Cartesian to Cylindrical Coordinates

Convert Cartesian coordinates (x, y, z) into cylindrical coordinates (ρ, φ, z). Get the radial distance, azimuth in degrees and radians, and height at once.

Input

Enter Cartesian coordinates (x, y, z) to convert them into cylindrical coordinates (ρ, φ, z).

x coordinate

y coordinate

z coordinate

Result

Cylindrical coordinates (ρ, φ, z)

ρ 5, φ 53.130102°, z 5

Radial distance ρ

Azimuth φ (degrees)

53.130102°

Azimuth φ (radians)

0.927295 rad

Azimuth φ (0 to 360 degrees)

53.130102°

Height z

The azimuth φ is from atan2(y, x); in radians it ranges from greater than −π up to π. The height z is preserved.

How it works

The radial distance is the projection onto the xy plane, ρ = √(x² + y²).
The azimuth φ is computed with atan2(y, x), which distinguishes all four quadrants. Its range in radians is greater than −π and up to π.
The height z is preserved unchanged after the conversion.
Degrees are obtained by multiplying φ by 180 divided by π, and a value normalized to the range 0 up to 360 degrees is also shown.
When both x and y are 0 the azimuth is undefined, so it is treated as 0 by convention.

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