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My understanding is that in ATC, one of the constraints when considering the distribution of flights is the number of aircraft occupying a sector. Each sector can have different capacities.

I have read many academic approaches on how to calculate these capacities, but my doubt is: what is the method used right now, on February the 6th 2017?

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I think January 25th, 2017 is close enough.

For Eurocontrol—

To evaluate sector capacities, the Network Manager uses the Air Traffic Control (ATC) Sector Capacity Analyser (CAPAN) methodology – using a fast-time computer simulation model that calculates the capacity of an ATC sector based on the controllers' workload. CAPAN is used with the Reorganised ATC Mathematical (Model) Simulator (RAMS) simulation engine.

Above quotation answers the question in a general form. The workings of CAPAN are laid out in this PDF, titled Capacity assessment and planning guidance document.

The FAA (US) isn't much different—

... the US and Europe use a comparable methodology to balance demand and capacity.

More on that here (PDF), titled 2015 Comparison of Air Traffic Management-Related Operational Performance: U.S./Europe.

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    $\begingroup$ I appreciate your input, but I am trying to avoid long readings since I just need to get an intuition of how it works. could anyone just gloss over about the fundamentals? Are they setting sector capacities statically, do they weight different factors as weather...?. $\endgroup$
    – A. Fenzry
    Commented Feb 7, 2017 at 7:38

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