Calculator
Enter a Cartesian point and choose the angle convention that fits your chemistry workflow.
Example data table
| Label | x | y | z | r | θ Polar (deg) | φ Azimuth (deg) |
|---|---|---|---|---|---|---|
| Atom A | 1.0000 | 1.0000 | 1.0000 | 1.7321 | 54.7356 | 45.0000 |
| Atom B | 2.0000 | -1.0000 | 3.0000 | 3.7417 | 36.6992 | 333.4349 |
| Atom C | -2.0000 | 2.0000 | 0.5000 | 2.8723 | 79.9750 | 135.0000 |
| Atom D | 0.0000 | -3.0000 | 4.0000 | 5.0000 | 36.8699 | 270.0000 |
Formula used
Radius: r = √(x² + y² + z²)
Azimuth angle: atan2(y, x)
Polar angle: arccos(z / r)
Elevation angle: atan2(z, √(x² + y²))
This calculator first finds the radius from the Cartesian point. It then computes a quadrant-safe azimuth with atan2. The polar angle comes from the z-to-radius ratio. Chemistry and mathematics conventions assign θ and φ differently, so the selector lets you match your preferred notation.
How to use this calculator
- Enter the point label if you want a named result.
- Type the x, y, and z Cartesian coordinates.
- Select degrees or radians for angular output.
- Choose chemistry or mathematics angle notation.
- Set the number of decimal places.
- Add a distance unit label such as angstrom, nm, or pm.
- Click Find spherical coordinates to see the result above the form.
- Use the CSV or PDF buttons to export the current result.
FAQs
1. What are spherical coordinates in this calculator?
They describe a point using radius, polar angle, and azimuth angle. This format is useful for molecular geometry, orbital positioning, and any three-dimensional chemistry coordinate analysis.
2. Which angle convention should I choose?
Choose chemistry or physics convention when you want θ as the polar angle from the positive z-axis. Choose mathematics convention when you want θ as the azimuth in the xy-plane.
3. Why can the azimuth angle be close to 360 degrees?
The calculator normalizes azimuth to a positive full-circle range. A value near 360 degrees means the point lies just below the positive x-axis direction.
4. Can I enter negative x, y, or z values?
Yes. Negative Cartesian values are valid and often important in spatial chemistry problems. The quadrant-aware atan2 function keeps angle results consistent.
5. What happens when the point is at the origin?
The radius becomes zero. At that exact point, direction is undefined, so the calculator reports zero for the angles as a practical placeholder.
6. Why does the calculator use atan2 instead of atan?
atan2 identifies the correct quadrant by reading both x and y. That prevents ambiguous azimuth values and improves reliability for negative coordinates.
7. How is this useful in chemistry?
Spherical coordinates help describe atomic positions, bond directions, electron distributions, and spatial regions around a reference atom or origin in three dimensions.
8. Can I export the calculated results?
Yes. Use the CSV button for spreadsheet-friendly output and the PDF button for a compact report you can save, print, or share.