How do I convert Cartesian coordinates to polar coordinates?

Enter the x and y coordinates. The calculator computes the radius r = sqrt(x^2 + y^2) and the angle θ = atan2(y, x). The angle is given in degrees and radians.

What is the range of the angle in polar coordinates?

The angle θ is typically measured from the positive x-axis, ranging from -180° to 180° (or -π to π radians). This calculator uses the atan2 function to determine the correct quadrant.

Can I use negative coordinates?

Yes, negative x and y values are allowed. The calculator will correctly compute the radius (always non-negative) and the angle based on the quadrant.

Math

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Cartesian to Polar Calculator.

Convert Cartesian coordinates to polar radius and angle.

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Set your values

Results update as you type.

02 / ANSWER

x coordinate

y coordinate

Radius

Angle

0.927295rad

Angle

53.130102°

Results update automatically as you type.

Use Cases

Physics and Engineering Problems

Convert vector components to magnitude and direction for force, velocity, or electric field calculations.

Example: A force of (3, 4) N becomes 5 N at 53.13°.

Mathematics and Graphing

Transform rectangular coordinates to polar form for plotting or solving equations in polar coordinates.

Example: Point (1, 1) becomes (√2, 45°).

Frequently Asked Questions

How do I convert Cartesian coordinates to polar coordinates?: Enter the x and y coordinates. The calculator computes the radius r = sqrt(x^2 + y^2) and the angle θ = atan2(y, x). The angle is given in degrees and radians.
What is the range of the angle in polar coordinates?: The angle θ is typically measured from the positive x-axis, ranging from -180° to 180° (or -π to π radians). This calculator uses the atan2 function to determine the correct quadrant.
Can I use negative coordinates?: Yes, negative x and y values are allowed. The calculator will correctly compute the radius (always non-negative) and the angle based on the quadrant.

Tips & Common Mistakes

Tips

Ensure you enter the x and y values in the same unit system (e.g., both in meters).
The radius is always non-negative; if you get a negative, check your inputs.
Use the angle in degrees for navigation or degrees-based problems, and radians for calculus.
Remember that the angle is measured from the positive x-axis, counterclockwise.

Common Mistakes to Avoid

Forgetting that the angle depends on the quadrant; using arctan(y/x) without considering signs can give wrong angles.
Confusing degrees and radians; always check which unit the calculator outputs.
Entering coordinates in the wrong order (x vs y).

Last updated: August 13, 2026