A rigorous guide for athletes and coaches — from the physiological basis to practical testing, and everything that can go wrong in between.
Critical Power (CP) is the highest power output that can be sustained indefinitely in a metabolic steady state. In practice, no effort truly lasts forever — but CP is the asymptote of the power-duration relationship: the power level towards which your maximal sustainable output converges as duration increases.
Below CP, your body can reach a physiological steady state — lactate clearance matches production, oxygen uptake stabilises, and fatigue accumulates only slowly. Above CP, you are drawing on a finite anaerobic energy reserve called W′ (W-prime). Once W′ is exhausted, exercise at that intensity must stop.
This means CP is not just a performance number — it is a physiological boundary that governs which efforts are survivable and which are not. Understanding it is the foundation of rational pacing, training prescription, and race analysis.
Key distinction. CP is an asymptote, not a time-limited threshold. An athlete can theoretically hold CP indefinitely (in a metabolic sense). In reality, other factors — neuromuscular fatigue, thermal stress, substrate depletion — limit very long efforts, but CP remains the most mechanistically valid intensity demarcation available.
Figure 1. The power-duration relationship for a hypothetical athlete (CP = 280 W, W′ = 20 kJ). The curve is a rectangular hyperbola. Efforts above CP (red region) deplete W′ and are time-limited. The asymptote is CP. Recommended test durations are shown as points.
The curve in Figure 1 is described by a simple equation: P = CP + W′ / t. Two parameters fully characterise it — CP in watts and W′ in joules. From just two maximal efforts at different durations, you can estimate both.
The power-duration (P-t) relationship was first formalised by Monod and Scherrer in 1965 for isolated muscle groups, and extended to whole-body cycling by Moritani et al. in 1981. The model has two equivalent forms:
Hyperbolic form: P = CP + W′/t
Power declines hyperbolically with duration. At t → ∞, P → CP.
Work-time form: Wlim = W′ + CP · t
Total work done at exhaustion is a linear function of duration. The y-intercept is W′; the slope is CP.
These are mathematically identical. The work-time form is useful for fitting because it is linear and can be solved exactly with ordinary least squares from ≥2 data points.
| Parameter | Typical values | Physiological meaning |
|---|---|---|
| CP (W) | 180 – 420 W 2.5 – 5.5 W/kg |
Maximal metabolic steady-state power. Related to VO2max and mitochondrial density. Trainable over months. |
| W′ (kJ) | 10 – 35 kJ 0.15 – 0.45 kJ/kg |
Finite anaerobic reserve above CP. Reflects PCr stores, buffering capacity, and O2 stores. Partially trainable. |
| Pmax (W) 3-parameter only |
800 – 1800 W | Neuromuscular power ceiling. Improves model fit at very short durations (<2 min). Requires an additional short test. |
W′ is not a fixed tank. W′ reconstitutes during recovery below CP — that is the basis of W′bal modelling. But the total available W′ at the start of a fresh effort is what CP testing measures.
Functional Threshold Power (FTP) — popularised by Andrew Coggan and widely used in training platforms — is defined as the highest power an athlete can sustain for approximately one hour. In practice it is almost always estimated from a 20-minute maximal effort multiplied by 0.95.
This 0.95 factor is a population-level correction that accounts for the contribution of W′ to a 20-minute effort. It is not derived from your individual physiology. For athletes with a large W′ relative to their CP, the 20-minute estimate will overestimate CP. For athletes with a small W′, it will underestimate it.
CP is determined by the asymptote of your personal P-t curve, fitted from multiple efforts. It requires at least two tests at different durations, but the result is constrained by your actual physiology — not a generic scaling factor.
| Property | FTP | Critical Power |
|---|---|---|
| Tests required | 1 (typically 20 min × 0.95) | ≥ 2 at different durations |
| Mathematical basis | Empirical scaling factor (population) | Asymptote of your personal P-t curve |
| Gives W′ estimate | No | Yes — essential for W′bal modelling |
| Accuracy | ±5–15% vs true CP | ±2–8% (with well-chosen test durations) |
| Used for W′bal analysis | Not suitable — no W′ information | Yes — directly inputs CP and W′ |
| Sensitivity to pacing | High (all-in single effort) | Averaged across multiple efforts — more robust |
FTP can be a useful starting point. If you do not yet have CP and W′ values, setting CP ≈ FTP × 1.02 and W′ ≈ 20,000 J is a reasonable first approximation for a typical trained cyclist. But for W′bal analysis to be meaningful, you should determine CP and W′ properly from multiple tests.
Three main CP models are used in research and practice. All are forms of the power-duration relationship, but they make different assumptions and require different numbers of tests.
| Model | Formula | Parameters | Tests needed | Error (CP) | Error (W′) | Best for |
|---|---|---|---|---|---|---|
| 2-parameter (2P) |
P = CP + W′/t | CP, W′ | ≥ 2 | Low (3–6%) | Moderate (8–18%) | Most practical situations. Standard research model. Recommended first choice. |
| 3-parameter (3P / Morton) |
P = CP + W′/(t−1/Pmax) | CP, W′, Pmax | ≥ 3 | Low (2–5%) | Low (6–14%) | Athletes who include short (<90 s) test efforts. Better at short durations. |
| OmniCP | Complex nonlinear | CP, W′, Pmax, + shape | ≥ 4–5 | Very low | Very low | Research settings, comprehensive testing batteries. Rarely necessary in coaching practice. |
Figure 2. The 2P and 3P models fitted to the same set of test data (CP = 280 W, W′ = 20 kJ). The 3P model diverges at durations < 2 min where the 2P model overestimates power. For efforts between 2 and 20 min, both models are in close agreement.
Recommendation for most athletes: use the 2-parameter model with tests at 3–5 minutes and 10–20 minutes. This gives a well-constrained estimate with manageable testing burden. Add a third test at a different duration to cross-validate the fit.
The choice of test durations is the single most controllable source of error in CP determination. A poorly chosen pair of tests can produce CP estimates that are 10–20% off, even with perfect effort and power meter accuracy.
The P-t curve is most sensitive to changes in CP and W′ in the region of 2–15 minutes. Including at least one short test (2–5 min) and one longer test (8–20 min) ensures both parameters are well-constrained by the data.
| Duration | Typical power (at CP 280 W, W′ 20 kJ) | Constraint | Notes |
|---|---|---|---|
| 60–90 s | ~480–493 W | Weak (W′ only) | Dominated by PCr and fast glycolysis. 2P model systematically overestimates CP when short tests are included. Only use if fitting 3P model. |
| 2–3 min | ~393–443 W | Good (constrains W′) | Good upper constraint on W′. Still influenced by fast glycolysis. Recommended as the shortest test in a 2P battery. |
| 4–6 min | ~347–363 W | Good (constrains both) | Near-optimal for the 2P model. The VO2max effort zone. Most sensitive region of the curve. Ideal primary test duration. |
| 8–12 min | ~317–322 W | Good (constrains CP) | Excellent for constraining CP. Demanding but reproducible. Pair with a shorter test for the best 2P estimate. |
| 15–20 min | ~296–307 W | Good (constrains CP) | Close to CP — very good for anchoring the asymptote. The 20 min test is the most common FTP test and works equally well for CP. |
| >30 min | ~287 W | Redundant for 2P | Power approaches CP closely. Adds little additional constraint beyond a 20 min test. Very fatiguing and not recommended routinely. |
The most common mistake is using two tests at similar durations (e.g. 8 min and 12 min). Because the P-t curve is relatively flat in this range, small errors in power measurement produce large errors in the estimated asymptote. Spread your tests across the curve.
Practical recommendation. For a 2-test battery: 3 minutes + 12 minutes, both genuinely maximal, fully rested, indoor on a controlled setup. For a 3-test battery: add a 20-minute effort to cross-validate and reduce error. Allow ≥48 hours recovery between tests.
Sources of error in CP estimates:
CP and W′ are not fixed biological constants — they vary with conditions. Understanding these sources of variability is essential for interpreting test results and applying them to real-world performance.
An aggressive TT/triathlon position typically reduces CP by 3–8% compared to a road position, primarily due to reduced respiratory muscle efficiency and altered trunk muscle recruitment. W′ may be less affected. Always test in the position you will race or train in. Do not apply road-position CP values to TT efforts without correction.
Effect: moderateOutdoor testing on variable terrain introduces power spikes, coasting gaps (power = 0), and pacing errors that contaminate mean power calculations. A constant-gradient climb eliminates coasting and provides steady-state conditions. Indoor testing on a smart trainer is the most reproducible method, controlling for wind, gradient, and gear selection.
Effect: moderate (outdoor)Power meters vary in accuracy (±1–5%) and measurement method. Crank-based, pedal-based, and hub-based meters can give different absolute values for the same effort. Single-sided meters estimate total power by doubling one leg — this adds error if you have leg asymmetry. Use the same power meter for all tests and all analysis. Calibrate (zero-offset) before each test.
Effect: systematic biasCompetitive settings — group efforts, races, and supervised tests — tend to produce higher outputs than solo efforts. The effect is real and physiologically mediated (via central governor modulation). CP values derived from competition data may be slightly higher than those from solo testing. Consistency of motivation is more important than the setting itself — use the same conditions across tests.
Effect: small to moderateHeat stress reduces CP by approximately 3–5% at 35°C vs 20°C, with larger effects on W′. Cold conditions have complex effects depending on muscle temperature. Altitude reduces VO2max and CP in proportion to the hypoxic challenge (~1% per 100 m above ∼1500 m). Test in the conditions your CP values will be applied to, or correct appropriately.
Effect: moderate to largeW′ is highly sensitive to accumulated fatigue — it can be reduced by 30–50% in a fatigued state, even when CP appears relatively stable. This is not a measurement artefact; it reflects genuine depletion of the anaerobic reserve. CP testing requires full recovery: at minimum 48 hours of easy riding, ideally 72 hours and no hard training in the preceding 3–5 days.
Effect: large (especially on W′)CP and W′ respond differently to training. Base/aerobic training primarily improves CP. High-intensity interval training (HIIT) can improve both, but especially W′ in the short term. Tapering for competition can transiently increase CP slightly. Test at the appropriate time in your training cycle — avoid testing mid-block or after a major competition.
Effect: meaningful over weeksGlycogen availability does not directly limit CP (which is primarily aerobic), but W′ is more sensitive to carbohydrate status. Testing fasted or after heavy training days may reduce W′ estimates. Mild dehydration (>2% body mass) reduces CP and W′. Standardise pre-test nutrition: carbohydrate-adequate diet in the 24 hours before testing, fed state 3 hours pre-test.
Effect: moderate (W′ mainly)Choose the right time in your training year. CP testing is most meaningful when your fitness is representative of what you want to characterise — typically 2–4 weeks before a key event, after a short taper. Testing at the beginning of a build block establishes a baseline for prescription; testing before a key race validates current fitness.
Establish a standard protocol and stick to it. Every variable — power meter, bike, turbo trainer, room temperature, warm-up duration, time of day, nutritional state — should be replicated across tests and across seasons. Longitudinal comparisons of CP and W′ are only valid when conditions are standardised.
Pacing is everything. The 2P model assumes each test represents a genuinely maximal effort. A conservative or poorly paced effort produces a data point that lies below the true P-t curve, inflating apparent CP or deflating apparent W′. Self-paced all-out efforts (going out as hard as you can and holding it) are more reproducible than constant-power targets.
Suggested test protocol:
| Step | Detail |
|---|---|
| Pre-test | 48–72 h easy riding only. Carbohydrate-rich diet. Sleep well. |
| Warm-up | 15–20 min progressive, including 2–3 short (10 s) accelerations to open up. |
| Test 1 | All-out for your chosen shorter duration (3–5 min). Record mean power. |
| Recovery | ≥48 h before Test 2. Full recovery — do not accumulate fatigue between tests. |
| Test 2 | All-out for your chosen longer duration (12–20 min). Record mean power. |
| Fit | Enter both results in the CP determination tool. Review residuals. |
| Validate | Optional third test at a different duration. Good fit: residual < 5 W. |
The science behind CP and W′bal is well-developed. These resources are the most useful for athletes and coaches who want to understand the full picture.
The most practical and rigorous treatment of Critical Power and W′bal modelling available for a non-specialist audience. Covers the physiological basis, testing protocols, and application of W′bal to training and racing. Skiba is the researcher who developed the W′bal reconstitution model used in this tool. Essential reading for coaches and serious athletes. Available from VeloPress.
| Reference | Topic | Why it matters |
|---|---|---|
| Monod & Scherrer (1965) | Original P-t model | The foundation paper. Established the hyperbolic relationship for isolated muscle. |
| Moritani et al. (1981) | Whole-body CP | Extended the model to cycling. Introduced CP and W′ terminology. |
| Morton (1996) | 3-parameter model | Added Pmax as a third parameter to improve accuracy at short durations. |
| Skiba et al. (2012) | W′bal reconstitution | Developed the differential equation model for W′ expenditure and recovery. The basis of this tool. |
| Vanhatalo et al. (2011) | All-out testing | Validated that a single 3-min all-out test can estimate CP. Useful for practical testing. |
| Pugh et al. (2022) | Recovery rate models | Derived population and performance-level recovery rate constants (the Pugh models in this tool). |
Enter test results manually or upload power files. The tool fits your P-t curve and gives you CP, W′, and a residuals chart — then lets you use the values directly in W′bal analysis.
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