The diagram shows a circle contained in a square. What is the simplified ratio of the area of the circle to the area of the square?
[asy]
size(3cm);
path s=(-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle;
fill(s,blue+cyan);
draw(s);
path c=Circle((0,0),1);
fill(c,orange+pink);
draw(c);
[/asy]