Polar Coordinates Calculator

Polar Coordinates Calculator

Convert between Cartesian and polar coordinates in the plane.

Last updated: June 2026 | By Patchworkr Team

Result

Enter x and y as real numbers.

What are Polar Coordinates?

Polar coordinates describe a point by radius r and angle theta.

r = sqrt(x^2 + y^2)
theta = atan2(y, x)
x = r cos(theta), y = r sin(theta)

The calculator normalizes the angle when converting from Cartesian coordinates.

How to Use

1. Choose the conversion direction.

2. Pick the angle unit if you are converting from polar coordinates.

3. Enter the values and read the live result.

Worked Example

For Cartesian point (3, 4):

r = sqrt(3^2 + 4^2) = 5

theta = atan2(4, 3) = 53.130102 deg

FAQ

Can r be negative?

No. Radius is a distance and must be non-negative.

Can theta wrap around?

Yes. Angles are periodic, so the calculator normalizes them.

What if the point is at the origin?

Then r = 0 and the angle is effectively arbitrary.

Is this different from cylindrical coordinates?

Yes. Polar is the 2D version; cylindrical adds z.

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