Critical speed is the boundary that separates running speeds that can be sustained at a metabolic steady-state from speeds that cannot. Sometimes called critical velocity or “CV,” critical speed is known in the running world in partly due to its popularization by Tom “Tinman” Schwartz and his proteges, including Drew Hunter.^{[1]}

Critical speed is increasingly becoming the gold standard among physiologists for identifying the limit of what runners would call “high-end aerobic” or “steady-state” running speeds, and is gaining traction as a training tool as well. The critical speed model explains the body’s response to different speeds better than older models based on the lactate threshold.

Among exercise physiologists, critical speed (or a semi-related concept, the **maximum lactate steady state**, which we’ll also discuss) is rapidly becoming the gold standard for capturing the aerobic fitness of athletes.

Critical speed has its roots in early work in the 1960s, 70s, and 80s, but didn’t really start to emerge as the strongest physiological model for intense exercise until the last 15 years or so.

In this article, we’ll take a detailed look at the critical speed phenomenon, understand how it works on a mathematical and physiological level, see some of the problems and controversies surrounding it, and learn how to apply the concept of critical speed in your own training.

## What is critical speed in running?

Fundamentally, critical speed is a physiological and mathematical model for the intuitive notion that as you increase your running speed, there comes a point at which it rapidly becomes more difficult to run for a long time at that speed.

The theory of the critical speed model proposes there is a **hyperbolic relationship** between the duration of an all-out running event and the speed you can maintain for it (at least for events lasting ~2 to 20 minutes).

More importantly, the *asymptote *of this hyperbola—the **critical speed**—represents the boundary separating speeds that are sustainable at a metabolic steady-state from those that are not.

### The critical speed formula

The equation for the critical speed model looks like this:

Where is running speed, and is the “time limit” you can sustain a given speed. CS and D’ are two parameters that vary from one runner to another, and that can change as your fitness level grows or declines.^{[2]}

Before worrying about how to fit these CS and D’ parameters, it helps to actually look at this hyperbolic relationship in action to get an understanding of what the critical speed model is doing.

Here’s a concrete example: the plot below shows my first-year college season best during indoor track at the mile, 3k, and 5k:

As expected, the critical speed hyperbola fit the data quite well. If my coach wanted to estimate what I could run for a 1200m leg on a DMR, this plot could predict my performance at that distance quite well—better, in fact, than a traditional pace chart.

Why a hyperbola? Initially, critical speed was inspired by hyperbolic models of muscle function (muscle fibers produce hyperbolically less force as a function of how fast they’re contracting), and hyperbolas do tend to fit all-out performance data reasonably well for 2 to 20 minute performances.

But the hyperbolic speed-duration relationship is interesting not because it’s a good fit to the data (indeed, other equations can model performance data just as well or better) but because the hyperbolic model has two parameters—CS and D’—that have a meaningful physiological interpretation.

### Understanding CS and D’: the two parameters of the critical speed model

We just saw that the critical speed model has two parameters that affect its fit: CS and D’.

**CS** is “the” critical speed, sometimes abbreviated as CS: it corresponds to the **asymptote **of the hyperbola, i.e. the speed that the hyperbola gradually approaches, but never reaches.

**D’** is usually just called “D-prime,” “distance-prime,” or the “curvature constant.” It determines how steeply the hyperbola curves upwards.

As an aside, it’s a little unfortunate that the *critical speed model *(the hyperbolic time-speed relationship and its physiological implications) shares a name with *the critical speed parameter itself *(CS), as it’s a little confusing. Just remember they’re different things!

#### Critical speed is a two-parameter model

It’s useful to contrast the critical speed model against popular calculators like Jack Daniels’ VDOT system or the McMillan system. Both of these are *one-parameter *models: your performances across all distances (and your training paces, e.g. E, T, I, and R in the Daniels system) are predicted based on a single performance.

The critical speed model has ** two **parameters, and as such, it can’t be fit to just one race performance—you need multiple performances over different distances to fit a critical speed curve.

One-parameter models like the Daniels and McMillan systems are convenient, but can’t explain why some runners have similar performances at one distance but vastly different performances at another—e.g. two teammates who both can run 17:00 in the 5k, but one has a 4:45 mile PR while the other has a 5:00 mile PR.

The critical speed model deals with this situation quite well, and more importantly, provides insights into *why *two runners might perform better or worse at different distances.

#### CS: The asymptote of the hyperbolic curve

The critical speed parameter, CS, corresponds to the lower bound of the time-speed relationship and is expressed in meters per second (easily converted to min/mi or min/km). Here’s the same indoor track data from above, with the CS labeled:

Or as pace in minutes per mile:

Now, we’ve bumped into one of the most common criticisms of the critical speed model, which is that it seems to suggest that 19-year-old me could’ve sustained 5.0 m/s (5:22/mi pace) *indefinitely*—clearly, that cannot be the case.

We’ll come back to this problem at length later on; for now, let’s just make a note of the fact that the critical speed model does not seem to predict performances very well beyond events lasting more than about twenty minutes (or less than two minutes, but for different reasons).

#### D’: A finite energy resource

D’, the other parameter to the critical speed model, determines the steepness of the hyperbola.

D’ represents a *finite energy resource*: when running faster than your critical speed, your body only has a certain amount of energy it can produce before you “go bankrupt” and have to stop because of exhaustion.

The interpretability of D’ is another strength of the critical speed model—a less well-known property of hyperbolas (well, one I don’t remember learning in algebra II) is that t*he area between the asymptote and the curve itself is constant*, regardless of where you are on the curve.

Here’s the critical speed curve from above illustrating this finite energy property:

Both green rectangles have the same area, and represent an extra but fixed amount of energy you can spend "on top of" your energy expenditure at critical speed.

It’s a little confusing as to why D’ is measured in meters. You might think of it as a quirk of the math. But in truth, there's a deeper interpretation.

For runners, **distance is essentially just a unit of energy**, because the caloric cost of running one mile is independent of how fast you run it—the longer duration of slower speeds is exactly offset by the lower energetic cost.

So perhaps for me, a mile is 100 calories no matter how fast I run it, so my D’ parameter can be interpreted as *either *a distance or an amount of energy.

One historical interpretation of D’ was that it represented an “anaerobic energy reserve” or your “anaerobic work capacity.”

This was a very convenient interpretation, but experimental research shows pretty conclusively this interpretation cannot be correct—for example, breathing air with extra oxygen raises CS (as expected) but also D’, which should not happen if D’ consisted only of anaerobic energy [1].

### D' is not related to fast-twitch fibers (but maps well to the "fast-twitch athlete" concept)

D’ is also not correlated with your proportion of fast-twitch glycolytic (type IIx) muscle fibers, which would be very surprising if D’ was a purely glycolytic property of an athlete [2].

Nevertheless, thinking of D’ as a finite energy budget is extremely useful both for understanding race performances across different distances and for insights into using critical speed models to plan interval workout recovery (a more advanced topic we'll return to in a later article).

Even though D’ is emphatically not related to the literal proportion of fast twitch fibers that an athlete has, it does map pretty well onto common ideas about training for “fast-twitch” vs. “slow-twitch” athletes.

Athletes with a higher D' relative to their critical speed are more speed-oriented, and thus have different strengths and weaknesses. They likely also require a different approach to training.

To the extent that D’ holds up as a metric, it may force coaches and athletes to reconsider the physiological mechanisms for short-distance vs. long-distance prowess—and appropriate training for speed vs. endurance-oriented athletes.

## How to calculate critical speed for running

*If this part seems like a lot of work, fear not—I’m building a free web app to calculate critical speed automatically! **Sign up for my email list** to find out when it’s done.*

Here’s how to calculate your critical speed:

First, take a minimum of two, and preferably three or more, recent races or time trials over events of different distances, all of which lasted between 2 and 20 minutes.

You can push it a bit on the high end if you really need to, but using an 8k or 10k is inappropriate, as they last too long for an appropriate model fit.^{[3]}

Then, make a plot (in Excel, Google Sheets, etc.) of **race distance**, in meters(x axis) against your **race time**, in seconds (y axis). Then you **fit a linear trendline **to these data points. Here’s that plot using the mile / 3k /5k data from earlier: ^{[4]}

Distance (meters) | Race time (min:sec) | Time (seconds) |
---|---|---|

1609.34 | 4:31 | 271 |

3000 | 9:05 | 545 |

5000 | 15:48 | 948 |

Now, from our trendline we’ve got a slope and an intercept (the classic ).

Here’s how the slope and intercept translate into critical speed (CS) and, if you want it, D’:

Note that you have to use your calculated CS from the first step to calculate D’.

In our data above, we get:

CS = 5.005 m/s = 3:20/km or **5:22/mi**

and

D’ =** 260.1 meters**

### Critical power estimates from Zwift, Stryd, and other devices

Some power-based training devices, like Zwift, Stryd, COROS, and a few others, calculate “running power” and/or "critical power."

Though the algorithms they use are proprietary (read: not disclosed to or validated by anyone outside the company!), I suspect they are * not *merely doing the standard critical speed fitting done above, because most people do not have enough all-out performances over different distances in the past few weeks.

Likely, Zwift, Stryd, COROS, et al. are doing a weighted combination of the longest and fastest sessions you do, possibly incorporating some advanced techniques to deal with interval workout recovery—something the critical speed can handle quite well, and which I’ll cover in a separate article.

In any case, there’s an easy way to test whether your device’s critical power estimate and its predictions are accurate—run a few time trials and fit critical speed the real way!

## The physiology of critical speed

What’s interesting about the critical speed model is not that it merely fits performance data well—it’s that it makes *concrete predictions *about the physiological response of the body to exercise, *and these predictions are correct!*

At the beginning of this article, I said that critical speed (CS) is the boundary between speeds that can be sustained at a metabolic steady-state and speeds that cannot.

To understand what a “metabolic steady-state” means, we’ll look at two well-known physiological metrics that almost every runner has heard of: **VO2 **and **blood lactate**, plus a few other biomarkers that are more difficult to measure, but reveal additional insights into the metabolic processes going on inside a muscle.

**VO2 **is oxygen consumption, the “V-dot” in the famous Daniels VDOT training system. It’s a direct measurement of your body’s aerobic energy generation, since oxidizing fuel for energy in your muscle mitochondria requires oxygen (hence the “oxi-” prefix). VO2 goes up as a function of speed, until your body reaches its maximum possible level of oxygen extraction from the air—this is your **VO2max**.

**Blood lactate **is another marker of metabolic level, though its interpretation is more complicated.

In brief, lactate is generated in proportion to your muscles’ overall metabolic rate (aerobic and otherwise), and its production accelerates when your muscles are relying increasingly on glycolysis (the “anaerobic system”) for energy.

Lactate is emphatically not merely a waste product, and is continually produced even at fully aerobic speeds, but the fact remains that exponentially rising levels of lactate in the blood are widely believed to be a clear marker that you’re running at a speed that’s quickly becoming unsustainable from a metabolic perspective.

### Metabolic steady-states during running

Let’s take a look at how VO2 and blood lactate evolve over time during running.

Standard in-lab exercise testing usually uses a single run, done in a stepwise progressive fashion, but this kind of protocol doesn’t reveal the full strength of critical speed (which, remember, we can estimate from a few recent all-out races or time trials).

Rather, let’s consider what happens during *long *constant-speed running.

Suppose we brought a runner with similar times to 19-year-old me (5k pace: ~5:05/mi, CS = 5:22/mi), into a physiology lab on several different occasions to do a treadmill run at a variety of different speeds.

#### Metabolic steady-state at slow to moderate speeds

**Visit #1: 8:00/mi.** Let’s say we bring our runner in for a run at 8:00/mi pace (circa 40% of 5k pace). Here’s what VO2 would look like over the first few minutes of the run—a quick rise, then a plateau after about three minutes.

As for lactate, aside from the possibility of a transient and small rise in the first few minutes, our runner’s blood lactate levels would be indistinguishable from his baseline a few minutes into the run, resting blood lactate concentration: probably around 0.8 to 1.2 mM (millimoles of lactate per liter of blood).

Note that “indistinguishable” here does not mean “literally the same”—blood lactate measurements are a bit noisy; commercially available meters like the Lactate Pro 2 or The Edge can bounce around by 0.2 to 0.4 mM, so a one-off measurement of, say, 1.3 mM of lactate wouldn’t be a meaningful difference from 1.1 or 1.2 mM.

Importantly, we could come back 10, 20, or 30 minutes later, with our runner still on the treadmill, and both VO2 and blood lactate would be *completely unchanged*. This finding would be good evidence that our runner was at a metabolic steady-state.

**Visit #2: 7:00/mi.**Now suppose a few days later, we bring our runner back for another run at 7:00/mi (60% 5k pace). Our runner’s physiological profile would look…exactly the same!

Except that his VO2 would plateau (again, within a few minutes) at a moderately higher level.

Blood lactate would again be indistinguishable from a normal resting level. And, importantly, VO2 and lactate would *stay *at the same level for 10, 20, 30+ minutes.

#### Metabolic steady-state during moderate to strong speeds

**Visits #3, 4, 5: 6:15/mi, 6:00/mi, 5:45/mi. **Things might start getting more interesting in the vicinity of 6:00/mi pace (maybe a bit faster, maybe a bit slower).

We’d still see the same initial rise in VO2 in the first few minutes of the run, but over the course of the next six to eight minutes, we’d see a smaller, slower rise in oxygen consumption beyond that initial value at three minutes.

This phenomenon is termed the “VO2 slow component” and is thought to represent a loss of muscular efficiency—it’s taking (modestly) more energy to produce the same amount of force in your muscles.

We’d also see blood lactate levels rise to a level that’s identifiably different from baseline.

Still low, though, perhaps around 1.8 to 2.2 mM. This phenomenon has a huge number of names, but I prefer **LT1**—the **first lactate threshold**.

The appearance of the VO2 slow component and the crossing of the first lactate threshold denote the transition from what physiologists call “moderate” domain of exercise to the “heavy” domain of exercise.

This transition is, as far as I can tell, mostly an academic one—it’s probably a gradual transition, not a sudden one, and it usually can’t be identified with much precision anyways.

More importantly, LT1 does *not *denote the transition to a metabolically unsustainable speed.

If we come back 10, 20, or 30 minutes later, we’d find *exactly the same *VO2 levels and blood lactate levels. Again, clear evidence that our runner is at a metabolic steady-state.

This pattern repeats itself at speeds above LT1—we see a higher initial rise in VO2, a greater slow component of VO2, and an elevated level of blood lactate that is stable over time, even for 30+ minutes.^{[5]}

#### Metabolic steady-state, and its breakdown, at faster speeds

**Visits #6, 7, 8: 5:35/mi, 5:25/mi, 5:15/mi.**

The real action is at speeds in the range of 90-100% of 5k pace. Suppose we observe the following data:

** 5:35/mi pace: **We again see an initial rapid rise in VO2, followed by a slower rise that eventually plateaus; and a rapid rise in blood lactate to a value of around 3.5-4.0 mM, that then plateaus or decreases slightly over time.

We check back in 10, 20, and 30 minutes, and see the same unchanged values in both VO2 and blood lactate. This pace is definitely a metabolic steady-state.^{[6]}

** 5:25/mi pace: **We see an initial rapid rise in VO2 (to a higher value than 5:35/mi pace), followed by a slower rise (again to a higher value than the ultimate plateau of 5:35/mi). But this VO2 value still plateaus after about 15 minutes, with no increase even after 25–30 minutes of running.

*However*, we see a slow but steady rise in blood lactate, from 4.5 mM at 10 min into the run to 5.7 mM after 30 minutes. Our runner finds this run challenging, but is able to complete the full 30 minutes, reporting a 9/10 effort level. Is this a metabolic steady-state?^{[7]}

** 5:15/mi pace: **We see an initial rapid rise in VO2 (to a higher value than 5:35/mi pace), followed by a slower rise that never plateaus, but that instead drives our runner’s VO2 all the way up to his VO2max by 12 minutes into the run.

We also see a steady rise in blood lactate, up to a very high level (likely beyond 10 mM). Moreover, our runner is too fatigued to continue after about 16 minutes and must stop the test.

This pace is quite clearly *not *in a steady-state: our runner has progressed into what physiologists call the “severe” domain of exercise, and our runner was using unsustainable glycolytic energy production to maintain this faster speed.

Let’s try to make sense of these results.

### The maximum lactate steady-state (MLSS) perspective

If your principle measure of steady-state is blood lactate, it’s clear that the breakdown in steady-state happened at some speed between 5:35/mi and 5:25/mi.^{[8]}

Blood lactate starts to rise inexorably, so the energetic situation in the muscles must be unsustainable.

This is the perspective taken by people who believe that the gold standard for metabolic steady-state is the **maximum lactate steady-state** or **MLSS**. In our data above, we’d identify this pace as 5:30/mi.^{[9]}

Advocates of lactate threshold training would endorse doing intervals at MLSS as a highly productive way to improve aerobic fitness.

### The critical speed perspective

The critical speed model puts oxygen consumption at the forefront, pointing to the fact that VO2 is still in a steady state at 5:20/mi.

More importantly—and I constructed our hypothetical data to reflect what happens in the real world—5:20/mi is at a speed that’s distinctly *above *the MLSS, but distinctly *below *the critical speed.

In reading the research on critical speed, I’ve become convinced that the critical speed perspective is correct.

One specific paper changed my mind—a 2021 study by Rebekah Nixon and others at the University of Exeter [4], which used a protocol very similar to the one I just outlined above.

Ten runners did several all-out time trials to establish critical speed, a VO2max test, then several continuous runs at speeds closely surrounding MLSS and critical speed on either side.^{[10]}

The results were exactly the same as in our hypothetical example: oxygen consumption can plateau, even at speeds above MLSS, as long as that speed is significantly below critical speed.^{[11]} Moreover, that speed is sustainable for at least 30 minutes.

Observe the following data:

However, running at a speed that is even *slightly *above critical speed leads to an inexorable rise in oxygen consumption (and lactate, of course) and rapid fatigue (usually in 10-20 minutes).^{[12]}

#### Critical speed is about more than lactate as a biomarker for steady-state

Advocates for critical speed point to earlier research showing that other biomarkers of metabolic intensity, like intramuscular levels of pH, phosphocreatine, and phosphate, all show a steady-state below critical power (in cycling or leg extensions) and an inexorable rise (or fall, for pH and phosphocreatine) above critical power [5,6].

Here's data from quad exercises showing distinctively different intramuscular metabolic profiles during exercise just above and just below "critical torque," the quad extension equivalent of critical speed:

Admittedly, some of these papers use more aggressive buffers of +/- 10% on either side of critical power, which would likely put you below MLSS as well, but it’s still strong evidence that critical power (or critical speed, in running) demarcates a “phase shift” in a whole *ensemble *of indicators of muscle metabolism, not just lactate alone.

Another key finding from these metabolic-ensemble papers is that the metabolic situation in your muscles at the end of an all-out effort is more or less the same for a wide range of intensities, as long as all of them are above critical speed.

However, the metabolic situation in your muscles after an all-out effort at a speed below critical speed (e.g. a one-hour time trial) is *different*—you don’t have the combination of low pH, high blood lactate, low phosphocreatine, and high phosphate levels that characterize all-out efforts above critical speed.

#### Critical speed’s insights into “vVO2max” and VO2max training

Critical speed offers another useful insight that upends older tenets of physiology.

Many runners and coaches obsess over the “velocity at VO2max”, or the **vVO2max**. In theory, it’s the unique speed that elicits your VO2max, as estimated by an incremental treadmill test.

Depending on the person, endurance at vVO2max can range from as little as 2.5 minutes to as much as 10 minutes [7]. vVO2max is also the motivating target of Daniels’ “I” pace, as well as the numerous VO2max-targeting intensities in programs like Pfitzinger/Douglas and Coe/Martin.

But the critical speed phenomenon shows why there *is *no unique speed that elicits VO2max—*any *speed faster than critical speed will inexorably drive your oxygen consumption to its maximum, and the metabolic situation in your muscles at the end of a 1500, 3k, or 5k is more or less the same.

This is great, because it means you have a lot more flexibility in terms of workout paces.

You can stimulate the same metabolic systems using a wide range of speeds, while getting the specificity benefits you need (e.g. running 5k pace for 5k runners, or 1500 pace for 1500 runners).

vVO2max is not a magic pace; running faster and shorter or slower and longer will produce the same metabolic situation in your muscles, as long as you’re running above critical speed.

## Critical speed is a boundary, not a magic training pace

We now have a good understanding of my initial definition of critical speed—it is a boundary that separates metabolically sustainable speeds from those that are not metabolically sustainable.

Physiologists would say it separates the “heavy” domain of exercise (metabolically sustainable) from the “severe” domain of exercise (metabolically unsustainable).

In coaching terms, I think of critical speed as separating “high-end aerobic” speeds from “anaerobic” speeds. I tend to avoid “anaerobic” as a term in most cases but it does seem apt here.

### Just because it’s a metabolic steady-state doesn’t mean you aren’t getting tired

Anyone who’s raced a half marathon knows that “metabolic steady-state” doesn’t mean “no fatigue.”

Half marathon pace is definitely slower than both MLSS and critical speed, yet it certainly doesn’t feel easy after seven or eight miles.

Rather, running at a metabolic steady state means *fatigue builds up much more slowly, and for different reasons *than running at a speed that’s above metabolic steady-state.

Fatigue in a well-paced half marathon feels pretty different from fatigue in a well-paced 5k, which is exactly the idea behind the metabolic steady-state.^{[13]}

Part of the value in training at metabolic steady-states is that you can rack up a huge amount of volume with a stable biochemical situation inside your muscles.

For example, consider repeats at MLSS (~Daniels’ “T” pace): the metabolic situation in your muscles is constant throughout the workout, so you can rack up 30+ minutes of work pretty comfortably.

In contrast, doing repeats at vVO2max (~Daniels’ “I” pace), each repeat is the metabolic equivalent of a freight train rolling downhill without any breaks—you’re always in an unsustainable metabolic situation, with classic markers of fatigue including lactate, pH, phosphocreatine, and phosphate headed towards their limits, which puts hard constraints on how long and how far you can go in the workout.

### Unlike lactate threshold and MLSS, you should not train *at* critical speed

There is an important practical distinction between maximum lactate steady state (MLSS) and critical speed that’s worth emphasizing.

Because MLSS is defined as a speed that *is sustainable *(based on the lack of a definite rise in blood lactate levels over a 30 minute run), it’s fine to train at MLSS, or its approximate value from a lactate threshold test or race prediction formula.^{[14]}

However, critical speed is a *boundary*. Running ** at **your critical speed is like standing on a cliff edge—not wise, and bound to lead to unpredictable results.

Why? Because as with any metric, there’s always error in your estimate for CS.

If your nominal CS from your mathematical model is 0.5% above your true critical speed for that day, and you attempt to do a fast continuous run at that pace, you’re going to have a very rough time! The strength of critical speed is that this error is *quantifiable*, and you can use these error bounds to identify speeds that are, and are not, aerobically sustainable.

### CS+ and CS- are the training speeds you should use instead of critical speed

This idea of training just above, and just below, critical speed gives rise to the idea of "**CS+**" and "**CS-**" as training paces.

For high-end aerobic training, you want to run a bit *slower *than critical speed (CS-), and for improving your anaerobic capabilities , you want to train (at least) a bit *faster *than critical speed (CS+).

Here's a quick and dirty way to estimate these speeds. After that we'll see the "official" way.

### A quick and dirty estimate of speeds above and below critical speed (CS+ / CS-)

As noted earlier, running *at *critical speed isn’t really the goal.

Knowing critical speed and D’ can perhaps provide training insights, but if you want to do workouts that are pretty surely on either the faster side (CS+) or slower side (CS-) of critical speed, a quick and dirty trick is to just use **95% of 5k pace **as CS-, and **100% of 5k pace** as CS+ (or 102-103% if your 5k time is slower than 18:00). You can use my pace percentage app to calculate both.

For *most *runners, these two paces will be solidly above (100% 5k) and solidly below (95% 5k) your critical speed, and are thus pretty good options for doing workouts that either are, or are not, metabolically sustainable.

I should caution that this quick and dirty strategy is not going to be a good idea for middle distance runners, or for very undertrained runners (both of whom probably have a greater D’ relative to their CS, and as such might risk exceeding CS even at 95% 5k pace).

### A more precise way to estimate CS+ and CS-

If you already know your critical speed, a very good approximation for CS+ and CS- in most cases is to just use ±3% of CS as CS+ and CS-.

Again, you can use my pace percentage app to calculate both - technically you should use percent of speed, not percent of pace, but the difference doesn't matter for such a small percentage.

### Critical speed uncertainty: exact CS+ and CS- calculations (advanced material!😱)

If you’re an expert in linear regression, you can also use the standard error of the regression slope from your linear fit to calculate the 95% confidence intervals around critical speed by using ± 1.96 times the standard error of the m (or ) coefficient. In our example above we’d get 5:17/mi for CS+ and 5:25/mi for CS-.

Do note that you need to calculate your uncertainty bounds for your slope, *then *take its reciprocal to get CS+ and CS-. If you're using statistical software like R (which is what I used above), you'll get very different results if you use the built-in confidence-interval method because it uses a T distribution with much heavier tails when you have few data points (as we do here).

As far as I can tell, physiologists just sort of sweep that issue under the rug and use the standard errors as if they're from a normal distribution.

The reason these boundaries are so tight is because the fit to the data is so good (see plot above). If CS+ and CS- vary by more than about 5%, physiologists usually deem the fit inadequate and collect more time trial performances until the fit improves.

In the end it doesn't make a huge difference - had we used the quick and dirty 95% / 100% of 5k pace from above, we’d get 5:06/mi for CS+ and 5:22/mi for CS-. If we use ±3% we get 5:32 and 5:13. Not too bad!

Here's an illustration of CS+ and CS-, plus a visualization of the uncertainty around our estimate for the true critical speed curve:

### How long can you run at critical speed?

For a typical well-trained and well-rounded road runner, critical speed corresponds roughly to the pace you could sustain in a ~25 minute race.

But, as above, running *at *critical speed is not really the point—and moreover, it’s going to lead to unpredictable results, because of the inherent uncertainty in estimating critical speed.

Different studies have found people able to sustain critical speed (or critical power) for anywhere between 17 to 45 minutes, which makes total sense given the uncertainty around where *exactly* your critical speed lies, and the huge impact that running even a few seconds per mile faster vs. slower than critical speed.

The strength of critical speed is that it’s still a valid concept in runners who *are not *well-trained, well-rounded road runners—couch-to-5k runners, 800m runners, and ultramarathoners all have a critical speed even if their speed/performance curve looks very different from an all-around road runner - and very different from their "25min race performance."

## The physiological correlates of critical speed

The critical speed parameter (CS) is, not surprisingly, *highly *correlated with running performance across distances as short as 1000m up to at least the half marathon, and probably the marathon too [8,9,10]. So, what are the physiological mechanisms that determine critical speed?

### VO2max and critical speed

VO2max is the most obvious physiological mechanism related to critical speed.

The more oxygen you have available, the greater your oxidative (aerobic) energy production capabilities, which means you can sustain a high speed at a metabolic steady-state.

But training to improve VO2max is old-hat and well-studied (in short: intervals with repeats that elicit at least 90% VO2max, lasting at least two minutes each [11]). It's also hard to improve VO2max a lot in someone who's pretty fit already.

The non-VO2max-related parameters linked to critical speed are far more interesting.

### Mitochondria and critical speed

Because oxidative energy production happens inside the mitochondria, it stands to reason that increasing the number and the energy throughput of your mitochondria should increase your critical speed.

Some initial research suggests this might be the case—a paper from just a few months ago studied critical torque (the critical speed equivalent measured during isometric quad extensions) and mitochondrial protein expressions in the quad muscles in 12 men and 12 women [12].

Both the men and women showed moderately strong correlations between mitochondrial protein expression and their critical torque.

Supposing we believe that this study will translate to running, how do you increase the quantity and quality of your mitochondria?

A meta-analysis from 2018 found that, for increasing the number of mitochondria that you have (your mitochondrial density), *volume *is king—after normalizing for total workload (i.e. counting 10 min at 100% VO2max as equal to 20 min at 50% of VO2max), training intensity had no effect on mitochondrial density, but training volume had a steady positive correlation with increases in mitochondrial density [13].

On the other hand, for boosting the energy output of the mitochondria you already have, intensity is crucial—you need to do interval training at 90-100% of VO2max, but no greater—intensities above 100% VO2max have a decidedly weaker (but not null) effect on mitochondrial respiratory power, according to that same 2018 meta-analysis.^{[15]}

Since critical speed occurs between 80 and 90% of VO2max in most runners [14], these findings suggest that a combination of workouts at “CS+” and workouts or continuous runs at “CS-” are the ticket to boosting mitochondrial respiratory power.

### Muscle fiber composition and critical speed

Muscle fiber composition is a better-established correlate of critical speed.

Numerous studies have found a link between critical speed (or power) and the proportion of slow-twitch muscle fibers, both in absolute and relative terms—i.e., among two athletes with the same VO2max, the one with the greater percentage of slow-twitch muscle fibers is likely to have the higher critical speed [15].

The same is true, though to a weaker extent, with regards to the proportion of intermediate “fast-oxidative” type II fibers.

Can you change your muscle fiber type composition? The answer is yes, though *how *to do so—aside from the vague recommendation of “endurance training”—is unclear.

Research on recreational runners training for a marathon (presumably doing mostly or entirely easy/moderate mileage) has found shifts of one to six percentage points in muscle fiber type composition over a 16-week training program [16].

Some tantalizing evidence suggests that much greater shifts in muscle fiber type composition are possible over the long-term.

A study from 2018 describes a pair of identical twins in their 50s, one of whom was a sedentary truck driver who never exercised regularly, and the other of whom was a high school track coach and 3:01 marathoner who had logged nearly 40,000 miles of running over the previous 30 years [17].

The difference in muscle fiber type composition in the quadriceps was dramatic: only 40% of the muscle fibers in the sedentary twin were slow-twitch, while the endurance-trained twin had * over 90%* slow-twitch fibers!

^{[16]}

Now, we don’t have good data on how different types of running workouts induce muscle fiber type shifts, but it stands to reason that easy to moderate mileage should stimulate pure slow-twitch (type I) fibers the most, and speeds that are between the first lactate threshold (LT1) and CS- (a few percent slower than critical speed) *might *stimulate both slow-twitch and “fast-oxidative” type II fibers more strongly.^{[17]}

Even so, it does seem like shifts in muscle fiber composition are a long-term project with major shifts taking place over the course of years, not weeks or months.

### Capillary density and critical speed

Capillaries deliver oxygen to muscle fibers, so they are also a strong candidate for targeted training to improve critical speed.

Capillary density—and more specifically, the number of capillaries contacting each muscle fiber—is the strongest correlation of critical speed discovered thus far.

Capillary-to-fiber contacts look like this:

A 2018 study on 14 cyclists and triathletes found a very strong correlation between critical power (in cycling) and the number of capillaries per muscle fiber in the quadriceps [18]. This finding was even stronger when it was expressed as capillaries per *slow-twitch *muscle fiber.

A review of nearly 50 different training studies published in 2022 indicates that, at least in untrained people, the most effective way to stimulate capillary growth is with exercise that elicits between 80 and 100% of VO2max [19]—a task perfectly-suited for workouts at CS-.

## Training to improve critical speed

Enough theory—let’s talk training. To boost critical speed, we want to improve the key physiological traits that determine critical speed: mitochondria, fiber type composition, and capillary density.

From the findings above, we saw there are three main tools we can use in training to boost critical speed.

### High-volume easy to moderate mileage

Classical high-mileage training will cause an increase in mitochondrial density, and should help slowly shift your muscle fiber type distribution over time.

Mileage alone, though, is not the quickest or most effective way to increase critical speed.

**Key workouts:**

- Easy to moderate runs
- Long easy runs
- Doubles

### High-end aerobic workouts at LT1 to CS-

Training in the “heavy” domain of exercise—above the first lactate threshold, and below critical speed—should impose a powerful stimulus on capillary growth and might help transform fast-glycolytic fibers into fast-oxidative fibers.

The high end of this pace range, getting close to CS-, may also help trigger adaptations in mitochondrial respiratory power.

**Key workouts:**

#### Long fast runs and “aerobic threshold” runs

Examples:

- 12mi at 80% 5k pace
- 7mi at 85% 5k pace

#### Daniels-style tempo runs and cruise interval workouts

Examples:

- 8 x 4 min at 92% 5k pace w/ 1 min jog
- 5mi continuous at 90% 5k pace

#### CS- workouts

Examples:

- 10 x 3 min at CS- (or ~95% 5k pace) w/ 1.5min jog
- 4 x 2 km at CS- (or ~95% 5k pace) w/ 3 min jog

### Aerobic power training at CS- and CS+

A combination of workouts at CS-, to push your aerobic system to its maximum steady-state limit, and CS+, to push your aerobic output to its maximum (i.e. your VO2max), is the best combination of sessions to trigger adaptations in mitochondrial respiratory power, and will also contribute to capillary growth was well.^{[18]}

**Key workouts:**

#### CS- workouts (below critical speed)

Examples:

- 4–6 km continuous at CS- (~95% 5k)
- 8 x 1 km at CS- (~95% 5k) w/ 1.5min jog
*See above for a few more CS- workout suggestions*

#### CS+ workouts (above critical speed)

Examples:

- 8 x 800m at CS+ w/ 2 min jog (~100-102% 5k pace)
- 10 x 2 min at CS+ w/ 1.5min jog (~100-102% 5k pace)

## Using critical speed with Daniels-style training

If you use Daniels-style training, it’s fairly easy to incorporate critical speed sessions. You can use CS+ and CS- as “plug-in” replacements for workouts at I pace and T pace, with the following modifications:

### Critical speed workouts instead of Daniels T pace

For training sessions at T pace, you can use your calculated CS- (CS-minus) pace as a drop-in replacement by reducing the workout volume by 10-20% and increasing the recovery by 50-100%.

For example, looking at the following session:

**5–6 x mile at T, 1 min rest** (Week 7 / Phase II of the 5k to 15k program)

A modified critical speed-based session at CS- would be:

**4–5 x mile at CS-, 1.5-2 min rest**

### Critical speed workouts instead of Daniels’ I pace

For training sessions at I pace, you can use your calculated CS+ (CS-plus) pace as a drop-in replacement by increasing the workout volume by 0–25% and reducing the recovery by 25-50%.

For example, looking at the following session:

**4–5 x 1200m at I pace w/ 3-4 min rest **(Week 13 / Phase III of the 5k to 15k program)

A modified critical speed-based CS+ session would be:

**5–6 x 1200m at CS+ pace w/ 2–3 min rest**

### Adding, not replacing, workouts

Especially if Daniels-style training has worked for you, you don’t want to completely scrap your use of T and I pace workouts. One of my favorite maxims of training comes from Renato Canova, who says “*Training is not to REPLACE, but to ADD*”—meaning that you should add in CS+ and CS- to your workout rotation.

A good starting point would be to switch back and forth between using T pace and using CS- pace on alternating weeks—ditto for using I pace and using CS+ pace.

Even if you are not a Daniels acolyte, the “add, not replace” advice is useful. Critical speed-based workouts should be an additional tool in your toolkit, not a single magic pace that you default to for every workout.

## The difference between critical speed, critical velocity, and critical power

You’ve probably noticed that I’ve used the term “critical speed” exclusively throughout this article, even though you see the term “critical velocity” or its abbreviation “CV” used more in conversation among runners than “critical speed.” These terms refer to the same thing.

This is a minor point, but mechanically speaking, a “velocity” has a magnitude *and* a direction. Unless it’s an exceptionally windy day, your metabolic response is not going to depend on what direction you’re running.

Moreover, “critical speed” or “CS” is the term and abbreviation used almost universally in the scientific literature when talking about this phenomenon in runners.

Therefore, **the correct term is “critical speed” or “CS,”** not “critical velocity” or “CV.” That’s why I’ve been using the terms “critical speed” and “CS” throughout this article. Sorry to be pedantic.

### In runners, it’s (usually) “critical speed,” not “critical power”

The critical speed model is a *metabolic *phenomenon. In a perfect world, we’d measure it with energy expenditure (in calories burned per hour) or oxygen consumption (in VO2) and model metabolic power as a function of event duration. However, for athletes in the real world, we need something more practical.

In cycling, there’s an easy substitution: just use a power meter on the bike, and reference critical power using watts of *mechanical *power instead. In cycling, it’s easy to measure mechanical power output: it’s the product of the force you apply to the pedal and the angular velocity of the crankset.

There’s a very tight relationship between this mechanical power as measured by a bike power meter and your body’s metabolic power, so it’s the most convenient way to quantify power in cycling—especially since your speed on the bike is affected to a great degree by surface quality, incline, and drafting.

With running, the situation is different. There’s no cycling equivalent of mechanical power.

“*But what about how hard you push off the ground?*” you might ask. Well first, that’s not easy to measure—you need a $100,000 treadmill to do it.

And even if you have one, the relationship between the force applied to the ground and your metabolic power output is much less straightforward than in cycling. The metabolic demand of running depends a lot on *how that force is aligned with your body*, and even the specific lengths and velocities of your muscle fibers as you’re producing that force.

With running, ** speed** is the best proxy for metabolic power. Since virtually every exercise physiology study uses a treadmill, studies on runners usually measure and use

**critical speed**, not critical power.

In theory you can also fit critical power models to energetic output (replacing speed with VO2 or caloric expenditure), in which case you could fairly call it a “critical metabolic power” model.

But basically nobody does this, because you’d need to do multiple all-out time-trials in an exercise physiology lab with a metabolic analyzer, then do all your training with the same such device!

## Conclusion

Critical speed is the boundary that separates speeds that are metabolically sustainable from speeds that are not. Running at speeds above versus below critical speed, even by only a few percent, results in a very different metabolic situation inside your muscles.

You can calculate your critical speed from at least two recent races or time trials, as long as they last between two and 20 minutes.

For a typical well-trained runner, critical speed falls somewhere in between 5k pace and 10k pace, and is faster than the traditional lactate threshold.

Unlike lactate threshold training, the key to improving critical speed is *not *to run at exactly your critical speed. Instead, you should use a combination of interval workouts at 3-4% faster than critical speed (CS+) and intervals and/or fast continuous runs at 3-4% slower than critical speed (CS-).

These speeds, along with other foundational aspects of training like high-volume easy to moderate runs and high-end aerobic sessions, target the physiological mechanisms that determine your critical speed: your mitochondria, muscle fiber type distribution, and capillaries.

Critical speed is an incredibly useful tool for understanding training and racing, but it’s not the end-all be-all.

Workouts focused on improving critical speed should be part of your rotation of high-end aerobic sessions, but should exist alongside long-standing proven techniques for improvement.

## Learn more about training and physiology

If you enjoyed this article, sign up for my email list! I have more articles in the works on the latest research findings on performance, injuries, and more. My email list is the best way to find out when I release new content.

If you want to learn more about physiology, you should also **check out my book on Amazon.com** - it includes a simplified view of aerobic and anaerobic energy systems, plus tips on how to incorporate these concepts into your training for everything from 800m to the 10k.

## Footnotes

*Tap on the [bracketed] number on each footnote to return to your spot in the main article*

^{[1]} Tinman does not use the actual critical speed model when prescribing “CV” workouts, though his view on “CV” as a pace modestly faster than lactate threshold is clearly in keeping with the modern understanding of critical speed

^{[2]} Canonically, the critical speed model is always fit in SI units (meters, seconds, meters per second) but it’s easy to convert back to race times and per-mile / per-kilometer paces afterwards.

^{[3]} In research studies, the minimum number of performances is three, not two, because checking the error of the model to the performances of a given subject is a part of evaluating whether the critical speed model is appropriately fitting the data. You can fit a critical speed model to two races, but its fit will always be perfect! When you only have two race distances, you also cannot calculate CS- and CS+ the normal way, though “fudging” with a standard +/- 3% margin is a viable option.

^{[4]} There are other ways to plot and fit regression lines to the same data, e.g. plotting speed as a function of 1/time is popular. However this 1/time method and others have some arcane statistical issues; see my boring tech note on why the time-distance method is the appropriate one for time trial performances. The way I’m presenting here is the right (or almost-right) way to do it.

^{[5]} Many labs use the “gas exchange threshold” or GET as a surrogate for LT1. The GET appears as a modest excess in carbon dioxide (CO2) in the air being exhaled by the runner, relative to VO2. Identifying this point of “excess” CO2 has similar “different from baseline” issues as the first lactate threshold. Like LT1, methods to determine the gas exchange threshold (GET) sometimes fall into the gazing-at-tea-leaves trap, particularly older methods that attempt to use breathing rate to determine the so-called “ventilatory threshold” or VentT, which is yet another surrogate for LT1. Exercise physiology textbooks will tell you that GET and VentT occur simultaneously with LT1, but this is often not the case. Researchers like GET and VentT principally because it does not involve blood draws.

^{[6]} Nobody really knows why this slow decline in blood lactate happens! It does seem to be more common in well-trained runners. I suspect it might have something to do with the paltry and inadequate warm-up in many studies (e.g. 5 min of slow jogging)—I’d recommend a much more rigorous warmup for a fast continuous run, but that’s merely a hunch.

^{[7]} Running 5:20/mi for 30 min would be a fairly challenging but doable run for our athlete; this pace would be backed off about ~8sec/mi from 10k pace.

^{[8]} Had our runner done a traditional, single-visit lactate assessment, it’s likely that his second lactate threshold, or LT2, would have been identified somewhere in the 5:35-5:15/mi range. The proliferation of methods for determining LT2 is even worse than those for LT1; one paper reports calculating 56 different lactate threshold variants [X]! Terms like lactate turnpoint (LTP), onset of blood lactate accumulation (OBLA), and the traditional 4.0 mM lactate concentration cutoff, are all attempting to do the same thing: estimate maximum lactate steady-state from a single lab visit. The general consensus seems to be that the best of these LT2 methods do an okay job, but are no replacement for a real MLSS test for research purposes.

^{[9]} The technical definition of MLSS is *the fastest speed at which blood lactate rises by less than 1.0 mM between 10 and 30 minutes in a constant-speed run* [X]. To be more precise, the maximum lactate steady-state is an experimental measurement that is trying to approximate the maximum *metabolic *steady-state, or MMSS, which cannot be directly measured. Ditto for critical speed. The CS vs. MLSS debate is about which measurement is a better estimate of the underlying MMSS.

^{[10]} I often criticize exercise science studies for relying on small samples of “a few guys,” and this paper is no exception (ten males). The small sample size is somewhat mitigated by the fact that the authors were looking at *within-subject *differences, though, which is doable with high precision in smaller samples, since person-to-person differences wash out with these repeated-measurement designs.

^{[11]} The paper used the lower bound of the 95% confidence interval given by the standard errors of the linear regression model model fit to the all-out performance data, so “significantly below” here really does mean significant in the statistical sense. For most runners it works out to about 2-3% slower than critical speed, or about 5-8 seconds per kilometer. This pace is the “CS-minus” (CS-) pace I recommend later in the article.

^{[12]} “Even slightly above” again means the *upper *95% confidence interval limit for critical speed for that runner, about 2-3% faster than critical speed or 5-8 seconds per kilometer.

^{[13]} The exact mechanisms of fatigue in races that last ~30-75 minutes are still unclear—in fact, one weakness of the critical speed model is that it doesn’t fully explain the fatigue mechanisms operating in this range. Races lasting 30-75 minutes are too short for glycogen depletion to be a serious problem, and yet they don’t show the same out-of-control metabolic situation seen at faster than critical speed. So what causes fatigue in a 10k or 15k? And why is the difference between 5k and 10k pace (~5%) similar to the difference between 10k and HM pace (~5%) for a well-trained runner?

^{[14]} The fact that MLSS will by definition be below a steady-state is one criticism of MLSS: it will systematically underestimate the boundary separating metabolically sustainable and non-sustainable speeds. Moreover, the MLSS estimate will be sensitive to how finely-grained you do your successive steady-state treadmill runs; finer speed increments mean more in-lab sessions. The critical speed model has no such discrete limitation, and provides a precise estimate of CS.

^{[15]} Most studies on training intensity still prescribe exercise as a percentage of VO2max, even though prescribing it relative to critical power / critical speed or MLSS would be a better option. That’s why this meta-analysis used %VO2max as a way of categorizing intensity. Moreover, studies were “binned” into discrete buckets, so we shouldn’t put too much importance on the >90% vs <90% distinction. Intensities that are “>100% VO2max” really just mean “at an intensity greater than the workload (or speed, in running) that elicited VO2max in a one-visit incremental test.” Usually you just extrapolate from the speed-oxygen consumption relationship at slower speeds.

^{[16]} The differences in overall markers of health between the twins are incredible too: compared to the sedentary truck driver, the marathoner had 37% lower body fat, 30% lower LDL cholesterol (the bad one), 11% higher HDL cholesterol (the good one), 28% lower triglycerides, and 17% lower blood glucose levels.

^{[17]} My reasoning for the LT1-to-CS- range has to do with the slow component of VO2: because that slow component is thought to represent increased reliance on fast-oxidative muscle fibers, the strongest aerobic demand on these fast-twitch fibers should occur in the “heavy” domain of exercise, where you are at a metabolic steady-state but below your critical speed. This is just some informed speculation though.

^{[18]} “Aerobic power” is a Renato Canova term; he most often uses it to refer to 95% of 5k. I don’t think it’s an accident that this pace corresponds very closely to CS-!

One of the best training articles I've ever read. You summarize so much of the significant and substantial research from the last few years in an easily digestible manner. I'll be recommending this to all of my coaching friends.

Thank you, glad you enjoyed it!

Hi John, very interesting article. Can I just clarify my understanding about something - "the longer duration of slower speeds is exactly offset by the lower energetic cost. ... a mile is 100 calories no matter how fast I run it"

I thought, perhaps erroneously, that the oxygen cost of running a mile was the same no matter how fast it was run but the energy cost increased with speed?

Thanks

Oxygen cost is *almost* the same thing as energy cost (measured in food calories) - the main difference is that at slow to moderate speeds, oxygen cost isn't quite as good as energy cost because you're burning more fat, and fat has about a 7% lower energetic yield per unit of oxygen, compared to carbohydrates.

At high speeds (like close to marathon pace and above) it's basically a wash, since most of your energy is coming from carbs anyways, so O2 cost trends will be basically the same as energetic cost trends. Looking at what I wrote, I'm realizing that, because of the VO2 slow component, it isn't correct to say that faster speeds "exactly offset" the increased energetic cost, but it's still very close.

Here's a plot of true energetic cost as a function of speed, albeit from a pretty small study. The two lowest datapoint are at speeds so slow that any healthy adult would rather walk than run---that transition happens around 2.1 m/s or 12:45/mi pace. In fact the higher cost of transport at those speeds is a big part of *why* you'd rather walk! This plot shows O2 cost as a function of speed in the initial cohort of the Breaking2 athletes. Very flat on average, though there is some individual variation.

Hello John

I'm happy to wrote this article. I have written an article of similar breadth and scale on my blog and yours touches upon some points I don't, but a lot of it is similar. I have taken note of the paper arguing against the use of critical power which you have addressed in your new blog post so I will review and comment there.

https://www.georgeron.com/2020/04/Critical-Power-Concept.html