Cylindrical Coordinates
Convert between cylindrical and Cartesian coordinates with instant radial distance, azimuthal angle, and height calculations. Free online 3D coordinate converter for math and engineering.
About This Calculator
This cylindrical coordinates calculator converts a Cartesian x-coordinate to the radial distance ρ in the cylindrical coordinate system using the formula ρ = sqrt(x^2 + x^2) (for points on the line y = x). Cylindrical coordinates (ρ, φ, z) extend polar coordinates with a height component, making them ideal for problems with rotational symmetry in physics, engineering, and 3D graphics. Enter your x value to find the radial distance from the z-axis.
Frequently Asked Questions
What are cylindrical coordinates?
Cylindrical coordinates (ρ, φ, z) are a 3D coordinate system that extends polar coordinates by adding a vertical height component. ρ is the radial distance from the z-axis, φ is the azimuthal angle in the xy-plane measured from the x-axis, and z is the height above the xy-plane.
How do you convert between cylindrical and Cartesian coordinates?
To convert from cylindrical (ρ, φ, z) to Cartesian (x, y, z): x = ρ cos φ, y = ρ sin φ, z = z. To convert from Cartesian to cylindrical: ρ = sqrt(x^2 + y^2), φ = arctan(y/x), z = z. Our calculator handles these conversions instantly.
When should I use cylindrical coordinates?
Cylindrical coordinates are ideal for problems with cylindrical symmetry, such as calculating electric fields around wires, fluid flow in pipes, heat transfer in cylindrical objects, and 3D graphics rendering. They simplify equations where the system is symmetric about an axis.
What is the difference between cylindrical and spherical coordinates?
Cylindrical coordinates (ρ, φ, z) use radial distance from a vertical axis, an azimuthal angle, and a height. Spherical coordinates (r, theta, φ) use radial distance from the origin, a polar angle from the vertical axis, and an azimuthal angle. Cylindrical is best for axisymmetric problems like cylinders and pipes.
Is this cylindrical coordinates calculator free?
Yes, all calculators on Calculy are completely free to use. There are no hidden charges, subscriptions, or usage limits. You can convert between coordinate systems as many times as you need.