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I assume by sector you mean the equivalent of a pie or pizza slice you cut out of a whole pie or pizza. You need to know the angle of the sector and the radius (or diameter) of the circle to which it belongs.

The angle at the centre of a circle is 360 degrees and the area of a circle is (pi)r^2, where (pi) is a number a little larger than 3. The area of the sector is in the same proportion to the area of the circle as the sector angle is to 360. So (area of sector)/((pi)r^2)=(angle of the sector)/360. For example, if you divide a circle into 4 equal segments, the area of each segment is (pi)r^2/4 because the angle of each segment is 90 degrees, or a right-angle.

If by sector you mean the piece cut off by a chord, which is just the result of joining two points on the circle's circumference, to find the area you need to know the length of the chord and the diameter of the circle. There's no simple proportion formula for this. The formula is something like r^2(sin^-1(a/r)-(a/r)sqrt(1-(a/r)^2)), where a is half the length of the chord. If, for example, a=r/2, the sector area is r^2((pi)/6-(1/4)sqrt(3)).

 

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