How this calculator works
Cartesian coordinates measure perpendicular offsets. The radial coordinate measures distance from the origin in the xy plane. 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 cos(theta), y = r sin(theta); r = hypot(x, y), theta = atan2(y, x) reduced to [0, 2pi). The z coordinate is unchanged.
Worked example
Cartesian (3, 4, 12) becomes (r, theta, z) = (5, 53.130102 degrees, 12). The height does not contribute to the cylindrical radius.
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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.
Are these latitude and longitude?
No. These are geometric coordinates. Convert geographic locations before applying this flat coordinate system.