Maths & numbers
Cartesian & spherical coordinates
Translate 3D Cartesian coordinates and radius/azimuth/polar-angle coordinates.
A clear answer. Here’s how.
Uses x=r sin(θ) cos(φ), y=r sin(θ) sin(φ), z=r cos(θ), with θ the polar angle from +z and φ the azimuth from +x toward +y. Returns azimuth in [0°,360°) and polar angle in [0°,180°]. Reports the horizontal/cylindrical radius too. At the origin both angles are undefined; on the z-axis azimuth is undefined. All Cartesian lengths and radii share one unit.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Input coordinates
- Cartesian x, y, z
- X
- 1
- Y
- 1
- Z
- 1
Example result
- Cartesian x
- 1
- Cartesian y
- 1
- Cartesian z
- 1
- Spherical radius
- 1.73205080757
- Horizontal / cylindrical radius
- 1.41421356237
- Azimuth from +x
- 45 °
- Polar angle from +z
- 54.7356103172 °