How do you calculate critical power?
Critical power comes from a stubborn regularity in how long people can hold a power: plot the work done in each all-out effort against its duration and the points fall on a straight line. The slope of that line is CP — the power that draws nothing from your finite reserve — and where it crosses the axis is W′, the size of the reserve in joules. Monod and Scherrer wrote it down in 1965 and it has survived sixty years of testing: W = CP × t + W′.
Two efforts fix the line. Hold 350 W for 3 min and 275 W for 12 min: that's 63,000 and 198,000 joules of work. CP is the difference in work over the difference in time — 135,000 ÷ 540 = 250 W — and W′ is what's left of the short effort once CP's share is removed: 63,000 − 250 × 180 = 18.0 kJ. With three or more efforts the calculator fits the line by least squares and reports how well the points agree; with exactly two, the fit is perfect by construction, which is a warning, not a compliment.
W′ ("W prime") is the amount of work you can do above critical power before you stop — a battery, measured in kilojoules, that drains whenever you're over CP and recharges when you drop under it. It isn't one physiological store; it's the combined budget of stored phosphates, anaerobic glycolysis and the oxygen deficit you can tolerate. The useful part is the arithmetic: at 320 W on a CP of 250, you spend 70 joules every second, so a 4 min interval costs 16.8 kJ — 93% of an 18 kJ battery — and holding that power to exhaustion would take 4:17.
Which efforts should you use for a CP test?
The two-parameter model is only honest between roughly 2 and 20 minutes. Shorter, and neuromuscular power the model doesn't know about inflates W′; longer, and fatigue, fueling and boredom drag the point below the line. Within that window, spread the durations out — the fit is far more stable when the long effort is at least twice the short one:
| Protocol | Efforts | Best for |
|---|---|---|
| Classic pair | 3 min + 12 min | Most riders; one session with 30+ min easy between, or two days |
| Three-point | 3 + 5 + 12 min | A real fit statistic; catches a badly paced effort |
| Race-derived | Best 3, 5, 10 and 20 min from recent maximal riding | No test day — but only if those efforts were truly all-out |
| Long-form | 5 min + 20 min | Diesel riders; the 20-min doubles as an FTP test |
Pace each effort evenly and finish empty — a fast start that fades counts as a shorter effort at a higher power and bends the line. Do the short effort first if you're testing in one session.
Critical power vs FTP: which is higher?
CP, almost always. FTP is defined around an hour; CP is the power you can hold for something like 30–40 minutes before the model's "indefinitely" gives way to reality, so it sits a few percent above. The common coaching convention is FTP ≈ 96% of CP — 240 W for the 250 W rider above — and published comparisons put the gap anywhere from 3 to 9%. The two numbers measure different things and neither is wrong; what matters is not mixing them up in your zones. Feed this calculator your FTP and it tells you where your CP sits relative to it and whether that gap is the usual one.
The comparison exposes a quiet disagreement between testing methods. The model above predicts a 20-minute power of 265 W, which the standard 20-minute rule would call an FTP of 252 W — while the CP convention says 240 W. Same rider, same legs, 12 W apart, and the model's own 60-minute prediction (255 W) is higher than both, because the hyperbola never quite comes down to CP. That spread is the honest error bar on "your FTP", and it's why the FTP calculator talks so much about which test flatters whom.
What does CP predict for other durations?
Once you have the two numbers, the model hands you a whole power curve: sustainable power at any duration is CP + W′ ÷ t. For the 250 W / 18 kJ rider:
| Duration | Predicted power | Trust it? |
|---|---|---|
| 1 min | 550 W | Overpredicts — sprint power isn't in the model |
| 2 min | 400 W | Edge of the valid range |
| 3 min | 350 W | Valid (a test input here) |
| 5 min | 310 W | Valid — the classic 5-min check |
| 10 min | 280 W | Valid |
| 20 min | 265 W | Valid — compare with a 20-min test |
| 30 min | 260 W | About the limit of what CP itself can be held for |
| 60 min | 255 W | Overpredicts — FTP sits below this |
CP + W′/t, computed by the calculator's engine from the worked example. The two test efforts reproduce exactly because they defined the line; every other row is an extrapolation, and the ends of the table are where the two-parameter model is known to be generous.
How long can you hold a power above CP?
Turn the formula around and it becomes a pacing tool: time to exhaustion at a power P is W′ ÷ (P − CP). Every watt above CP is a rate of spend, and the reserve is fixed:
| Power | Above CP | Time to empty |
|---|---|---|
| 275 W | +25 W | 12 min |
| 300 W | +50 W | 6 min |
| 325 W | +75 W | 4 min |
| 350 W | +100 W | 3 min |
| 400 W | +150 W | 2 min |
CP 250 W, W′ 18 kJ, from a full battery. At or below CP the answer is "not from W′" — the limit becomes fuel, heat and will, none of which the model tracks.
This is what makes CP more useful than FTP for racing decisions. A 300 W surge to close a gap costs this rider a known slice of a known reserve, and the model says how long a recovery below CP needs to be before the next one is affordable. Head units that show "W′ balance" live are running exactly this arithmetic, with a recharge model bolted on.
Pacing errors don't land evenly. Ride the 3-minute effort 10 W harder and CP moves −3.3 W while W′ jumps +2.4 kJ; ride the 12-minute effort 10 W harder and CP moves +13.3 W while W′ drops 2.4 kJ — all computed by refitting the line. So when a result looks odd, the long effort is the one to distrust for CP and the short one for W′. It's also why a lazy long effort produces a rider with a modest CP and a heroic W′: the line tilts, and the intercept goes up.
What is a good W′?
W′ scales with muscle mass and rider type more than with fitness, which is why a bigger number isn't automatically better. Ranges compiled by coaches who test it routinely:
| Rider type | Typical W′ |
|---|---|
| Endurance / diesel | 9–15 kJ |
| All-rounder | 15–20 kJ |
| Punchy / criterium | 20–25 kJ |
| Sprinter / track | 25–35 kJ |
Broad ranges from High North Performance's testing pool; women's values run roughly a third lower for the same rider type, and real riders straddle the lines. Under 5 kJ or over 40 kJ, suspect the efforts before the physiology — the calculator says so.
The interesting number is the ratio. An 18 kJ reserve on a 250 W engine makes an all-rounder; the same reserve on a 310 W engine is a time trialist, and 28 kJ on 250 W is a rider who should be picking races with hills short enough to sprint over. Training moves CP a lot and W′ a little; choosing events moves the odds.
What the two-parameter model gets wrong
The straight line is a simplification, and it's worth knowing where it bends. Under about two minutes, real riders produce more power than CP + W′/t predicts, because sprint power comes from mechanisms outside the model — three-parameter versions add a ceiling to fix it. Past 30 minutes, riders produce less: CP is not a power you can hold "indefinitely", and the gap to a genuine hour is the FTP discussion above. In between, the model is only as good as the efforts — a non-maximal input doesn't produce an error, it produces a confident wrong answer, which is why the calculator flags a short effort with less power than a longer one and durations too alike to separate slope from intercept. And recharge is a separate question: how fast W′ refills below CP varies rider to rider and isn't captured by either number.
How to train with CP and W′
Use CP the way you'd use FTP for threshold work — it's the same boundary seen from the physiology side — but set the zones with the right anchor: the power zones calculator wants FTP, so hand it 96% of CP rather than CP itself, or your Zone 4 will quietly be Zone 5. Use W′ to size intervals: a set of 4 min efforts at 320 W each spends 93% of the 18 kJ battery, which tells you how much rest makes the next one repeatable and why the fifth one fails. And track both over a season: CP rising is the aerobic engine growing; W′ drifting is usually the test, not the rider. Log the training load in the meantime with the TSS calculator — the two together are the whole picture the platforms charge for.