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

In standard presentation, cylindrical projections map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.

Projection	Images	Creator	Year	Notes
Equirectangular (= equidistant cylindrical = rectangular = la carte parallélogrammatique)		Marinus of Tyre	c. 120 AD	simplest geometry
Gall–Peters (= Gall orthographic)		James Gall Arno Peters	1855	equal-area
Lambert cylindrical equal-area		Johann Heinrich Lambert	1772	equal area
Mercator (= Wright)		Gerardus Mercator	1569	preserves angles cannot show the poles
Miller (= Miller cylindrical)		Osborn Maitland Miller	1942	Intended for Mercator-like presentation, but including the poles.

Pseudocylindrical

Main article: Pseudocylindrical Map Projection

In standard presentation, pseudocylindrical projections map the central meridian and each parallel as a single straight line segment. Other meridians are curves (or possibly straight from pole to equator), and regular intervals of meridians from the sphere intersect any given parallel with constant spacing along that parallel on the map.

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

Conical

Main article: Conical map projection

In standard presentation, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles.

Projection	Images	Creator	Notes
Albers conic		Heinrich C. Albers
Equidistant conic
Lambert conformal conic		Johann Heinrich Lambert

Pseudoconical

In standard presentation, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs.

Projection	Images	Creator	Notes
Bonne		Rigobert Bonne
Werner		Johannes Werner
American polyconic		Ferdinand Rudolph Hassler

Azimuthal

Main article: Azimuthal map projection

In standard presentation, azimuthal projections map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical. In any presentation (or aspect), they preserve directions from the center point. This means great circles through the central point are represented by straight lines on the map.

Projection	Images	Creator	Notes
Azimuthal equidistant			This projection is used by the USGS in the National Atlas of the United States of America.
Lambert azimuthal equal-area		Johann Heinrich Lambert

Pseudoazimuthal

In standard presentation, pseudoazimuthal projections map the equator and central meridian to perpendicular, intersecting straight lines. They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian.

Projection	Images	Creator	Notes
Aitoff		David A. Aitoff
Hammer		Ernst Hammer
Winkel tripel		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. Some cartographers prefer the Fisher/Snyder equal-area projection for each face. Other cartographers prefer a conformal projection for each face.

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		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
stereographic projection
Lambert conformal conic		Johann Heinrich Lambert
Mercator		Gerardus Mercator
Transverse Mercator		Johann Heinrich Lambert
Gauss–Krüger		Carl Friedrich Gauss Johann Heinrich Louis Krüger
Peirce quincuncial		Charles Sanders Peirce
Adams hemisphere-in-a-square		Oscar Sherman Adams
Guyou hemisphere-in-a-square		Émile Guyou

Equal-area

• Mollweide (ellipse)
• Bonne and Bottomley projection, a family of map projections that includes as special cases
  • sinusoidal
  • Werner (cordiform)
• Collignon
• cylindrical equal-area, a family of map projections including:
  • Gall–Peters
  • Lambert cylindrical equal-area
  • Behrmann
  • Smyth equal-surface, also called Craster rectangular
  • Trystan Edwards
  • Hobo–Dyer
  • 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 + Lambert cylindrical equal-area
• Goode homolosine: sinusoidal + Mollweide
• Philbrick Sinu-Mollweide: sinusoidal + Mollweide, oblique, interrupted.
• Hatano asymmetric: 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

A two-point equidistant projection of Asia

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
  • Cassini — a transverse aspect of the Plate carrée centered on some selected meridian. Also called Soldner projection or Cassini–Soldner, particularly in ellipsoidal form.
• 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
• 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 preserves distances along parallels.
• Sinusoidal—distances along parallels are conserved
• Lambert azimuthal equal-area—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—distances along the parallels are preserved; as is distance along the central meridian.

Gnomonic

Projection	Images	Creator	Notes
Gnomonic

Retroazimuthal

Projection	Images	Creator	Notes
Craig retroazimuthal

Compromise projections

Projection	Images	Creator	Notes
Robinson		Arthur H. Robinson	A compromise between conformal and equal-area projections.
Van der Grinten		Alphons J. van der Grinten	A compromise between conformal and equal-area projections.
Miller		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).
Bernard J.S. Cahill		Bernard Joseph Stanislaus Cahill
Waterman butterfly projection		Steve Waterman
Kavrayskiy VII		V. V. Kavrayskiy
Wagner VI			Wagner VI is equivalent to the Kavrayskiy VII vertically compressed by a factor of $\sqrt{3}/{2}$.