Wagner VII


The Wagner VII or Hammer-Wagner projection is a modification of the Lambert azimuthal equal-area projection. All parallels are convex toward the equator, which gives the projection a unique appearance and relatively low distortion characteristic compared to some equal-area pseudocylindrical projections.

The projection was introduced by Karl Heinrich (Karlheinz) Wagner in 1941. It is available in ArcGIS Pro 1.2 and later and in ArcGIS Desktop 10.4 and later.

An example of the Wagner VII projection
The Wagner VII map projection is shown centered on Greenwich.

Projection properties

The subsections below describe the Wagner VII projection properties.


Wagner VII is a modified azimuthal projection. The meridians, except the central meridian, are curves concave toward the central meridian. The central meridian is a straight line, half the length of the projected equator. All parallels are convex toward the equator. Both parallels and meridians are unequally spaced. The pole lines are curved and also convex toward the equator. They have the same shape as the 65° parallel on the Lambert azimuthal equal-area projection in equatorial aspect. The graticule is symmetric across the equator and the central meridian.


Wagner VII is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are distorted. The distortion is moderate near the center and increases toward the edges. The values are symmetric across the equator and the central meridian.


The Wagner VII projection is appropriate for small-scale mapping, especially for thematic world maps illustrating area characteristics and analysis requiring accurate areas.


For an ellipsoid of revolution, geodetic latitudes are first converted to authalic latitudes and an authalic radius is used for the radius.


Wagner VII parameters are as follows:

  • False Easting
  • False Northing
  • Central Meridian
  • Latitude Of Origin


Wagner, K. H. (1941). Neue Ökumenische Netzentwürfe Für die Kartographische Praxis. In: E. Lehmann, ed. Jahrbuch Der Kartographie 1941. Leipzig: Bibliographisches Institut, p. 176-202.

Wagner, K. H. (1949). Kartographische Netzentwürfe. Leipzig: Bibliographisches Institut.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.