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Spherical Coordinates Calculator.

Convert radius, polar angle, and azimuth to Cartesian coordinates.

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01

Set your values

Results update as you type.

Result: x: 2.50000000 · y: 2.50000000 · z: 3.53553391

Result

x: 2.50000000 · y: 2.50000000 · z: 3.53553391

Use Cases

Physics and Engineering Problems

Convert spherical coordinates to Cartesian for problems involving electric fields, gravitational fields, or 3D motion where spherical symmetry is present.

Example: Given r=5, polar=45°, azimuth=30°, find the Cartesian coordinates.

3D Graphics and Game Development

When working with 3D models or scenes, convert spherical coordinates to Cartesian to position objects or cameras accurately.

Example: Place a camera at r=10, polar=60°, azimuth=90°.

Frequently Asked Questions

What are spherical coordinates?
Spherical coordinates describe a point in 3D space using three values: radius (distance from origin), polar angle (angle from positive z-axis, in degrees), and azimuth angle (angle in xy-plane from positive x-axis, in degrees).
How do I convert spherical to Cartesian coordinates?
The calculator uses the standard formulas: x = r * sin(polar) * cos(azimuth), y = r * sin(polar) * sin(azimuth), z = r * cos(polar). Enter radius, polar angle, and azimuth angle in degrees, and it computes x, y, z.
What units are used for the angles?
Both polar and azimuth angles are entered in degrees. The calculator converts them to radians internally for the trigonometric calculations.

Tips & Common Mistakes

Tips

  • Ensure the radius is non-negative; negative radius is not physically meaningful in standard spherical coordinates.
  • Polar angle (θ) should be between 0° and 180° (0 to π radians) to represent all points uniquely.
  • Azimuth angle (φ) can be any angle; the calculator handles values outside 0-360° by using periodic properties.
  • Double-check your angle units: this calculator expects degrees, not radians.

Common Mistakes to Avoid

  • Entering angles in radians instead of degrees, leading to incorrect results.
  • Using a negative radius, which is not standard and can produce unexpected coordinates.
  • Confusing the polar angle (from z-axis) with the azimuth angle (in xy-plane).

Last updated: August 13, 2026