1. What is Rectangular to Cylindrical Conversion?

Rectangular (Cartesian) to cylindrical coordinate conversion transforms (x,y,z) coordinates to (ρ,φ,z) coordinates, where ρ is the radial distance, φ is the azimuthal angle, and z remains the same.

2. How Does the Calculator Work?

The calculator uses the following equations:

Where:

• \( \rho \) — Radial distance from z-axis
• \( \phi \) — Azimuthal angle in xy-plane (from positive x-axis)
• \( z \) — Same as rectangular z-coordinate

Note: The atan2 function is used for proper quadrant determination of φ.

3. Applications of Cylindrical Coordinates

Details: Cylindrical coordinates are widely used in physics and engineering, particularly in problems with cylindrical symmetry like fluid flow in pipes, electromagnetic fields around wires, and mechanical systems with rotational symmetry.

4. Using the Calculator

Tips: Enter x, y, and z coordinates in rectangular system. The calculator will output ρ (always positive), φ in both radians and degrees, and z (same as input).

5. Frequently Asked Questions (FAQ)

Q1: What's the range of φ?
A: φ ranges from -π to π radians (-180° to 180°) using atan2 function, which determines the correct quadrant.

Q2: How is this different from polar coordinates?
A: Cylindrical coordinates extend 2D polar coordinates to 3D by adding the z-coordinate.

Q3: When should I use cylindrical coordinates?
A: Use them when dealing with problems that have cylindrical symmetry, like circular pipes, wires, or rotational systems.

Q4: Can ρ be negative?
A: No, ρ is always non-negative as it represents a distance.

Q5: How do I convert back to rectangular coordinates?
A: Use: \( x = \rho\cos\phi \), \( y = \rho\sin\phi \), \( z = z \)