Cylindrical to Cartesian Coordinates

Convert cylindrical coordinates (rho, phi, z) into Cartesian coordinates (x, y, z). Supports degrees and radians and shows an xy-plane projection.

Input

Enter cylindrical coordinates (rho, phi, z) to convert them into Cartesian coordinates (x, y, z). The azimuth phi can be switched between degrees and radians.

Radial distance rho

Azimuth phi

Height z

Result

Cartesian coordinates

(x=2.5, y=4.330127, z=2)

x coordinate

2.5

y coordinate

4.330127

z coordinate

Azimuth (radians)

1.047198 rad

Azimuth (degrees)

60°

x = rho cos phi, y = rho sin phi, z = z. The height z is unchanged by the conversion.

How it works

The conversion from cylindrical (rho, phi, z) to Cartesian (x, y, z) uses x = rho cos phi, y = rho sin phi, and z = z.
Here rho is the radial distance from the origin in the xy plane, phi is the azimuth angle measured from the positive x axis, and z is the height along the cylinder axis.
The z component is unchanged by the conversion. The cylindrical z becomes the Cartesian z directly.
The azimuth phi can be entered in degrees or radians. Internally it is converted to radians before computing. To convert degrees to radians, multiply by pi divided by 180.
When rho is 0 the point lies on the z axis, so both x and y become 0.

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