Critical Power Calculator (CP and W')
FTP is a single number that flattens your physiology. We explained why. The CP/W' model (Monod & Scherrer, 1965) uses two: the power you can sustain (CP) and your anaerobic battery (W'). Two maximal efforts are enough to measure them.
The protocol
- Short effort (3 to 5 min): flat out from start to finish, properly paced. Not a kamikaze launch that collapses halfway.
- Long effort (12 to 20 min): same brief, sustained maximal. Rest 24 h between the two (or spread them across the same week).
- Optional: a third data point (~12 min) tightens the regression: the R² will tell you whether your test was clean.
Comparable conditions (same road or same trainer, same kit, fresh legs). Sub-maximal efforts give you a model that flatters you. You do not want to be flattered, you want to know.
How to read your numbers
CP: the durable ceiling
Below CP your metabolism finds a near steady state: the limit becomes fuelling, heat, your head. Above it, you start a physiological countdown that nothing pauses. Every watt beyond CP draws on W'.
W': the battery
Expressed in kilojoules (typically 10 to 30 kJ). It is your budget for attacks, surges and rollers swallowed above threshold. Empty means you blow up, however brave you feel. It only recharges while you ride below CP.
What is critical power
The definition
Critical power is the highest power you can hold without your body starting a countdown. Below it, oxygen uptake, blood lactate and the state of your muscle settle into something close to steady. Above it, nothing settles: every extra watt draws on a finite reserve, and when the reserve is gone you stop, whatever your motivation says.
That reserve is W', said "W prime". It is measured in kilojoules, and for a trained cyclist it usually sits between 10 and 30 kJ. A battery that only drains above CP and only recharges below it.
The model comes from Monod and Scherrer in 1965. They noticed that, for maximal efforts, the
work you can do grows in a straight line with time: work = CP × t + W'. The
slope of the line is CP, the intercept is W'. That is all the calculator above does: it fits
that line to your efforts and reads off the two numbers. Jones and colleagues reviewed the
physiology in 2010 and placed CP at the boundary between the heavy and the severe exercise
domains. That is why it is worth more than a percentage of something else: it is a threshold
your body actually recognises.
How to test it
You need at least two maximal efforts of different durations, both inside the range where the model holds, roughly 2 to 15 minutes. The house protocol is 3 minutes and 12 minutes, on separate days or with a full recovery between them, on the same road or the same trainer.
Each effort has to be genuinely maximal and evenly paced. Start too hard and fade, and you have measured your pacing, not your physiology. A third effort of 5 to 8 minutes tightens the fit, and the R² the calculator returns tells you whether the test was clean: below 0.98, one of your efforts was not what you think it was.
Two to four efforts between 2 and 15 minutes. That is the whole test. No lab, no lactate strips, no ramp protocol whose result depends on the ramp.
Three riders, one model
The table runs the calculator on three riders who each did the 3 + 12 minute protocol. The last three columns are what the model predicts from those two efforts alone.
| Rider | 3 min effort | 12 min effort | CP | W' | Predicted 20 min | Predicted 60 min | Time at CP + 30 W |
|---|---|---|---|---|---|---|---|
| 200 W rider | 280 W | 220 W | 200 W | 14.4 kJ | 212 W | 204 W | 8 min |
| 250 W rider | 350 W | 275 W | 250 W | 18.0 kJ | 265 W | 255 W | 10 min |
| 300 W rider | 420 W | 330 W | 300 W | 21.6 kJ | 318 W | 306 W | 12 min |
Read the last columns. The 250 W rider holds 265 W for 20 minutes but 255 W for an hour: a classic 20 minute test, cut by 5 %, would have given an FTP of 252 W, a couple of watts off CP. The 300 W rider sits 30 W above CP for 12 min before the lights go out; the 200 W rider for 8 min. Same margin, different battery.
What the number changes in training
Pacing. Anything you have to hold for 30 minutes or more, a climb, a time trial, the last hour of a race, is ridden at or just under CP. Every watt above it is a withdrawal you will pay for before the line.
Intervals. Above CP you are spending W', and t = W' / (P - CP)
tells you how long a given interval can last. The 250 W rider's 18.0 kJ
battery buys 10 min at CP + 30 W and 3 min at CP + 100 W. Plan the interval from the
battery, not from a percentage of FTP, and the session stops lying to you.
Two dials instead of one. A block of long steady work tends to raise CP and shave W'. A block of short, savage efforts does the opposite. A single FTP number hides that trade, and you end up wondering why your threshold went up while your sprint finish vanished. Track both and you know what your training did.
Once you have CP, treat it as your threshold and build your training bands from it with the power zones calculator. Where most of your week should sit inside those bands, and whether sweet spot earns its reputation, is another argument: the sweet spot has no paper.
Where the model breaks
- It only holds between about 2 and 30 minutes. Shorter, and neuromuscular power takes over. Longer, and fuel, heat and drift bend the line: CP overestimates what you can hold for 3 hours. Treat it as a ceiling, not a target for a long ride.
- Two points make an exact line. Any error in one effort passes straight into CP and W'. Sub-maximal efforts do not give you a bad R², they give you a flattering model with no warning. A third point is how you catch that.
- W' does not recharge in a straight line. The model assumes a full battery at the start of each effort. Real recovery between surges is slower and depends on how far below CP you drop, so the mid-race predictions are rougher than the fresh ones.
- The two-parameter fit is optimistic. Jones and colleagues note that it returns a slightly higher CP than models with a third parameter or longer efforts. If your longest effort was 12 minutes, expect your one-hour reality a few watts under the line.
Frequently asked questions
What is the difference between critical power and FTP?
FTP is a convention: 95 % of your best 20 minute power, or whatever you can hold for about an hour. Critical power is a parameter of a physiological model, fitted to two or more maximal efforts. The two often land within a few watts of each other, but CP comes with a second number, W', and a validated meaning: the boundary between the heavy and severe exercise domains.
How do you do a critical power test?
Ride two to four maximal efforts of different durations between 2 and 15 minutes, on separate days or with full recovery, in comparable conditions. The house protocol is 3 minutes and 12 minutes. Pace each one evenly and empty the tank by the end. Enter the durations and average powers above: the calculator fits the line and returns CP and W'.
What is W' (W prime)?
W' is the finite amount of work you can do above critical power before you have to stop, expressed in kilojoules. Trained cyclists typically sit between 10 and 30 kJ. It drains whenever you ride above CP, faster the further above you go, and recharges only when you drop back below CP. Think of it as a battery, not a fitness score.
How long can I hold a power above my critical power?
The model gives a direct answer: time = W' divided by (power minus CP). A rider with CP 250 W and W' 18 kJ holds 280 W for 600 seconds, 10 minutes, and 350 W for 3 minutes. The calculator does this sum for any target you type in. Above about 30 minutes, and below 2, trust the prediction less.
Can I use my 20 minute FTP test as one of the efforts?
Yes, as long as it was a true maximal effort and not a paced sub-maximal one. Pair it with a hard 3 to 5 minute effort ridden on another day. A 20 minute effort sits at the long end of the model's validity, so a third point around 8 to 12 minutes will make the fit, and the R² you get back, more trustworthy.
Sources
Monod H, Scherrer J (1965). The work capacity of a synergic muscular group. Ergonomics · 8(3):329-338 · the original two-parameter model, work = CP × t + W' · 10.1080/00140136508930810
Jones AM, Vanhatalo A, Burnley M, Morton RH, Poole DC (2010). Critical power: implications for determination of VO2max and exercise tolerance. Med Sci Sports Exerc · 42(10):1876-1890 · review of the physiology behind CP and W', heavy and severe domains · 10.1249/MSS.0b013e3181d9cf7f
Allen H, Coggan AR (2010). Training and Racing with a Power Meter. VeloPress · 2nd edition · the FTP convention and the 20 minute test the calculator compares CP against