Is the capacity of an airspace sector related to the number of routes it crosses?
Calculating the capacity of an ATC sector is a complex issue, you should not expect to find one single determining factor.

A few obvious factors come to mind:


Lateral extend of the sector (size)
Vertical extend of the sector
Whether or not surveillance is available (RADAR etc.)
The route structure, and whether traffic is forced to follow certain airways or not (free route airspace)
Military areas, their activation frequency and extend
Type of traffic in the sector
Uniformity of traffic in the sector
The actual traffic flow in the sector. Is it mainly an en-route sector where aircraft will enter and leave at the same level, or do a lot of aircraft need to climb/descend within the sector?
ATC staffing. Is the sector manned by a single controller, or by a pair (executive+planner)?
Radio coverage, and whether or not CPDLC is available
Weather - for example, is it an area with frequent thunderstorms?
Runway configurations of any airports covered by the sector, as well as possible noise restrictions


There is no formula that couples all these factors together. In the end, the capacity of an ATC sector is an estimate based on an evaluation of the above (and probably more) factors, experience and trial-and-error. In many cases, it will be an iterative process.