Critical velocity
calculator

Enter two all-out efforts — a shorter fast one and a longer one — and get your critical velocity (critical speed) pace, your D' reserve, and race-time predictions. With the two limits most critical-speed tools leave out.

What critical velocity is

Critical velocity (CV), also called critical speed, is the fastest pace the model says you can hold in a metabolic steady state — the boundary between running you can sustain and running that marches you toward exhaustion. It comes from a straight line through two maximal efforts: plot distance against time for both, and the slope is CV while the intercept, D' ("D-prime"), is the finite distance you can cover above CV before you stop. It's the running form of the critical-power concept used in cycling FTP work.

How the math works

Two maximal efforts define one line. Over the range where the model holds, distance rises linearly with time:

Given a shorter effort (d₁, t₁) and a longer one (d₂, t₂), the slope and intercept fall straight out:

Pace is the reciprocal of speed, scaled to the distance unit (the mile factor is exact, 1 mile = 1609.344 m):

Once you have CV and D', the line predicts a time for any distance beyond the reserve, or a distance for any time:

This is the linear distance–time model (Monod & Scherrer 1965; Hill 1993; Jones et al. 2010), applied to running as a field test by Galbraith et al. (2014), whose single-visit protocol used three track runs of 3,600, 2,400, and 1,200 m. Two efforts are the minimum; three tighten the fit.

Worked example

A runner does two maximal efforts: 1,200 m in 4:00 (240 s) and 3,600 m in 13:00 (780 s).

• Critical velocity: (3600 − 1200) ÷ (780 − 240) = 2400 ÷ 540 = 4.444 m/s
• D' reserve: 1200 − 4.444 × 240 = 133 m
• Pace: 1609.344 ÷ 4.444 = 362 s = 6:02 / mile; 1000 ÷ 4.444 = 225 s = 3:45 / km
• Speed: 9.94 mph (16.0 km/h)
• Predicted 3,000 m: (3000 − 133) ÷ 4.444 = 645 s = 10:45
• Predicted 5,000 m: (5000 − 133) ÷ 4.444 = 1095 s = 18:15

Run the same line out to 10,000 m and it prints 37:00 — but that effort lasts past the model's window, so it flatters the runner. The line has no term for the slow fatigue that sets in over a long race, so the further past ~30 minutes you extrapolate, the more optimistic the time.

When this calculator is wrong

The two-point model is honest arithmetic on two efforts, so it inherits whatever those two efforts don't capture. Three limits matter.

• Critical velocity is not your all-day threshold pace. CV marks the top of the sustainable domain, and that boundary sits above the maximal lactate steady state: Pringle & Jones (2002) found critical power occurred at a significantly higher output than MLSS, so a pace set at CV is a few percent faster than the pace you could truly hold at a lactate steady state. Program long, steady tempo runs a touch under CV, not at it. The exception: for pacing shorter time trials and for critical-speed interval targets, CV is exactly the right anchor — the overshoot only bites when CV pace is treated as an easy, hold-forever tempo.
• D' depends on which two efforts you pick. D' is an intercept, and intercepts move: two plausible trial pairs for the same runner can hand back a D' that nearly doubles (133 m from a 1,200 m/3,600 m pair, 250 m from a 1,500 m/3,000 m pair). The model is fitted on maximal efforts of roughly 2–15 minutes (Jones et al. 2010; Pringle & Jones 2002); trials much shorter or longer, or two efforts close together in duration, distort the line. Use one short, hard effort and one longer one, both genuinely all-out, and don't read D' as a fixed personal constant.
• Predictions past the window run optimistic. The line is straight, but real race pace decays with distance. Predictions inside about 1,500 m to 10,000 m are usable; extrapolate to a half or full marathon and the model prints a time faster than most runners will run, because it assumes endurance the two short trials never tested.
• It needs real maximal efforts, and it was built on trained adults. The field-test data come from distance runners running all-out (Galbraith 2014). Sandbagged trials, uneven pacing, hills, heat, or wind all skew the line, and there is no primary normative "good CV" table to grade yourself against — the useful reference is your own retest.

What to do with the result

Use CV pace as an interval and threshold anchor, not a race target. A common session is critical-speed intervals — repeats at CV pace with short rest — which trains the exact boundary the number marks. Set easy running clearly below CV, and hard intervals above it, where the D' reserve is what you're spending. Retest with the same two distances every few weeks under similar conditions and watch CV pace drift down as fitness improves; that trend is more trustworthy than the absolute number. When you want a race target rather than a training anchor, cross-check the prediction against a VDOT estimate and a Riegel race-time prediction, and trust them less the further the goal distance is from the efforts you actually ran.

Common questions

What is critical velocity, and is it the same as critical speed?

Yes — critical velocity and critical speed are the same quantity, the fastest pace the two-point model says you can hold in a metabolic steady state. "Velocity" and "speed" are used interchangeably in the running literature; both are the slope of the distance–time line through two maximal efforts.

What two efforts should I use?

One shorter, faster all-out effort and one longer one, ideally both lasting between about 2 and 15 minutes — for many runners that's something like 1,200 m and 3,600 m, or 1,500 m and 5,000 m. Keep the two durations well apart, run both genuinely maximally, and use the same track or flat course for each.

What is D' (D-prime)?

D' is the intercept of the line: the finite distance you can cover above critical velocity before exhaustion, drawing on anaerobic capacity. Galbraith calls it anaerobic running capacity (ARC). It's real, but it's sensitive to which efforts you enter, so treat it as an estimate that moves, not a fixed number.

Is critical velocity the same as lactate threshold or FTP?

They're close cousins but not identical. Critical velocity is the running analog of critical power (the cycling concept behind FTP), and it sits slightly above the maximal lactate steady state — Pringle & Jones (2002) found critical power higher than MLSS. So CV pace is a little faster than a true lactate-threshold pace; use it as a ceiling, not an all-day tempo.

Can critical velocity predict my race times?

For distances roughly between 1,500 m and 10,000 m, yes, within the usual limits of any model. Beyond about 30 minutes of running the straight-line prediction runs optimistic, because it has no term for the fatigue that builds over a long race — so a marathon predicted from two middle-distance trials will read too fast.

How is this different from a VDOT calculator?

VDOT fits your result to Daniels' oxygen-cost tables to set training paces across zones; critical velocity fits two of your own maximal efforts to a distance–time line to find one threshold pace and your anaerobic reserve. They answer different questions — VDOT for a full pace ladder, critical velocity for the sustainable/severe boundary — and cross-checking them is a good sanity test.