TITLE: Get the size of an area defined by 2 overlapping circles
QUESTION [8 upvotes]: I have two circles, like this:

I know the radii of the circles, and I know the X + Y of the center of both circles.
Can I get the size of the area that is black in my picture?

REPLY [6 votes]: This link helped me out in this situation. The MathWorld version is very descriptive, but I think the above link explains what is going on more clearly. I created a javascript function for this purpose, given below in case it is useful to anyone else.
function areaOfIntersection(x0, y0, r0, x1, y1, r1)
{
  var rr0 = r0*r0;
  var rr1 = r1*r1;
  var c = Math.sqrt((x1-x0)*(x1-x0) + (y1-y0)*(y1-y0));
  var phi = (Math.acos((rr0+(c*c)-rr1) / (2*r0*c)))*2;
  var theta = (Math.acos((rr1+(c*c)-rr0) / (2*r1*c)))*2;
  var area1 = 0.5*theta*rr1 - 0.5*rr1*Math.sin(theta);
  var area2 = 0.5*phi*rr0 - 0.5*rr0*Math.sin(phi);
  return area1 + area2;
}