Spherical to Cylindrical Coordinates Converter

What are Spherical Coordinates?

Spherical coordinates (r, θ, φ) describe a point in three-dimensional space. Here, r is the radial distance from the origin, θ is the azimuthal angle in the xy-plane from the positive x-axis, and φ is the polar angle from the positive z-axis.

What are Cylindrical Coordinates?

Cylindrical coordinates (ρ, φ, z) also describe a point in three-dimensional space. Here, ρ is the radial distance in the xy-plane, φ is the azimuthal angle in the xy-plane from the positive x-axis, and z is the vertical distance from the xy-plane.

How to Use the Calculator

1. Enter the spherical coordinates (r, θ, φ) in the input fields. Ensure that θ and φ are in degrees.
2. Click the "Calculate" button to convert the spherical coordinates to cylindrical coordinates.
3. The resulting cylindrical coordinates (ρ, φ, z) will be displayed in the result fields. Note that φ in cylindrical coordinates is the same as in spherical coordinates, while ρ and z are calculated based on r and φ.

Example

Suppose you have a point with spherical coordinates (r = 5, θ = 45°, φ = 30°). The corresponding cylindrical coordinates would be:

• ρ = 5 * sin(30°) = 5 * 0.5 = 2.5
• φ = 45°
• z = 5 * cos(30°) = 5 * 0.866 = 4.33

So, the cylindrical coordinates are (ρ = 2.5, φ = 45°, z = 4.33).