I've been wondering how to calculate the area of intersection of two overlapping circles in terms of their radii. There's two cases I'm interested in: The easier case: Suppose there are two circles of radius R and r (R > r). The center of the larger circle is at the origin, and the center of the other circle is at (x,y)=(R,0). How can I find the area of the overlap in terms of R and r? I can't think of any clear way to do this by hand. The more complicated case: Do the same except let the center of the smaller circle lie between (R-r,0) < (x,y) < (R+r,0) I've attached a drawing to help show the problem. Thanks for any insight. This isn't for school, so there's no rush or anything. Just curious.