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).
Worked example
The point (3, 4) has radius 5 and azimuth about 53.130102 degrees. Radius 2 at 90 degrees converts to (0, 2), apart from floating-point roundoff.
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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.