The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.


Home Coordinate Systems 3D Conversion of 3D Coordinate Systems
See also: Conversion between Polar and Cartesian Coordinates, Three-dimensional Cartesian Coordinate System, Cylindrical Coordinate System, Spherical Coordinate System 

Conversion between 3D Coordinate Systems

Conversion from cartesian to cylinrical coordinates:

Cartesian [x, y, z] Cylindrical [r, j, z']

 
j = arctan(y/x) for x > 0
j = p/2 for x = 0 and y > 0
j = p + arctan(y/x)  for x < 0
j = 3p/2 for x = 0 and y < 0
z' = z  

Conversion from cylindrical to cartesian coordinates:

Cylindrical [r, j, z'] Cartesian [x, y, z]

x = rcos j
y = rsin j
z = z'

Conversion from spherical to cartesian coordinates:

Spherical [r, q, j] Cartesian [x, y, z]

x = rsin qcos j
y = rsin qsin j
z = rcos q

Conversion from cartesian to spherical coordinates:

Cartesian [x, y, z] Spherical [r, q, j]



Conversion from spherical to cylindrical coordinates:

Spherical [r, q, j] Cylindrical [r, j', z']

r = rsin q
j' = j
z' = rcos q

Conversion from cylindrical to spherical coordinates:

Cylindrical [r, j, z] Spherical [r, q, j']


q = arctan(r/z)
j' = j

Last Update: 2007-Sep-03