vector - Trying to calculate the slope of a plane from a normal -

i have set of 3d normal vectors points on 3d mesh, , need calculate slope of area below each of them. have no idea how this. don't need x or y slope, need total incline of point in question (although fair, don't know how derive total slope x , y slope individually, part of problem). did see this article, couldn't make heads or tails of it... vectors outward-facing. if can explain 1 me, i'd grateful.

if have normal vector, you're there. need angle (look dot product) between normal , vertical line (what vertical means depends on application).

if your normal vectors normalized (have length 1) , vertical (0 0 1), cosine of slope angle z coordinate of normal vector.

to demonstrate this: take pen , let stand on table. table's normal vector. angle between vector , vertical line zero, table has no slope @ all. if tilt table amount, angle between normal , vertical line increase same amount.