Cartesian to Cylindrical Coordinate Converter
This tool converts Cartesian coordinates (x, y, z) to Cylindrical coordinates (ρ, φ, z). Ideal for students, engineers, and professionals dealing with three-dimensional space problems.
Coordinate Converter
Data Source and Methodology
All calculations are based on standard transformation formulas. Consult this source for detailed mathematical grounding. All calculations strictly follow the provided data.
The Formula Explained
The cylindrical coordinate conversion formulas are:
\(\rho = \sqrt{x^2 + y^2}\)
\(\phi = \tan^{-1}(\frac{y}{x})\)
\(z = z\)
Glossary of Terms
- ρ (Rho): The radial distance from the z-axis.
- φ (Phi): The angle in the xy-plane from the positive x-axis.
- z (Z): The height above the xy-plane.
How It Works: A Step-by-Step Example
Given Cartesian coordinates (3, 4, 5), the conversion to cylindrical coordinates is:
- ρ = √(3² + 4²) = 5
- φ = tan⁻¹(4 / 3) ≈ 53.13°
- z = 5
Frequently Asked Questions (FAQ)
What is the cylindrical coordinate system?
The cylindrical coordinate system extends the two-dimensional polar coordinate system to three dimensions by using a height (z) value.
Why use cylindrical coordinates?
Cylindrical coordinates are particularly useful for dealing with problems involving cylinders, spirals, and other geometries where symmetry about an axis is present.
How do I convert from cylindrical to Cartesian coordinates?
Use the formulas \(x = \rho \cos(\phi)\), \(y = \rho \sin(\phi)\), and \(z = z\) to convert from cylindrical to Cartesian coordinates.
Tool developed by Ugo Candido. Content reviewed by the expert team. Last reviewed for accuracy on: October 10, 2023.