Spherical Coordinates Calculator
Use the Spherical Coordinates Calculator for a transparent, instant calculation with validated inputs and cited sources. For a query such as “spherical coordinates”, enter the matching values and units below and review the stated assumptions.
How to use this calculator
Enter the requested values and units.
Review the assumptions and any warnings shown with the result.
Use the result together with the cited source and your real-world requirements.
Formula
Radius = √(x² + y² + z²), azimuth = atan2(y,x), and polar angle = arccos(z/r); angular coordinates are undefined at the origin.
Worked example
Worked example: Inputs: x: 1; y: 1; z: 1. Outputs: Radius: 1.7320508076; Azimuth: 45 °; Polar angle: 54.7356103172 °.
Assumptions and limits
- The result depends on the values, units, and assumptions entered. It does not infer missing context.
Sources
- OpenStax, Rice University: Precalculus 2eReference material reviewed for the stated method, units, or domain. Confirm that its scope matches your use case. Reviewed 2026-08-14.
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Verification
How this calculator is checked
Trust comes from reproducible evidence, not model confidence. You can inspect the formula, assumptions, worked example, and cited sources on this page.
- Versioned calculationFormula logic is kept separate from the interface and covered by automated registry and behavior checks.
- Cited evidenceSources linked for independent checking: 1.
- Transparent AI useAI may assist drafting or adversarial review. Agreement between models is not proof, and no human expert review is claimed unless a named reviewer is shown.
Frequently asked questions
How does the Spherical Coordinates Calculator work?
Radius = √(x² + y² + z²), azimuth = atan2(y,x), and polar angle = arccos(z/r); angular coordinates are undefined at the origin.
What should I enter?
x, y, z
What should I verify?
Review the assumptions and any warnings shown with the result. The result depends on the values, units, and assumptions entered. It does not infer missing context.
Last updated 2026-08-25 · math-spherical-coordinates-v1 · opportunity-source-2026-08-24 · Published by YunFanLabs