Critical Power Calculator (CP and W′ from Two Efforts)
Your critical power and W′ from two maximal efforts of different lengths, with the time you can hold a chosen power and predicted 5- and 20-minute powers.
Results
The dashed line marks the value you entered.
What this tool does
The critical power model, introduced by Monod and Scherrer in 1965, says there is a power you can in theory hold for a long time, the critical power CP, and a fixed store of work, W′, that you can spend above it. Plot work against time for maximal efforts of about 3 to 20 minutes and you get a straight line whose slope is CP and whose intercept is W′. Two efforts are enough, for example a 3-minute and a 12-minute all-out test, though more points give a more reliable line. CP usually sits close to, and often a little above, functional threshold power; both are estimates, and the model fits worst for efforts under about 2 minutes or over about 30.
Formula
work = CP × t + W′ · CP = (P₂t₂ − P₁t₁) ÷ (t₂ − t₁) · W′ = (P₁ − CP) × t₁ · time to exhaustion = W′ ÷ (P − CP)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p1 | Average power in the shorter test | W |
t1 | Length of the shorter test | min |
p2 | Average power in the longer test | W |
t2 | Length of the longer test | min |
pt | A power you want to hold | W |
CP | Critical power (CP) | W |
WP | W′ — work you can do above CP | kJ |
TH | How long you can hold that power | min |
P20 | Predicted best 20-minute power | W |
P5 | Predicted best 5-minute power | W |
Worked example
- Average power in the shorter test380 W
- Length of the shorter test3 min
- Average power in the longer test290 W
- Length of the longer test12 min
- A power you want to hold320 W
- Critical power (CP)260 W
- W′ — work you can do above CP21.6 kJ
- How long you can hold that power6.0 min
- Predicted best 20-minute power278 W
- Predicted best 5-minute power332 W
Limitations
- This tool is informational only. It does not diagnose, treat or replace a qualified health professional. Speak to a doctor before making decisions about your health.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.