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Critical Speed Calculator (with D′)

Calculate your critical speed (CS) and D′ from two or three all-out efforts, then use them to set threshold paces and interval targets.

Your time trials

Use 2–3 maximal efforts lasting roughly 2–15 minutes each, ideally within the same couple of weeks.
distance (m) · time
distance (m) · time
improves the fit
Training targets from your critical speed

What is critical speed?

Critical speed (CS) is the running equivalent of cycling’s critical power. It marks the boundary between the heavy exercise domain, where your body can reach a physiological steady state, and the severe domain, where oxygen uptake and fatigue keep rising until you have to stop. In practice it is a pace you could race for roughly 30–40 minutes, close to what many coaches call threshold.

D′ (“D-prime”) is the fixed amount of distance you can run above critical speed before exhaustion — a kind of anaerobic battery. Runners with a big D′ tend to have strong kicks and handle surges well.

How critical speed is calculated

For efforts lasting roughly 2 to 15 minutes, the distance you can cover is almost a straight line when plotted against time. The slope of that line is your critical speed and the intercept is D′:

distance = CS × time + D′
with two efforts: CS = (d₂ − d₁) ÷ (t₂ − t₁), D′ = d₁ − CS × t₁

Worked example

1200 m in 4:20 (260 s) and 3600 m in 14:10 (850 s): CS = (3600 − 1200) ÷ (850 − 260) = 2400 ÷ 590 = 4.07 m/s, a pace of 4:06 per km. D′ = 1200 − 4.07 × 260 ≈ 142 m.

Good test protocols

ProtocolEffortsNotes
Distance-based1200 m + 3600 mEasy to run on a track; can be done on separate days or with 30 minutes of recovery.
Time-based3 min + 12 min all-outPopular with GPS watches and treadmills; record distance covered.
Race-basedRecent mile + 5KUses genuine all-out efforts; keep them within a few weeks of each other.
Three-point800 m + 1600 m + 3200 mA third effort shows how well the straight-line model fits you.
Distance–time relationship (example: CS 4:06/km)
010002000300040002 min: 6312 min4 min: 11194 min6 min: 16076 min8 min: 20958 min10 min: 258310 min12 min: 307112 min15 min: 380315 min
Each point is the distance the example runner could cover in that time. The slope is critical speed; the line meets the vertical axis at D′ (about 142 m).

Using CS in training

Below CS

Threshold sessions — e.g. 3–5 × 8–10 minutes at 92–97 % of CS speed — build the pace you can sustain without drifting into the severe domain.

At CS

Short blocks right at CS are hard but repeatable; many coaches keep them to 20–30 minutes of total work.

Above CS

VO2max intervals spend D′ on purpose. With a known D′ you can estimate how long a rep at a given pace should take you to near-exhaustion.

Racing

In races longer than about 40 minutes you run below CS; shorter races use part of D′ — ideally saved for the finish.

Model limits. The linear model works best for efforts between about 2 and 15–20 minutes. Very short sprints or very long efforts do not fit the straight line well, so avoid them as inputs.

Compare CS with your threshold pace from the VDOT calculator, predict race times with the race time predictor, and set heart rate targets with the heart rate zone calculator.

  • Jones AM, Vanhatalo A (2017). The ‘critical power’ concept: applications to sports performance with a focus on intermittent high-intensity exercise. Sports Med 47(Suppl 1):65–78.
  • Poole DC, Burnley M, Vanhatalo A, Rossiter HB, Jones AM (2016). Critical power: an important fatigue threshold in exercise physiology. Med Sci Sports Exerc 48(11):2320–2334.

Last reviewed: September 2026 · Health disclaimer

FAQ

Critical Speed questions

Critical speed (CS) is the highest speed you can sustain while your body stays in a physiological steady state. It sits close to the boundary between heavy and severe exercise — typically a pace you could race for roughly 30–40 minutes — and is a useful anchor for threshold training.

D′ is the finite distance you can cover above critical speed before you fatigue — like a battery. A bigger D′ helps with surges, hills and finishing kicks.

Run two or three all-out efforts that last between about 2 and 15 minutes (for example 1200 m and 3600 m, or 3 and 12 minutes). Plot distance against time: the slope of the best-fit line is CS, and the intercept is D′.

Threshold sessions are often run slightly below CS, so you stay in a steady state. Intervals above CS, such as 1000 m repeats, deliberately use part of your D′ and build VO2max.