How to find the central angle with radius and area?

The area of an entire circle = PI*radius^2
area of a sector = (central angle / 360) * PI * radius^2

Therefore,
central angle / 360  = (sector area) / (PI * radius^2)

central angle = (360 * sector area) / (PI * radius^2)
Source:
http://www.1728.org/radians.htm