Nabla in cylindrical and spherical coordinates: Meaning (information, definition, explanation, facts)

This is a list of some vector calculus formulae of general use in working with standard coordinate systems.

Table with the del or nabla in cylindrical and spherical coordinates

Operation	Cartesian coordinates (x,y,z)	Cylindrical coordinates (ρ,φ,z)	Spherical coordinates (r,θ,φ)
Definition of coordinates
Non-trivial calculation rules: (Laplacian) Lagrange's formula for the cross product:

• Note: the spherical coordinates would have been more natural if θ had been defined as the angle with the X-Y-plane.