Cartesian to Polar Calculator
Convert Cartesian coordinates (x, y) to polar (r, θ) using r = √(x² + y²) and θ = atan2(y, x), with the angle in degrees.
How it works
r = √(x² + y²) · θ = atan2(y, x), reported in degrees on (−180°, 180°]
Polar coordinates describe a point by its distance from the origin and its direction. The distance r is just the Pythagorean length √(x² + y²). The angle comes from atan2(y, x), the two-argument arctangent, which uses the signs of both x and y to place the angle in the correct quadrant — something plain arctan(y ÷ x) cannot do. The result runs from −180° to 180°; add 360° to a negative angle if you prefer the 0°–360° range.
Worked example
Convert (x = 3, y = 4). The radius is √(3² + 4²) = √25 = 5. The angle is atan2(4, 3) ≈ 53.13°, which sits in the first quadrant since both coordinates are positive. So the polar form is (5, 53.13°), matching the classic 3-4-5 right triangle.
Sources: Polar coordinate system — Wikipedia
Frequently asked questions
Why use atan2 instead of arctan?
Plain arctan(y ÷ x) loses the individual signs of x and y, so it can’t tell the first quadrant from the third, or the second from the fourth. atan2(y, x) keeps both signs and returns the angle in the correct quadrant, from −180° to 180°.
What angle does the origin get?
At (0, 0) the radius is 0 and the direction is undefined, since every angle points to the same origin. By convention the calculator reports 0° there so the result stays a valid number.
How do I turn a negative angle into 0°–360°?
Add 360°. For example −90° becomes 270°. Both describe the same direction; it is purely a choice of range for how you label the angle.
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This calculator is for educational purposes. Double-check important results before acting on them.