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Map Projections
 
Map Projection Pages
 
The following web pages on this web site contain extensive information about map projections from U.S. Geological Survey documents.
 
General Information
 
Map Projections Overview
General overview of map projection concepts. Includes examples.
 
Glossary
Definitions of map projection terms.
 
Longitude and Latitude Overview
How to locate a point on Earth using meridians, parallels, and grids.
 
The Datum and the Earth as an Ellipsoid
Accounting for the Earth not being perfectly round.
 
The rest of this page lists links to specific map projections, listed by types of projections which were categorized by John P. Snyder (see book references at the end of this page). All images on this page are from those books.
Terms Used In This Page:
      Meridian  – Longitude line.
     
Parallel  – Latitude line.
     
Conformal  – Projection on which all angles at each point are preserved.
     
Equal-Area  – Projection on which the areas of all regions are shown in the same proportion to their true areas. Shapes may be greatly distorted.
     
Equidistant  – Projection that maintains constant scale along all great circles from one or two points.

See the Definitions Page
 

 
Cylindrical Map Projections
 
Cylindrical projections are used primarily for complete world maps, or for maps along narrow strips of a great circle arc, such as the Equator, a meridian, or an oblique great circle. In the normal (regular) aspect, meridians and parallels are straight lines.
Cylindrical Regular
Regular
Cylindrical Transverse
Transverse
Cylindrical Oblique
Oblique
 
Plate Carree (Geographic) Plate Carree (Geographic)
This widely used projection simply consists of plotting longitude and latitude points on an evenly spaced X,Y (Cartesian) graph. Meridians and parallels are equally spaced, forming squares.
 
Equirectangular Equirectangular
A modification of the Plate Carree (Geographic) projection, with the meridians spaced closer together, forming rectangles with the parallels instead of squares.
 
Cassini Cassini
The Cassini map projection is the transverse aspect of the Plate Carree projection. Equidistant.
 
Mercator Mercator
The Mercator projection has area distortion, but is the only map projection that shows true compass bearings for navigation. Historically used in combination with the Gnomic. Conformal.
 
Transverse Mercator Transverse Mercator
The transverse aspect of the Mercator projection, used to map quadrangles throughout the world. Conformal.
 
Oblique Mercator Oblique Mercator
The oblique aspect of the Mercator projection, used to map regions having greater extent in an oblique direction, such as Hawaii and the Alaska panhandle. Conformal.
 
Gall Gall
A cylindrical projection used for world maps in British atlases. Looks like the Mercator, but takes up less space on the printed page.
 
Miller Cylindrical Miller Cylindrical
A cylindrical projection used for world maps in American atlases. Similar to the Gall.
 
Cylindrical Equal-Area Cylindrical Equal-Area
Easy to construct equal-area maps, used for education purposes. Equal-area.
 

 
Pseudocylindrical Projections
 
Like the Regular Cylindrical projections, the Pseudocylindrical (or “false cylindrical”) projections have latitude lines that are straight and parallel, and longitude lines (meridians) that are equally spaced. But in the pseudocylindrical, only the central meridian is straight; all other longitudinal meridians are curved. Some of these projections are interrupted to reduce curvature of meridians.
Sinusoidal
Interrupted Sinusoidal
 
Robinson Robinson
Used for world maps.
 
Eckert IV Eckert IV
Used for thematic and other world maps in numerous atlases and textbooks and for sheet maps. Equal-area.
 
Eckert VI Eckert VI
Used for thematic world maps in the Soviet World Atlas of 1937. Some recent use for climatic maps by U.S. publishers. Equal-area.
 
Sinusoidal Sinusoidal
Used for world maps, and maps of continents and other regions especially those bordering the Equator. Used in atlases to map Africa and South America. Also used for interruptions (see above), transformations, and in combination with other projections. Equal-area, Equally spaced parallels.
 
Mollweide
Mollweide
Mollweide
An equal-area projection of the Earth bounded with an ellipse. The basis of several other map projections. Example of interrupted form to show oceans. Equal-area.
 
Goode Homolosine Goode Homolosine
Interrupted projection used for world maps. A merging of the Mollweide and Sinusoidal projections. Equal-area.
 
Boggs Eumorphic Boggs Eumorphic
Based on the Mollweide and Sinusoidal projections. Equal-area.
 
Wagner IV Wagner IV
A flat pole projection with equally spaced meridians as portions of semi-ellipses. Equal-area.
 
Craster Parabolic Craster Parabolic
Used for thematic world maps in textbooks. Meridians are equally spaced parabolas intersecting at the poles. Equal-area.
 
McBryde-Thomas McBryde-Thomas
Flat-Polar Sinusoidal Projection. Basis of merged projections by McBryde. Equal-area.
 
McBryde S3 McBryde S3
World map interrupted to show oceans or land masses, by McBryde. Equal-area.
 

 
Conic Projections
 
To show a region for which the greatest extent is from east to west in the temperate zones, conic projections are usually preferable to cylindrical projections.
Regular Conic
 
Equidistant Conic Equidistant Conic
The most common projection in atlases for small countries. It was also used to map the Soviet Union.
 
Albers Equal-Area, North America Albers Equal-Area
One of the most commonly used projections for maps of the conterminous United States. Equal-area.
 
Lambert Equal-Area Conic Lambert Equal-Area Conic
A conic projection with one standard parallel, and the pole as a point. Equal-area.
 
Lambert Conformal Conic Lambert Conformal Conic
Used for large-scale mapping of regions of predominantly east-west extent, including topographic quadrangles for many of the U.S. State Plane Coordinate System zones. Conformal.
 
Bipolar Oblique Conic Conformal Bipolar Oblique Conic Conformal
Shows North and South America in one map.
Conformal.
 
Polyconic Polyconic
The Polyconic projection shows meridians curved, not straight
 
Bonne Bonne
A pseudoconic projection, popular in atlases for maps of continents until the mid-20th century. Equal-area.
 
Werner Werner
Used in the 16th and 17th centuries. Mathematically similar to the Bonne. Equal-area.
 

 
Azimuthal Projections
 
While cylindrical and conic projections are related to cylinders and cones wrapped around the globe, the azimuthal projections are formed onto a plane which is tangent to the globe.
 
      Azimuthal Projections Overview
          by John P. Snyder, U.S. Geological Survey
Polar Azimuthal
Polar
Oblique Azimuthal
Oblique
 
Perspective Azimuthal Projections:
 
Oblique Orthographic Orthographic
The Earth as viewed from deep space.
Perspective projection.
 
General Vertical Perspective, equatorial aspect General Vertical Perspective
The Earth as viewed from near space (for example, as viewed from the position of a satellite). Perspective.
 
Stereographic Stereographic
Used to map polar regions, and large continent-sized areas that extend similarly in all directions. Also has many other applications. Conformal, Perspective.
 
Oblique Gnomonic Gnomonic
Also called the “Gnomic,” it diplays all great circles as straight lines, showing the shortest distance between any two points. All great circles are shown as straight lines, not merely those passing through the center of the projection. Historically used for navigation. Perspective.
 
Nonperspective Azimuthal Projections:
 
Lambert Azimuthal Equal-Area Lambert Azimuthal Equal-Area
Areas are correct, and the overall scale variation is less than that found on the major perspective azimuthals. Equal-area.
 
Azimuthal Equidistant Azimuthal Equidistant
Distances from the center of the projection to any other point are shown correctly. Overall scale variation is moderate compared to the perspective azimuthals. Equidistant.
 
Polar Airy projection Airy
The mimimum-error azimuthal projection of the region enclosed by a great or small circle of chosen radius from a given center. Nonperspective, neither conformal nor equal area.
Minimum-error.
 
Modified Azimuthal Projections:
 
Hammer (Hammer-Aitoff) Hammer (Hammer-Aitoff)
Used for whole-world maps. Less shearing on the outer meridians near the poles than there is on pseudocylindrical projections.
Equal-area.
 
Winkel Tripel Winkel Tripel
Also used for whole-world maps.
 
Wagner VII Wagner VII
A modification of the Hammer projection. Used for world maps, such as climatic maps prepared by the U.S. Department of Commerce.
Equal-area.
 
Eckert-Greifendorff Eckert-Greifendorff
Whole-world map, derived from the equatorial aspect of the Lambert Azimuthal Equal-Area projection. Equal-area.
 
Briesemeister Briesemeister
Whole world maps showing continents grouped near the center. Derived from the oblique aspect of the Hammer projection. Equal-area.
 
Miller Oblated Stereographic Miller Oblated Stereographic
Used for areas that can be contained within an oval shape to minimize the scale distortions in the area.
Conformal.
 
Two-Point Azimuthal Two-Point Azimuthal
A geometric tilting of the Gnomonic. Rarely used, but can be used to find the location of a ship at sea with a radio direction finder and known locations of radio transmitters.
 
Two-Point Equidistant, Honolulu - Wash., DC. Two-Point Equidistant
Shows true distances, but not true azimuths, from either of two chosen points to any other point on the map. Has received moderate use and interest.
 

 
Miscellaneous Projections
 
Van Der Grinten Van Der Grinten
The world enclosed in a circle.
 
Space Oblique Mercator Space Oblique Mercator
Suitable for mapping imagery from Landsat and other vertically scanning satellites.
 
Satellite Tracking Satellite Tracking
Also for mapping the groundtrack of orbiting satellites.
Cylindrical or Conic
 
GS50 Projection GS50 Projection
Mathematical projection for displaying the U.S. with minimal distortion. Developed by John P. Snyder.
 
Armadillo Projection Armadillo Projection
Most of the world, projected onto a portion of a torus ring (similar to a doughnut).
 

 
Resources
 
 
An Album of Map Projections An Album of Map Projections
USGS Professional Paper 1453
by John P. Snyder and Philip M. Voxland
1994, 249 pp.
 
Map Projections:  A Working Manual Map Projections: A Working Manual
USGS Professional Paper 1395
by John P. Snyder
1997, 383 pp.
 
Note:
John P. Snyder was the U.S. Government's leading cartographer.
 
 
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