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.
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