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Critical Power & W′ Calculator (Run & Bike)
Find CP/critical speed and your W′ from two efforts.
What critical power and W′ mean
Critical power (CP) is the highest intensity you can hold in a quasi-steady state — the boundary between the heavy and severe exercise domains. W′ (“W-prime”) is the fixed amount of work you can do above CP before you have to back off: think of it as a battery that drains when you exceed CP and recharges when you drop below it.
The two-parameter model
Over short, maximal efforts the total work done is linear in time: W = CP × t + W′. Two efforts of different durations give two points on that line, so CP is the slope and W′ is the intercept. In algebra, CP = (W₁ − W₂) ÷ (t₁ − t₂) and W′ = W₁ − CP × t₁, with work W = power × time.
Running: critical speed and D′
The same idea works for runners using distance instead of work: distance = CS × t + D′, where CS is critical speed and D′ is a finite distance you can cover above it. From two time trials, CS = (d₂ − d₁) ÷ (t₂ − t₁) and D′ = d₁ − CS × t₁.
Picking good test efforts
Choose two hard, well-paced efforts that bracket your target — commonly around 3 and 12 minutes. Efforts that are too close in duration make the slope unstable and can throw the estimate off badly, so keep them well separated and run them rested.
Questions
What are critical power and W′?
Critical power (CP) is the highest intensity you can sustain in a quasi-steady state — roughly the boundary of the heavy and severe domains. W′ ("W-prime") is the finite work you can do ABOVE CP, like a battery that drains over CP and recharges below it.
How is it calculated?
From two maximal efforts of different durations, work = power × time is linear in time: W = CP·t + W′. Two points solve it — CP is the slope, W′ the intercept. For running the same model gives critical speed and D′ (a distance) from two time trials.
Which test durations should I use?
Pick two hard, well-paced efforts that bracket your target — commonly around 3 and 12 minutes (or a 9- and 3-minute pair). Avoid two efforts that are too close in duration; that makes the estimate unstable.