Calculator Input
Plotly Graph
The graph shows the Cartesian point and the line from the origin to that point.
Formula Used
Cartesian coordinates are written as (x, y), while polar coordinates are written as (r, θ).
The radius r is the distance from the origin to the point. The angle θ is measured from the positive x-axis. The atan2 function is preferred because it correctly identifies the quadrant.
How to Use This Calculator
- Enter the x-coordinate of the point.
- Enter the y-coordinate of the point.
- Select whether you want the angle in degrees or radians.
- Choose the number of decimal places for the output.
- Optionally scale the radius if your use case requires it.
- Enable angle normalization to keep degree output between 0 and 360.
- Press Convert Now to view the result above the form.
- Use the export buttons to save the result as CSV or PDF.
Example Data Table
| Cartesian (x, y) | Radius r | Angle θ (degrees) | Angle θ (radians) | Quadrant / Axis |
|---|---|---|---|---|
| (3, 4) | 5.0000 | 53.1301 | 0.9273 | Quadrant I |
| (-3, 4) | 5.0000 | 126.8699 | 2.2143 | Quadrant II |
| (-5, -5) | 7.0711 | -135.0000 | -2.3562 | Quadrant III |
| (6, -2) | 6.3246 | -18.4349 | -0.3218 | Quadrant IV |
| (0, 7) | 7.0000 | 90.0000 | 1.5708 | Positive Y-Axis |
FAQs
1. What does this calculator convert?
This calculator converts Cartesian coordinates, written as (x, y), into polar coordinates, written as (r, θ). It also shows quadrant details, graphs, and exportable results.
2. Why is atan2 used instead of arctan(y/x)?
atan2 uses both x and y values together, so it places the angle in the correct quadrant. A simple arctangent can produce misleading results when x is negative or zero.
3. What is the meaning of radius in polar form?
The radius is the straight-line distance from the origin to the point. It tells you how far the point is from the center of the coordinate plane.
4. Can the angle be shown in degrees and radians?
Yes. You can choose the preferred output unit in the form, and the result area also displays supporting angle values so you can compare both formats easily.
5. What happens if the point is at the origin?
When x and y are both zero, the radius becomes zero. The angle is not uniquely defined there, but the calculator still marks the point as the origin.
6. Why would I normalize the angle?
Normalization is useful when you want degree values shown within a standard 0° to 360° range. It makes graph reading and reporting more consistent.
7. Can students use this for homework checks?
Yes. It is suitable for learning, practice, and verification. The optional worked steps help students understand how radius and angle are calculated from x and y.
8. What file formats can I export?
You can export the computed result as a CSV file for spreadsheet use and as a simple PDF-style text download for easy record keeping.