How it works
distance = CS · time + D′ (CS = (d₂−d₁)/(t₂−t₁), D′ = d₁ − CS·t₁)
Between roughly three minutes and an hour, all-out running behaves in a surprisingly linear way: plot the distance of each maximal effort against its duration and the points land close to a straight line. That line’s slope is CS; its intercept is D′. With two tests the arithmetic is direct — CS is the difference in distance divided by the difference in time, and D′ is what remains of the shorter effort after subtracting CS × time. Worked through: a 1500 m test in 5:00 and a 3000 m test in 11:00 differ by 1500 m and 360 seconds, giving CS = 4.17 m/s (a 4:00 per km pace) and D′ = 250 m. Tests that bracket your goal race duration keep the estimate honest.
Sources
- Critical power / critical speed model Monod, H., & Scherrer, J. (1965). “The work capacity of a synergic muscular group.” Ergonomics 8, 329–338 — the linear work–time (distance–time) model behind critical speed.
- Critical speed in running Critical speed is the running analogue of critical power: the asymptote of the distance–time relationship, closely tied to the maximal metabolic steady state (≈ threshold).
- D' (anaerobic reserve) D′ is the finite distance that can be covered above critical speed, reflecting anaerobic work capacity.
FAQ
When should I use the critical speed calculator?
Use it after you have completed two recent maximal efforts at clearly different distances. Feed both in and you get a CS pace to anchor tempo and threshold sessions, plus a D′ figure showing how much running above CS your legs can absorb before the reserve empties.
What test efforts work best?
Two rested, evenly paced all-out runs of clearly different lengths — one in the 1200–1500 m range and one around 2400–3000 m is a common protocol. Track efforts beat GPS-measured road runs here, because distance error feeds straight into the slope of the fitted line.
How should I read the result?
CS marks the boundary between paces you can defend and paces that drain a finite reserve. Sustained work at or just under CS raises your steady-state ceiling; anything quicker spends D′, which only refills once you ease back below CS.
Does this work in miles and kilometers?
Yes — each effort has its own km/mi selector, so you can mix a metric track test with a mile-marked road segment. Distances are converted to meters before the line is fitted, and the resulting CS pace appears in the unit you picked.
Why might my real-world result differ?
The two-point model is only as good as the tests behind it. Going out too hard on either effort, picking distances that are too similar, GPS error, wind, or lingering fatigue will all tilt the fitted line and move both CS and D′.
Can beginners use it?
Yes, though the protocol asks for two genuinely maximal runs, which takes pacing practice. Newer runners can time-trial on separate days with full recovery between, then treat the resulting CS as a rough anchor rather than a precise threshold.
CS and D′ are fitted from just two data points and inherit every imperfection in your test runs. They are informational figures for structuring workouts — questions about health, injury, or whether maximal testing is wise for you belong with a professional.