Critical Power calculator (CP and W′), Yousuli Help

What it does

The Critical Power calculator fits the hyperbolic CP model:

P(t) = CP + W' / t

to three maximal efforts you ran at different durations. The fit returns:

CP (Critical Power, in watts) — the asymptote of your power-duration curve, where W' is fully spent.
W' (W-prime, in kJ) — your finite anaerobic work capacity above CP.

CP and W' together anchor the Yousuli bike zones and drive the bike split projection in race planning wizard step 2.

URL: /calculators/ then open Critical power. Direct path: /static/calculators/critical_power_calculator.html.

What the calculator wants — three efforts

Three time-and-power pairs, all positive numbers:

Effort 1: time (seconds), avg power (W).
Effort 2: time (seconds), avg power (W).
Effort 3: time (seconds), avg power (W).

The calculator solves the 3-point hyperbolic fit and surfaces CP and W'. If any of the six inputs is missing or zero, the fit aborts and the outputs read N/A — there's no fallback to fewer efforts.

Canonical triplet (recommended)

The shipped calculator's defaults and tip recommend:

~2-3 min all-out (anaerobic ceiling — drives W').
~5-7 min all-out (mid-curve — stabilises the fit).
~12-15 min all-out (close to threshold — pins CP).

These three points span the part of the power-duration curve where CP and W' have the most leverage. The defaults on the form are 120 s / 480 s / 900 s.

A workable protocol

20-30 min structured warm-up with 2-3 build efforts.
3-min all-out, fresh, even pacing.
15 min easy at Z1.
5-min all-out, even pacing.
15 min easy at Z1.
12-min all-out, even pacing.
Cool-down.

Total session ~75 minutes. Indoor (ERG-free) or on a known flat segment outdoors. The hardest effort is the 3-min — go hard from the start, hold on. The 12-min is the most informative for CP; don't sandbag it.

Other valid protocols (any 3 durations work)

The calculator doesn't constrain you to the canonical triplet — any 3 efforts at distinctly different durations work, as long as they span the curve.

What's a good spread

Far enough apart: at least 2x difference between adjacent durations. 2 / 5 / 12 spans the curve. 3 / 4 / 5 minutes does not — too tight to extract a stable CP/W' separation.
Anaerobic + threshold sandwich: include one effort under 3 minutes (W' anchor) and one effort over 10 minutes (CP anchor). The middle effort stabilises the fit.
Honest pacing: each effort must be a true all-out at its duration. Pacing a "5-min" like a "10-min" produces a low middle point that warps the model.

Examples that work

3-min / 8-min / 20-min — a longer-tail variant. CP comes out a touch lower; useful for time-trial-focused riders.
2-min / 5-min / 15-min — emphasises the W' anchor; useful for crit / track riders.
3-min / 5-min / 12-min — the historic Coggan-style triplet.
MMP-derived from a hard ride: scrape your 3-min, 5-min, and 12-min best-ever sustained powers from a single hard group ride or race. Looser than a controlled test but better than nothing.

What doesn't work

Just 2 efforts — the calculator needs all three pairs. If you only ran 3-min and 12-min, fake the middle by entering the average of the two (or run a 5-min on the next ride and plug it in later).
Three durations clustered tightly (e.g. 5, 6, 7 min) — the slope reads as noise, CP/W' separation is unreliable.
One effort badly mis-paced — re-run that one. The CP/W' fit is sensitive to any single point being off.

Different estimation paths (NOT inputs to this calculator)

These produce different anchors and live elsewhere — don't try to feed them into the CP calculator's 3-effort grid:

20-min TT × 0.95 = FTP estimate. Fast and one-effort, but outputs FTP only (not CP + W'). Use it as a quick sanity check or when a full 3-effort test isn't possible. FTP and CP are usually within a few watts of each other for typical athletes.
Ramp test → FTP estimate. Graded test that estimates FTP from your point of failure. One number out (FTP), no W'.
20-min average from a hilly group ride — useful as a CP proxy if the ride had a sustained finishing effort.

The Yousuli Hub stores FTP and CP separately in MetricHistory — they aren't aliases. If you only have FTP from a 20-min test, enter it as ftp in MetricHistory; the bike zones can be anchored on either CP or FTP depending on what's available.

Time-to-target predictions

Once CP and W' are set, the calculator answers two prediction questions:

Target Power + Time @ Target Power: how long you can hold a given power above CP, based on W' burn rate.
Target Time + Power @ Target Time: what power you can sustain for a given duration, based on CP and W'.

These use the same hyperbolic model: time at power P (where P > CP) = W' / (P − CP), with W' in joules.

Outputs

CP in watts.
W' in kJ.
AeT in watts (optional, separately entered — anchors the aerobic threshold band).
Predicted time at target power or predicted power for target time depending on the prediction pair you set.

When run from the race planning wizard, the saved CalculatorResult outputs include cpw (CP in watts) and wkj (W' in kJ); those become step 2's key values on the wizard dashboard.

When to retest

Every 4 to 8 weeks during a build phase.
Less often in base or recovery blocks.
After a structural change (new bike fit, new training stimulus, altitude block).

Critical Power calculator (CP and W′)