Download your PDF
Cartesian to Spherical Coordinates result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Cartesian to Spherical Coordinates — result sheet
Convert one non-origin Cartesian point into radial distance, azimuth, and polar angle with degree outputs.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: rho = sqrt(x^2 + y^2 + z^2); azimuth = atan2(y,x) normalized to 0..360 degrees; polar angle = acos(z/rho) in degrees.
The converter returns the distance from the origin, the angle of the xy projection from positive x, and the angle down from positive z. The origin is rejected because both spherical angles are undefined there.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Cartesian x — length units; x-coordinate in the chosen Cartesian length unit.; minimum -1000000; maximum 1000000
- Cartesian y — length units; y-coordinate in the chosen Cartesian length unit.; minimum -1000000; maximum 1000000
- Cartesian z — length units; z-coordinate in the chosen Cartesian length unit.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Cartesian x | 1 |
| Cartesian y | 1 |
| Cartesian z | 1 |
rho = sqrt(3), azimuth = 45 degrees, and polar angle = acos(1/sqrt(3)) = about 54.7356 degrees.
Assumptions and limits
- The point is expressed in one right-handed Cartesian frame with compatible length units.
- Azimuth is measured counterclockwise from positive x and normalized to 0 through 360 degrees; polar angle is measured from positive z.
- The Cartesian origin is excluded because direction angles have no unique value there.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.