Rectangular to Polar Converter
Convert rectangular coordinates (x, y) to polar (r, θ), with the angle reported in both degrees and radians using atan2.
How it works
r = √(x² + y²) · θ = atan2(y, x)
Rectangular coordinates locate a point by its horizontal and vertical distances; polar coordinates use distance and angle instead. The distance r is the hypotenuse √(x² + y²), and the angle is atan2(y, x), which places θ in the correct quadrant across the full −180° to 180° range rather than the limited range of plain arctan.
Worked example
For (3, 4): r = √(3² + 4²) = √25 = 5, and θ = atan2(4, 3) ≈ 0.9273 rad ≈ 53.13°. So the polar form is (5, 53.13°).
Sources: Polar coordinate system (Wikipedia)
Frequently asked questions
Why use atan2(y, x) rather than arctan(y/x)?
arctan(y/x) cannot distinguish the quadrant — it gives the same answer for (1, 1) and (−1, −1). atan2 looks at the signs of both x and y and returns the correct angle anywhere in the plane.
What is the angle range?
The principal value from atan2 lies in (−180°, 180°]. Add 360° if you prefer a 0°–360° convention; the point is identical.
What is the polar angle at the origin?
At (0, 0) the radius is 0 and the angle is undefined (any direction works). This calculator returns r = 0 and reports the angle as 0° by convention.
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This calculator is for educational purposes. Double-check important results before acting on them.