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)

Convert coordinates

x Cartesian

y Cartesian

Angle unit

Result (Polar)

r: –

θ (raw): –

θ (normalized): –

Raw angle is the direct output of atan2, which may be negative. Normalized angle is shifted into [0, 360°) or [0, 2π) depending on unit.

Need the opposite? Try Polar to Cartesian.

Formulas used

Given a point in the plane as (x, y), the polar coordinates (r, θ) are:

r = √(x² + y²)
θ = atan2(y, x)

atan2(y, x) is preferred over arctan(y/x) because it returns the correct angle for all quadrants and for x = 0.

Degrees vs radians

If you choose degrees, the tool converts the raw angle from radians to degrees via:

degrees = radians × 180 / π

Normalized angle

The angle from atan2 can be negative (for points below the x-axis). To make it more readable, we normalize it:

θ_norm = θ (if θ ≥ 0)
θ_norm = θ + 2π (if θ < 0)

For degrees we do the same but with 360°.

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.