List of map projections

This list sorts map projections by surface type. Traditionally, there are three categories by which projections are sorted: cylindrical, conic and azimuthal. As a result of the complexity of projecting great circles onto flat planes, most do not fit perfectly into one category. Alternatively, projections may be classified by the properties which they preserve namely: direction, localized shape, area and distance.

Projections by surface

Cylindrical

Main article: Cylindrical Map Projection

The term "cylindrical projection" is used to refer to any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude (parallels) are mapped to horizontal lines (or, mutatis mutandis, more generally, radial lines from a fixed point are mapped to equally spaced parallel lines and concentric circles around it are mapped to perpendicular lines).

Projection	Images	Creator	Year	Notes
Equirectangular projection		Marinus of Tyre	c. 120 AD	simplest geometry
Gall–Peters projection		James Gall Arno Peters	1855	equal-area
Lambert cylindrical equal-area projection		Johann Heinrich Lambert	1772	equal area
Mercator projection		Gerardus Mercator	1569	preserves angles cannot show the poles
Miller projection		Osborn Maitland Miller	1942	shows the poles

Pseudocylindrical

Main article: Pseudocylindrical Map Projection

Pseudocylindrical projections represent the central meridian and each parallel as a single straight line segment, but not the other meridians. Each pseudocylindrical projection represents a point on the Earth along the straight line representing its parallel, at a distance which is a function of its difference in longitude from the central meridian.

Projection	Images	Creator	Year	Notes
Eckert IV projection		Max Eckert-Greifendorff
Eckert VI projection		Max Eckert-Greifendorff
Goode homolosine projection		John Paul Goode	1923
Kavrayskiy VII projection		V. V. Kavrayskiy	1939
Mollweide projection		Karl Brandan Mollweide	1805
Tobler hyperelliptical projection		Waldo R. Tobler	1973
Wagner VI projection		K.H. Wagner
Hoelzel projection		Hoelzel	about 1960

Conical

Main article: Azimuthal Map Projection

Azimuthal projections have the property that directions from a central point are preserved (and hence, great circles through the central point are represented by straight lines on the map). Usually these projections also have radial symmetry in the scales and hence in the distortions: map distances from the central point are computed by a function r(d) of the true distance d, independent of the angle; correspondingly, circles with the central point as center are mapped into circles which have as center the central point on the map.

Projection	Images	Creator	Notes
Polyconic projection		Ferdinand Rudolph Hassler
Equidistant conic
Lambert conformal conic		Ferdinand Rudolph Hassler
Polyconic projection		Johann Heinrich Lambert

Pseudoconical

Projection	Images	Creator	Notes
Bonne projection		Rigobert Bonne
Sinusoidal projection		Nicolas Sanson John Flamsteed
Werner projection		Johannes Werner
Continuous American polyconic		Johannes Werner

Azimuthal

Projection	Images	Creator	Notes
Aitoff projection		David A. Aitoff
Azimuthal equidistant projection			This projection is used by the USGS in the National Atlas of the United States of America.
Craig retroazimuthal projection		James Ireland Craig
Hammer projection		Ernst Hammer
Lambert azimuthal equal-area projection		Johann Heinrich Lambert
Winkel tripel projection		Oswald Winkel

Polyhedral maps

Main article: geodesic grid

Polyhedral maps can be folded up into a polyhedral approximation to the sphere. Many polyhedral maps use a gnomonic projection for each face, but some cartographers prefer the Fisher/Snyder equal-area projection for each face or a conformal projection.

Projection	Images	Creator	Notes
B.J.S. Cahill's Butterfly Map		Bernard Joseph Stanislaus Cahill
Waterman butterfly projection		Steve Waterman
quadrilateralized spherical cube			equal-area
Peirce quincuncial projection		Charles Sanders Peirce	conformal
Dymaxion map		Buckminster Fuller	Retains much proportional integrity of area, loses contiguousness of areas (most often oceans).
Myriahedral Projections		Jack van Wijk	projects the globe on a myriahedron -- a polyhedron with a very large number of faces.

Projections by preservation of a metric property

Conformal

Projection	Images	Creator	Notes
Peirce quincuncial projection		Charles Sanders Peirce

Equal-area

• Mollweide projection (ellipse)
• Bonne and Bottomley projection, a family of map projections that includes as special cases
  • sinusoidal projection
  • Werner (cordiform)
• Collignon projection
• cylindrical equal-area projection, a family of map projections including:
  • Gall–Peters projection
  • Lambert cylindrical equal-area projection
  • Behrmann cylindric equal-area
  • Smyth equal-surface, also called Craster rectangular
  • Trystran Edwards
  • Hobo-Dyer projection
  • Balthasart
• Albers conic
• Lambert azimuthal equal-area
• Hammer
• Briesemeister
• Tobler hyperelliptical, a family of map projections that includes as special cases Mollweide projection, Collignon projection, and the various cylindrical equal-area projections.
• quadrilateralized spherical cube
• Snyder’s equal-area polyhedral projection, used for geodesic grids.

Hybrids that use one equal-area projection in some regions and a different equal-area projection in other regions are almost always designed to be equal-area as a whole, such as:

• HEALPix: Collignon projection + Lambert cylindrical equal-area projection
• Goode homolosine projection: sinusoidal projection + Mollweide projection
• Philbrick Sinu-Mollweide projection: sinusoidal projection + Mollweide projection, oblique, interrupted.
• Hatano asymmetric projection: two different pseudocylindric equal-area projections fused at the equator.

Equal-area polyhedral maps typically use Irving Fisher's equal-area projection, whereas most polyhedral maps use the (non-equal-area) gnomonic projection.

Equidistant

Equidistant projections preserve distance from some standard point or line.

• Azimuthal equidistant - distances along great circles radiating from centre are conserved
• Equirectangular - distances along meridians are conserved
  • Plate carrée - an Equirectangular projection centered at the equator
• Equidistant conic: - distances along meridians are conserved, as is distance along one or two standard parallels
• Werner cordiform distances from the North Pole are correct as are the curved distance on parallels
• Cassini–Soldner

A two-point equidistant projection of Asia

• Two-point equidistant: two "control points" are arbitrarily chosen by the map maker. The two straight-line distances from any point on the map to the two control points are correct.
• orthographic projection preserves distances along parallels.
• Sinusoidal - distances along parallels are conserved
• Lambert azimuthal equal-area projection - the straight-line distance between the central point on the map to any other map is the same as the straight-line 3D distance through the globe between the corresponding two points.
• American polyconic projection -- distances along the parallels are preserved; as is distance along the central meridian.

Gnomonic

Projection	Images	Creator	Notes
Gnomonic projection

Retroazimuthal

Projection	Images	Creator	Notes
Craig retroazimuthal

Compromise projections

Projection	Images	Creator	Notes
Robinson projection		Arthur H. Robinson	A compromise between conformal and equal-area projections.
Van der Grinten projection		Alphons J. van der Grinten	A compromise between conformal and equal-area projections.
Miller cylindrical		Osborn Maitland Miller
Winkel Tripel		Oswald Winkel	The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection
Dymaxion map		Buckminster Fuller	Retains much proportional integrity of area, loses contiguousness of areas (most often oceans).
B.J.S. Cahill's Butterfly Map		Bernard Joseph Stanislaus Cahill
Waterman butterfly projection		Steve Waterman
Kavrayskiy VII projection		V. V. Kavrayskiy
Wagner VI projection			Wagner VI is equivalent to the Kavrayskiy VII vertically compressed by a factor of ${\sqrt {3}}/{2}$.