, and CP from several shorter efforts. CP tends to come out a little higher.
What time format should I use?
Write minutes and seconds, such as 3:00 or 12:30, or hours as 1:00:00. A single number counts as minutes.