Critical speed: definition, formula, example

Plot your best times from a few minutes to about twenty against the distance covered and the points fall almost on a straight line. Its slope is your critical speed: the speed you could add, metre after metre, for every extra second of effort. The line does not start at zero. It crosses the distance axis a little above it, at a value called D′ (D prime): a fixed amount of distance you can cover faster than critical speed before you have to slow down.

The idea comes from Monod and Scherrer (1965), who described it for work done by a group of muscles, under the name critical power. It transfers to running with speed in place of power and distance in place of work. Physiologically, critical speed is the boundary between efforts where oxygen uptake and lactate settle at a steady level, and efforts where they keep drifting up until you stop (Poole et al., 2016). It sits close to, and slightly above, the maximal lactate steady state that the lactate threshold tries to estimate.

How critical speed is calculated

With two maximal efforts you can solve the line by hand. With three or more, you fit it by least squares, and the scatter of the points around the line tells you how much to trust the slope. The efforts should last between about 2 and 20 minutes: shorter ones lean on sprint qualities the model does not describe, longer ones bring in fatigue and fuelling.

A worked example

A runner has four recent bests: 1,000 m in 3:10 (190 s), 2,000 m in 6:55 (415 s), 3,000 m in 10:30 (630 s) and 5,000 m in 18:00 (1,080 s).

• Fitting distance against time gives a slope of 4.50 m/s: critical speed is 16.2 km/h, or 3:42 per km.
• The intercept is D′ ≈ 145 m.
• With four points, the 95% interval on the slope is ±0.11 m/s, so critical speed is somewhere between 3:37 and 3:48 per km.
• At 3:20 per km (5.0 m/s), D′ runs out after 145 / (5.0 − 4.50) ≈ 290 s, about 1,450 m. The model predicts a 1,500 m in roughly 5:01.

Note that the 5K pace (3:36 per km) is faster than critical speed. That is expected: any race short enough to finish before D′ is empty is run above it.

How to use it in training

Critical speed splits your paces into two worlds. Below it, fatigue builds slowly and the limit is mostly time and fuel. Above it, every metre over the line is taken from D′, and when D′ is gone, you slow down, whatever your motivation says.

• Intervals above CS: 5 × 1,000 m at 3:30 per km (4.76 m/s) for the runner above. Each rep covers 1,000 − 4.50 × 210 ≈ 55 m above critical speed, about 38% of D′. Recoveries refill part of it, not all, which is why the last reps feel harder (Jones and Vanhatalo, 2017).
• Work just below CS: 3 × 10' at 3:48 to 3:52 per km. Hard, but the steady state holds.
• Pacing races: start a 5K faster than CS and you spend D′ early. Spread it over the distance and you finish faster.

Smyth and Muniz-Pumares (2020) showed that critical speed can be estimated from the raw training data of recreational marathon runners, without dedicated tests, and that it relates to their marathon times. OpenAthlete’s statistics do the same in their Capacities view: they fit the line to your best efforts between 2 and 20 minutes (at least three of them), show the 95% interval, and do the same with power for critical power on the bike. The features page lists what else is computed from your history.

Limits

Bests from training are not maximal tests. If your 3,000 m best was a tempo effort, the fitted speed is lower than your real one: the result is at most what your efforts show. Efforts bunched at similar durations give a wide interval, and a GPS best set downhill or with a tailwind pulls the line up. The model also says nothing about long events. Critical speed is not a pace you can hold for hours, and a marathon is run well below it, at a share that depends on endurance and fuelling more than on the line itself. For those, combine it with race-based tools like the race predictor or the pace charts, and keep VMA for the short end of the curve.