Spherical to Cylindrical Converter

Convert spherical coordinates (r, θ, φ) into cylindrical coordinates (ρ, φ, z). Computes ρ = r sinθ and z = r cosθ instantly, with angles shown in degrees and radians.

Input

Enter spherical coordinates (r, θ, φ) to convert them into cylindrical coordinates (ρ, φ, z). Here θ is the polar angle from the z axis and φ is the azimuthal angle. Enter angles in degrees.

Radius r

Polar angle θ (deg)

Azimuth φ (deg)

Result

Cylindrical (ρ, φ, z)

ρ = 4.330127, φ = 30°, z = 2.5

Radial ρ

4.330127

Azimuth φ

30°

Height z

2.5

Azimuth φ (rad)

0.523599 rad

ρ = r sinθ and z = r cosθ. The azimuthal angle φ is carried over unchanged from the spherical input.

How it works

Converts spherical coordinates (r, θ, φ) into cylindrical coordinates (ρ, φ, z). Here r is the distance from the origin, θ is the polar angle measured from the positive z axis, and φ is the azimuthal angle in the xy plane.
The cylindrical radial distance is ρ = r sinθ and the height is z = r cosθ. The azimuthal angle φ is carried over unchanged from the spherical input.
Angles θ and φ are entered in degrees. They are converted to radians for the calculation, and results are reported in both degrees and radians.
When θ is 0 degrees the point lies on the z axis so ρ is 0, and when θ is 90 degrees the point lies in the xy plane so z is 0.

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