Cylindrical Coordinates Calculator

Cylindrical Coordinates Calculator

Convert between Cartesian and cylindrical coordinates in 3D space.

Last updated: June 2026 | By Patchworkr Team

Result

Enter x, y, and z as real numbers.

What are Cylindrical Coordinates?

Cylindrical coordinates describe a point with rho, phi, and z.

rho = sqrt(x^2 + y^2)
phi = atan2(y, x)
x = rho cos(phi), y = rho sin(phi), z = z

Rho is always non-negative; phi wraps around the z-axis.

How to Use

1. Choose the conversion direction.

2. Enter the coordinates in a consistent angle unit.

3. Read the live conversion and angle normalization.

Worked Example

For Cartesian point (5, 5, 10):

rho = sqrt(5^2 + 5^2) = 7.071...

phi = 45 deg

FAQ

Can rho be negative?

No. Rho is a radial distance from the z-axis.

Can z be negative?

Yes. Z can be any real number.

Why normalize phi?

So the angle stays in a standard wraparound range.

Is this the same as polar coordinates?

Polar coordinates are the 2D version of the same idea.

Related Tools