Available forms

Forward and inverse, spherical and ellipsoidal

Defined area






Input type

Geodetic coordinates

Output type

Projected coordinates


The HEALPix projection is area preserving and can be used with a spherical and ellipsoidal model. It was initially developed for mapping cosmic background microwave radiation. The image below is the graphical representation of the mapping and consists of eight isomorphic triangular interrupted map graticules. The north and south contains four in which straight meridians converge polewards to a point and unequally spaced horizontal parallels. HEALPix provides a mapping in which points of equal latitude and equally spaced longitude are mapped to points of equal latitude and equally spaced longitude with the module of the polar interruptions.


To run a forward HEALPix projection on a unit sphere model, use the following command:

proj +proj=healpix +lon_0=0 +a=1 -E <<EOF
0 0
# output
0 0 0.00 0.00



All parameters for the projection are optional.


New in version 6.3.0.

Rotation of the HEALPix map in degrees. A positive value results in a clockwise rotation around (x_0, y_0) in the cartesian / projected coordinate space.

Defaults to 0.0.


Longitude of projection center.

Defaults to 0.0.


The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lon_0=1.570796r

See Projection Units for more information.


False easting.

Defaults to 0.0.


False northing.

Defaults to 0.0.


The name of a built-in ellipsoid definition.

See Ellipsoids for more information, or execute proj -le for a list of built-in ellipsoid names.

Defaults to "GRS80".


Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.

Further reading

  1. NASA

  2. Wikipedia