Cylindrical to Spherical Coordinates Converter

Convert cylindrical coordinates (ρ, φ, z) to spherical coordinates (r, θ, φ). Get the radius r, polar angle θ in degrees and radians, and azimuth φ with a cross-section diagram.

Input

Enter cylindrical coordinates (ρ, φ, z) to convert them to spherical coordinates (r, θ, φ). Enter φ in degrees.

Radius ρ (distance from axis)

Azimuth φ (degrees)

Height z

Result

Spherical coordinates (r, θ, φ)

r = 5, θ = 36.869898°, φ = 60°

Radius r

Polar angle θ (degrees)

36.869898°

Polar angle θ (radians)

0.643501 rad

Azimuth φ (degrees)

60°

Azimuth φ (radians)

1.047198 rad

The polar angle θ is measured from the positive z axis and ranges from 0 to 180 degrees, while the azimuth φ carries over unchanged.

How it works

The conversion from cylindrical (ρ, φ, z) to spherical (r, θ, φ) uses r=√(ρ²+z²), θ=atan2(ρ, z), and φ=φ.
The radius r is the straight-line distance from the origin, built from the axial distance ρ and the height z.
The polar angle θ is measured from the positive z axis and ranges from 0 to 180 degrees (0 to π radians).
The azimuth φ carries over unchanged from cylindrical to spherical coordinates.
Enter φ in degrees; it is converted to radians internally for the computation.
Because ρ is a distance from the axis, enter a value of 0 or greater.

Reviews

Tell us what you think of this calculator.