How do you convert Cartesian to polar coordinates?

Given a point (x, y), compute r = √(x² + y²) for the radius and θ = atan2(y, x) for the angle. Using atan2 ensures the correct quadrant.

What is atan2 and why is it used?

atan2(y, x) is a two-argument arctangent that returns the angle in the correct quadrant, even when x is 0 or negative. It's more robust than just using arctan(y/x).

Can I get the angle in degrees?

Yes. This tool lets you choose degrees or radians. Internally it uses atan2, then converts to the unit you selected.

Cartesian to Polar Converter | Convert (x, y) to (r, θ)

How to Use This Converter

Enter the x and y coordinates for your point, choose degrees or radians, then click Calculate (or let the inputs update automatically). The results panel shows the radius and both the raw and normalized angles so you can plug values into math, engineering, or graphics workflows.

If you already have polar data, use the opposite tool at Polar to Cartesian to go back.

Methodology

We compute the radius as √(x² + y²) and the angle with atan2(y, x) so every quadrant, including x = 0, is handled correctly. The normalized value adds 360° or 2π to any negative angle, matching the selected unit.

atan2 provides the correct quadrant-aware angle even when x = 0.

Normalized θ keeps the range at [0, 360°) or [0, 2π) so the output is always positive.

Everything is formatted with six decimal places for consistency with the legacy converter.

Results use standard math functions and are for reference. If you need production-grade precision, double-check the values in your calculator or programming environment.

Full original guide (expanded)

Convert any 2D point (x, y) into polar form (r, θ). Choose degrees or radians, and get both the raw angle (from atan2) and a normalized 0–360° version.

When x and y are supplied, the converter uses the atan2 function so your angle is correct for every quadrant. The results panel echoes r and two angle representations so you can copy whichever works best.

Need the opposite? Try Polar to Cartesian.

FAQ

Why is my angle negative?

This is normal. Points in Quadrant IV (below the x-axis, x > 0, y < 0) have negative angles if you use atan2. Use the normalized value for a 0–360° representation.

What if x = 0?

atan2 handles it correctly. If x = 0 and y > 0, θ = 90° (π/2). If x = 0 and y < 0, θ = 270° (3π/2) in the normalized form.

What if the point is the origin?

If x = 0 and y = 0, then r = 0 and the angle is technically undefined. Here we set θ = 0 for convenience.

About this tool

Designed to match math, engineering, and programming conventions. Uses atan2, supports both angle units, and shows the normalized angle so you can copy it directly into your work.

Cartesian to Polar Converter

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