Cartesian to Polar Converter
Enter Cartesian coordinates (x, y) to convert them into polar form (r, θ).
What this convert cartesian to polar calculator does
This tool converts a point from Cartesian coordinates, written as (x, y), to polar coordinates, written as (r, θ). It gives you the distance from the origin and the direction angle in both degrees and radians.
It uses atan2(y, x), which is important because it automatically handles the correct quadrant. That means your angle is accurate even when x or y is negative.
Cartesian vs polar coordinates
Cartesian form
Cartesian coordinates locate a point with horizontal and vertical movement:
- x: movement left/right from the origin
- y: movement up/down from the origin
Polar form
Polar coordinates locate the same point using:
- r: radial distance from the origin
- θ: angle measured from the positive x-axis
Formulas used by the calculator
- r = √(x² + y²)
- θ = atan2(y, x) (in radians)
- θ° = θ × 180/π (in degrees)
The calculator also shows normalized angles: 0° to 360° and 0 to 2π radians.
How to use the calculator
- Type the x-coordinate.
- Type the y-coordinate.
- Choose your preferred angle display (degrees or radians).
- Click Calculate Polar Coordinates.
Worked examples
Example 1: (3, 4)
For x = 3 and y = 4:
- r = √(3² + 4²) = √25 = 5
- θ = atan2(4, 3) ≈ 53.13°
So the polar coordinate is approximately (5, 53.13°).
Example 2: (-2, 2)
For x = -2 and y = 2:
- r = √((-2)² + 2²) = √8 ≈ 2.828
- θ = atan2(2, -2) = 135°
The point is in Quadrant II, and the polar form is (2.828, 135°).
Common mistakes to avoid
- Using
tan⁻¹(y/x)alone and forgetting quadrant correction. - Mixing degrees and radians in later equations.
- Forgetting that the origin (0,0) has radius 0 and angle is convention-dependent.
Where this conversion is used
- Complex numbers and phasors in electrical engineering
- Robotics and navigation systems
- Physics problems with circular motion
- Computer graphics and game development
- Signal processing and wave analysis
Quick FAQ
Why is my angle negative?
A negative angle is still valid. It means clockwise rotation from the positive x-axis. The calculator also gives the normalized equivalent in the 0° to 360° range.
Can r ever be negative?
In standard Cartesian-to-polar conversion, r is reported as non-negative. Equivalent representations can be made using a negative r with angle adjustment, but this calculator uses the standard positive radius.
What happens at (0,0)?
Radius is 0. The angle is technically undefined because any direction points to the same location. By convention, many tools show θ as 0.
Final note
If you frequently move between rectangular and rotational systems, this convert cartesian to polar calculator gives you fast and reliable results with the right quadrant handling every time.