Calxsolver
Trigonometry

Cartesian to Polar Coordinates

Enter a point (x, y) in the Cartesian plane. The calculator computes the polar coordinates (r, θ) using r = √(x² + y²) and θ = atan2(y, x), reporting θ in both degrees and radians, normalized to [0°, 360°).

Cartesian to Polar Coordinates

Convert (x, y) to (r, θ), reporting θ in both degrees and radians.

Try:
Answer(r, θ) = (5, 53.1301°) = (5, 0.927295 rad)
  1. Cartesian point(3, 4)
  2. Radiusr = √(x² + y²) = √(9 + 16) = 5
  3. Angleθ = atan2(y, x) = 53.1301° = 0.927295 rad
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Worked examples

Convert (3, 4) to polar coordinates Find the radius and angle of a point given in Cartesian coordinates.

Frequently asked questions

Why atan2 instead of atan?

atan(y/x) loses sign information and is undefined when x = 0. atan2(y, x) returns the correct angle in every quadrant.

What is θ at the origin?

The angle is undefined at (0, 0); the calculator reports it as 0 by convention.

Why is θ normalized to [0°, 360°)?

Both conventions are used in textbooks; the normalized range is the more common one for cartesian-to-polar conversion. Adding 360° gives an equivalent coterminal angle.

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