I was trying to better understand the concept of angular diameter and was hoping for some clarification. Given some object's coordinates in RA and dec, is it possible to find that object's angular diameter in a different unit, such as degrees?
If you only have RA and Dec of a single point as @JamesK's answer supposes you won't have a size.
But if you have the celestial coordinates of several points around its perimeter like a nebula or even a constellation, then yes! you can get an angular size!
Let's say there's a "rectangular" patch that extends from 05h 33m to 05h 37m in RA and from -6. to -5 deg in dec.
Since angles in declination are real angles, it will be 1 degree tall.
4 minutes of RA is also 1 degree if it's on the equator, but we have to multiply by cos(dec) because the lines squeeze together at the top and bottom.
In this case cos(5.5 degrees) is almost 1 (0.995) so we can ignore it. But if your patch of sky is farther from the celestial equator, just don't forget to convert RA to degrees then multiply by cos(dec).
If you have a complicated shape defined by several vertices, like "How many square degrees does constellation X cover?" That will be an excellent new question!