i need to calculate the flux of a a field going threw a cirlce on the x-y plane

when the circle point -z direction

$\displaystyle \int \int F ndS=\int \int F(-\frac{dz}{dx}i-\frac{dz}{dy}j-k)dA$

in this formula i my formula of the area is not z dependant

what to writhe instead of z in this formula

?