Frequently Asked Questions
How do you convert (x, y) to polar coordinates?
r is the square root of x squared plus y squared. theta is atan2(y, x), measured from the positive x-axis.
Why atan2 instead of arctan?
atan2 takes both x and y as arguments so it can return the correct angle in any of the four quadrants. Plain arctan only gives an angle in the right half-plane.
Are polar coordinates unique?
Not entirely. Adding a full turn to theta gives the same point. By convention r is non-negative and theta is taken in the range minus pi to pi or zero to two pi.
What is the range of the angle in polar coordinates?
Using atan2(y, x), the angle θ runs from −π to π (−180° to 180°), which picks the correct quadrant automatically. You can add 2π to any negative result if you prefer the 0 to 2π convention.
How do you convert polar coordinates back to Cartesian?
Use x = r·cos θ and y = r·sin θ. Converting to polar and back returns the original point, which is a good way to check your work.
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