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automate calculating arc length?

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I'm working on writing a script for a viewshed model that will calculate the output of a viewshed in degrees. I'm basing this off of previous research that essentially buffers an observation point by a certain distance (i.e 1 mile) then sums the arc length(s) of visible areas within that 1 mile radius (see here for and example, page 14). The usual formula to determine this output has been

(sum of visible arc length/total circumference of the buffer)*360.

Sticking with my 1 mile example this formula would look like (sum of visible arc lengths/6.28miles)*360. I need a way to automate arc length calculations for this to work, but the only measuring tool that I'm aware of in ArcMap is the distance tool which in manual. Any thoughts on how to make this work?

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