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Cylindrical Coordinates Calculator.

Convert Cartesian x, y, z coordinates to cylindrical coordinates.

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Result: radius: 5.000000 · angleDegrees: 53.130102 · height: 2.000000

Result

radius: 5.000000 · angleDegrees: 53.130102 · height: 2.000000

Use Cases

Physics and Engineering Problems

Simplify calculations involving cylindrical symmetry, such as electric fields around wires, fluid flow in pipes, or stress analysis in cylindrical objects.

Example: Convert the position of a point on a cylinder's surface to cylindrical coordinates for easier integration.

3D Modeling and Computer Graphics

Convert point coordinates to cylindrical form to apply rotations or scaling around an axis, or to map textures onto cylindrical surfaces.

Example: Transform a 3D model's vertex positions to cylindrical coordinates for procedural generation.

Frequently Asked Questions

What are cylindrical coordinates?
Cylindrical coordinates are a 3D coordinate system that describes a point by its distance from the z-axis (r), the angle (θ) in the xy-plane from the positive x-axis, and the height (z) along the z-axis. They are useful for objects with circular symmetry.
How do I convert Cartesian coordinates to cylindrical coordinates?
To convert (x, y, z) to cylindrical (r, θ, z): r = √(x² + y²), θ = atan2(y, x) (in radians or degrees), and z remains the same. Our calculator does this instantly.
What is the range of θ in cylindrical coordinates?
The angle θ is typically measured in radians or degrees, ranging from 0 to 2π (or 0° to 360°). Our calculator outputs θ in radians by default, but you can convert to degrees if needed.

Tips & Common Mistakes

Tips

  • Ensure your x and y values are correct; r is always non-negative, so if you get a negative r, double-check your input.
  • Remember that θ is measured from the positive x-axis, so points in different quadrants will have different θ values.
  • If you need degrees, multiply the radian result by 180/π. Our calculator gives radians, but you can convert easily.
  • For points on the z-axis (x=0, y=0), θ is undefined; our calculator may output 0 or handle it as a special case.

Common Mistakes to Avoid

  • Forgetting to take the square root when calculating r: r = √(x² + y²), not x² + y².
  • Using the wrong quadrant for θ: use atan2(y, x) to get the correct angle, not just atan(y/x) which only works for the first quadrant.
  • Confusing the order: cylindrical coordinates are (r, θ, z), not (θ, r, z).

Last updated: August 13, 2026