Do you mean the angle between the 3d vector and the y-axis (vertical vector)?
If so a simple playing around with the dot product and arccos will do it:
a.b = |a||b|cos(Theta)
where a is your unit 3d normal, b is the unit normal pointing up (0,1,0) and |a| is the magnitude of a (ie 1) and same goes for |b|.
So arccos(a.b)=Theta.
Although I'm not sure that is what you are after.
If so a simple playing around with the dot product and arccos will do it:
a.b = |a||b|cos(Theta)
where a is your unit 3d normal, b is the unit normal pointing up (0,1,0) and |a| is the magnitude of a (ie 1) and same goes for |b|.
So arccos(a.b)=Theta.
Although I'm not sure that is what you are after.