Work out cylindrical coordinates instantly with clear inputs, formula shown and shareable results.
Cylindrical coordinates keep the Cartesian z and use polar coordinates in the xy-plane, so x = ρ·cos φ and y = ρ·sin φ. They suit problems with an axis of symmetry, such as pipes and rotating bodies.
Cylindrical to Cartesian
x = ρ·cos φ, y = ρ·sin φ, z = z
Spherical radius
r = √(ρ² + z²)
x ≈ 3, y ≈ 4 and z = 7, giving a spherical radius of √74 ≈ 8.6023253.
Whenever a problem is symmetric about an axis — flow in a pipe, a solenoid's field, or a spinning disc.