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How to calculate Critical Power and W′

The attachment is at the end, you have to read it first ;) But there is a critical power calculator here

There is something I've been searching for but haven't come across anywhere yet. While calculators are available, they don't provide insights into the actual calculation process. On a side note, I'm not a mathematician, I just need to see the whole picture, This is how I learn and my brain works!

This is a common situation, especially among students. They input data and receive an output without truly comprehending how that output is derived. From an educational standpoint, grasping this aspect is crucial. It's akin to returning to the fundamentals, like manually calculating gas exchange data from Douglas bags.

This process involves investing time in the data, enabling the identification of errors and problems before making decisions based on the data.

Whether dealing with data collected in the field or in a laboratory, comprehending the underlying principles helps determine the validity of the initial values. It aids in recognizing whether an athlete's testing was conducted too aggressively or conservatively.

The scope of this discussion revolves around the inverse calculation of time. The same methodology can be applied to calculate CP via the work time, and if you possess three or more data points, you can utilise the same approach to perform the calculation.

Error and Confidence:

An aspect frequently overlooked is the consideration of error and confidence intervals. Commonly, a 95% confidence level is employed. This percentage signifies that we hold 95% confidence that our value resides within the specified range.

Error pertains to the anticipated level of deviation. Our goal is to minimise this divergence as much as we can. Nevertheless, when utilising only two data points for critical power calculation, the aforementioned assessment cannot be conducted. In this scenario, the R^2 value will invariably be 1.

In situations where no error is present to evaluate, the rationale for incorporating additional tests becomes apparent, this is where knowing what the 'data' may look like.

As you can see below the R^2 value is poor, it's evident that the middle data point does not fit the other two. It may be a case that the other two are underpredicted values. I would suggest the latter if you are happy with the test conditions of the 12 and 3 minutes (left and far right respectively). As with most things it depends.

If you put these values in a calculated you would get 383 W for CP and 23.5 kJ for W'. At face value, this may 'look' normal.

Correlation graph of CP and W" R=0.79 Cp 383 E W and W' 23.5 kJ
Poor Correlation for CP

From a research vantage point, the aim is to ensure confidence in the influence of manipulations or prescriptions on the measured values. It's desirable to minimise error values and narrow confidence intervals. Without such refinement, any observed change might be attributed to noise or bias, presenting either a type 1 or type 2 error based on the study design.

So what?

This isn't an article going into the nitty gritty of stats, there are many areas covering this, but more of an appreciation of what is going on is key to understanding it.

''All models are wrong, some are just less wrong'' George Box

Critical Power

In the upcoming times, I have plans to compose an article elaborating on the utilisation of CP and W', encompassing not only their applications but also delving into the challenges and limitations they present.

It's important to note that my intention here isn't to advocate that CP is the ultimate or sole approach to be adopted. Instead, I find CP to be incredibly valuable in certain contexts, an opinion rooted in my own research, which extensively employs this framework. However, it's equally crucial to recognise the boundaries within which CP operates.

There exist alternative models that hold more favorability under certain circumstances. Consider it another tool in your toolbox.

If W' is 20 kJ it suggest you can do 20,000 W... Some of the limitations are obvious.

so don't take it all too seriously, here is an example of me not taking it seriously.

Alex Welburn - Looking Seriious


If you are testing athletes, please take into consideration some of the below points to help you decide/direct why you are doing it and things to consider when you do them

'Test in the environment you are going to train on, if testing in the field'

Frequently, athletes seek the highest possible numbers - all of us do, that is the aim, right? Those who state otherwise are likely not telling the truth. But if you will consistently be training in a different environment to where you will be training, that may not best reflect that environment! So, as with most things, context is key!

Perform tests where you'll be training the most. Power output will vary between environments, particularly uphill and on the flat and indoor vs outdoor.

It isn't uncommon to see a greater PO while climbing, if you go away on a camp and hit a new 20-40 minute power and start to use that for your zones for when you come back, there is a good chance they may be off. It isn't always the case but consider your environment.

If you spend a lot of time on the turbo, then while it may not be pleasant, it is advisable to test here!

'Is the information gathered, specific to the athlete and their aims?'

Power meters are a fantastic tool, but don't become a slave to the data! Yes, I'm a physiologist and researcher who revels in measuring everything, but don't lose sight of the athlete! Power meters are there to amplify your comprehension of strengths and weaknesses in line with your goals. Just because a piece of software states X doesn't imply that you must build everything around it.

Data-driven models rely on solid data, yet remember the broader perspective!

Anyway, have a play with the file below, If you use it anywhere, please reference it appropriately, these articles are here to be useful and informative.

Anyway, there are more articles in the pipeline! And if you want to calculate critical power, see how the maths is done then download the file below.

Here is the download file

Calculate Critical Power locked
Download XLSX • 211KB

Here you can calculate the 3 and 12 method.

3, 5, and 12 minute method to look at error and finally you can have the custom duration and power outputs to use as well.


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