Cartesian To Cylindrical Converter
Convert 3D Cartesian coordinates to cylindrical radius, azimuth and height.
Open toolCartesian To Spherical Converter
Convert a Cartesian 3D point to radius, azimuth and a selected spherical angle convention. Provide X, Y, Z to compute results directly in your browser. Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)). Zero point is rejected; Z-axis azimuth convention 0 is stated. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
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Enter the inputs, then select Calculate.
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How the Cartesian To Spherical Converter Works & Core Formula
The Cartesian To Spherical Converter evaluates X, Y, Z in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Convert a Cartesian 3D point to radius, azimuth and a selected spherical angle convention.
Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)). Zero point is rejected; Z-axis azimuth convention 0 is stated. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
Cartesian To Spherical Converter Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Cartesian To Spherical Converter below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: X | 1 | Range: -1000000000.0 to 1000000000.0 | Required workspace parameter |
| Input: Y | 1 | Range: -1000000000.0 to 1000000000.0 | Required workspace parameter |
| Input: Z | 1 | Range: -1000000000.0 to 1000000000.0 | Required workspace parameter |
| Input: Second spherical angle convention | (User supplied) | Options: Polar inclination from +Z, Elevation from XY plane | Required workspace parameter |
| Worked Case 1: Baseline run (X = 1) | Preloaded / test values | Convert a Cartesian 3D point to radius, azimuth and a selected spherical angle convention | X = 1; Y = 1; Z = 1; Second spherical angle convention = Polar inclination from +Z; Angle output = Degrees. The displayed output is Radius: 1.73205080757 Azimuth: 45 deg Polar inclination: 54.7356103172 deg Azimuth convention: Normalized to [0, 360 deg) or [0, 2*pi rad). |
| Worked Case 2: Comparison scenario (cartesian to spherical conversion) | Preloaded / test values | Convert a Cartesian 3D point to radius, azimuth and a selected spherical angle convention | X = 0; Y = 1; Z = 0; Second spherical angle convention = Elevation from XY plane; Angle output = Radians. The displayed output is Radius: 1 Azimuth: 1.57079632679 rad Elevation: 0 rad Azimuth convention: Normalized to [0, 360 deg) or [0, 2*pi rad). |
Step-by-Step Guide to Using the Cartesian To Spherical Converter
Follow these three steps to configure X, Y, Z, verify unit and boundary rules, and export your Cartesian To Spherical Converter output.
Input and settings
Complete the other inputs
Set y, z, second spherical angle convention, angle output. Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)).
Tool result
Calculate and read the output
Select Calculate to see the radius, azimuth and selected spherical angle. Copy result copies this text; Download saves it as a TXT file.
Review the details
Practical Worked Examples for Cartesian To Spherical Converter
These concrete scenarios illustrate how the Cartesian To Spherical Converter processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (X = 1)
X = 1; Y = 1; Z = 1; Second spherical angle convention = Polar inclination from +Z; Angle output = Degrees. The displayed output is Radius: 1.73205080757 Azimuth: 45 deg Polar inclination: 54.7356103172 deg Azimuth convention: Normalized to [0, 360 deg) or [0, 2*pi rad).
Comparison scenario (cartesian to spherical conversion)
X = 0; Y = 1; Z = 0; Second spherical angle convention = Elevation from XY plane; Angle output = Radians. The displayed output is Radius: 1 Azimuth: 1.57079632679 rad Elevation: 0 rad Azimuth convention: Normalized to [0, 360 deg) or [0, 2*pi rad).
Boundary & unit check (Cartesian To Spherical Converter)
When solving for 'cartesian to spherical converter', verify that X, Y, Z use consistent units and stay within the documented scope: Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)). Zero point is rejected; Z-axis azimuth convention 0 is stated. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
How to Read and Verify the Cartesian To Spherical Converter Output
The output panel reports the exact result derived from X, Y, Z alongside any unit or formatting notes.
The result is the radius, azimuth and selected spherical angle. Express a point using inclination or elevation as explicitly selected.
The angle conventions differ, and the zero point has no spherical direction.
Numerical output shows up to 12 significant digits. Floating-point arithmetic and display rounding can affect the last digits.
- Example input
- X = 1; Y = 1; Z = 1; Second spherical angle convention = Polar inclination from +Z; Angle output = Degrees
- Example output
- Radius: 1.73205080757 Azimuth: 45 deg Polar inclination: 54.7356103172 deg Azimuth convention: Normalized to [0, 360 deg) or [0, 2*pi rad)
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Cartesian To Spherical Converter output.
Operational scope: Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)). Zero point is rejected; Z-axis azimuth convention 0 is stated. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Cartesian To Spherical Converter
Answers about using Cartesian To Spherical Converter and understanding its results.
What formula or rule does the Cartesian To Spherical Converter use?
The Cartesian To Spherical Converter applies the rule: Convert a Cartesian 3D point to radius, azimuth and a selected spherical angle convention. Enter X, Y, Z into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Cartesian To Spherical Converter?
Yes. Provide X, Y, Z using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Cartesian To Spherical Converter?
Azimuth atan2(y,x) normalized [0,2*pi); inclination atan2(hypot(x,y),z), elevation atan2(z,hypot(x,y)). Zero point is rejected; Z-axis azimuth convention 0 is stated. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Cartesian To Spherical Converter free and does it keep my inputs private?
Yes. All calculations for the Cartesian To Spherical Converter execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
Get the radius, azimuth and selected spherical angle
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