How this calculator works
Cartesian coordinates measure perpendicular offsets. Spherical radius measures full distance from the origin, whereas inclination is measured down from the positive z axis. Azimuth turns anticlockwise from positive x when viewed from positive z. A nonnegative radius is required. On the axis, azimuth is omitted because no direction is singled out.
Formula
x = r sin(phi) cos(theta), y = r sin(phi) sin(theta), z = r cos(phi); r = hypot(x, y, z), phi = atan2(hypot(x,y), z).
Worked example
For (0, 0, 2), the spherical radius is 2 and inclination is 0 degrees. The azimuth is undefined. Radius 2, azimuth 0 and inclination 90 degrees gives (2, 0, 0).
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Frequently asked questions
Why use atan2 instead of arctangent?
atan2 uses both coordinate signs to place the angle in the correct quadrant and handles vertical directions.
What happens at the origin?
The radius is zero. Azimuth is undefined and is omitted. Inclination is also omitted at the origin.
Are these latitude and longitude?
No. These are geometric coordinates. Inclination is 90 degrees minus latitude under the usual spherical model.