# Wagner VII

## Description

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.

## Projection properties

The subsections below describe the Wagner VII projection properties.

### Graticule

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.

### Distortion

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.

## Usage

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

## Limitations

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

## Parameters

Wagner VII parameters are as follows:

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

## Sources

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.