# List of map projections

This list/table provides an overview of significant map projections, including those described by articles in Wikipedia. It is sortable by the main fields. Inclusion in the table is subjective, as there is no definitive list of map projections.

## Table of projections

Projection Images Type Properties Creator Year Notes
Equirectangular
= equidistant cylindrical
= rectangular
= la carte parallélogrammatique
Cylindrical Equidistant Marinus of Tyre 120 (c.) Simplest geometry; distances along meridians are conserved.

Plate carrée: special case having the equator as the standard parallel.

Cassini
= Cassini-Soldner
Cylindrical Equidistant César-François Cassini de Thury 1745 Transverse of equidistant projection; distances along central meridian is conserved.
Distances perpendicular to central meridian are preserved.
Mercator
= Wright
Cylindrical Conformal Gerardus Mercator 1569 Lines of constant bearing (rhumb lines) are straight, aiding navigation. Areas inflate with latitude, becoming so extreme that the map cannot show the poles.
Web Mercator Cylindrical Compromise Google 2005 A variation of the Mercator projection. The de facto standard for web mapping applications, used by all major online map providers, including Google Maps, Bing Maps, Mapquest, Mapbox, OpenStreetMap and others.
Gauss–Krüger
= Gauss conformal
= (Ellipsoidal) Transverse Mercator
Cylindrical Conformal Carl Friedrich Gauss

Johann Heinrich Louis Krüger

1822 This transverse, ellipsoidal form of the Mercator is finite, unlike the equatorial Mercator. Forms the basis of the Universal Transverse Mercator system.
Gall stereographic
similar to Braun
Cylindrical Compromise James Gall 1885 Intended to resemble the Mercator while also displaying the poles. Standard parallels at 45°N/S.
Braun is horizontally stretched version with scale correct at equator.
Miller
= Miller cylindrical
Cylindrical Compromise Osborn Maitland Miller 1942 Intended to resemble the Mercator while also displaying the poles.
Lambert cylindrical equal-area Cylindrical Equal-area Johann Heinrich Lambert 1772 Standard parallel at the equator. Aspect ratio of π (3.14). Base projection of the cylindrical equal-area family.
Behrmann Cylindrical Equal-area Walter Behrmann 1910 Horizontally compressed version of the Lambert equal-area. Has standard parallels at 30°N/S and an aspect ratio of 2.36.
Hobo–Dyer Cylindrical Equal-area Mick Dyer 2002 Horizontally compressed version of the Lambert equal-area. Very similar are Trystan Edwards and Smyth equal surface (= Craster rectangular) projections with standard parallels at around 37°N/S. Aspect ratio of ~2.0.
Gall–Peters
= Gall orthographic
= Peters
Cylindrical Equal-area James Gall 1855 Horizontally compressed version of the Lambert equal-area. Standard parallels at 45°N/S. Aspect ratio of ~1.6. Similar is Balthasart projection with standard parallels at 50°N/S.
Sinusoidal
= Sanson-Flamsteed
= Mercator equal-area
Pseudocylindrical Equal-area (Several; first is unknown) 1600

(c.)

Meridians are sinusoids; parallels are equally spaced. Aspect ratio of 2:1. Distances along parallels are conserved.
Mollweide
= elliptical
= Babinet
= homolographic
Pseudocylindrical Equal-area Karl Brandan Mollweide 1805 Meridians are ellipses.
Eckert II Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906
Eckert IV Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906 Parallels are unequal in spacing and scale; outer meridians are semicircles; other meridians are semiellipses.
Eckert VI Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906 Parallels are unequal in spacing and scale; meridians are half-period sinusoids.
Ortelius oval Pseudocylindrical Battista Agnese 1540

Meridians are circular.[1]

Goode homolosine Pseudocylindrical Equal-area John Paul Goode 1923 Hybrid of Sinusoidal and Mollweide projections.
Usually used in interrupted form.
Kavrayskiy VII Pseudocylindrical Compromise Vladimir V. Kavrayskiy 1939 Evenly spaced parallels. Equivalent to Wagner VI horizontally compressed by a factor of $\sqrt{3}/{2}$.
Robinson Pseudocylindrical Compromise Arthur H. Robinson 1963 Computed by interpolation of tabulated values. Used by Rand McNally since inception and used by NGS 1988–98.
Natural Earth Pseudocylindrical Compromise Tom Patterson 2011 Computed by interpolation of tabulated values.
Tobler hyperelliptical Pseudocylindrical Equal-area Waldo R. Tobler 1973 A family of map projections that includes as special cases Mollweide projection, Collignon projection, and the various cylindrical equal-area projections.
Wagner VI Pseudocylindrical Compromise K.H. Wagner 1932 Equivalent to Kavrayskiy VII vertically compressed by a factor of $\sqrt{3}/{2}$.
Collignon Pseudocylindrical Equal-area Édouard Collignon 1865 (c.) Depending on configuration, the projection also may map the sphere to a single diamond or a pair of squares.
HEALPix Pseudocylindrical Equal-area Krzysztof M. Górski 1997 Hybrid of Collignon + Lambert cylindrical equal-area
Boggs eumorphic Pseudocylindrical Equal-area Samuel Whittemore Boggs 1929 The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate.
Craster parabolic
=Putniņš P4
Pseudocylindrical Equal-area John Craster 1929 Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 Aspect.
Flat-polar quartic
= McBryde-Thomas #4
Pseudocylindrical Equal-area Felix W. McBryde, Paul Thomas 1949 Standard parallels at 33°45′N/S; parallels are unequal in spacing and scale; meridians are fourth-order curves. Distortion-free only where the standard parallels intersect the central meridian.
Quartic authalic Pseudocylindrical Equal-area Karl Siemon

1937

1944

Parallels are unequal in spacing and scale. No distortion along the equator. Meridians are fourth-order curves.
The Times Pseudocylindrical Compromise John Muir 1965 Standard parallels 45°N/S. Parallels based on Gall orthographic, but with curved meridians. Developed for Bartholomew Ltd., The Times Atlas.
Loximuthal Pseudocylindrical Karl Siemon, Waldo Tobler 1935, 1966 From the designated centre, lines of constant bearing (rhumb lines/loxodromes) are straight and have the correct length. Generally asymmetric about the equator.
Aitoff Pseudoazimuthal Compromise David A. Aitoff 1889 Stretching of modified equatorial azimuthal equidistant map. Boundary is 2:1 ellipse. Largely superseded by Hammer.
Hammer
= Hammer-Aitoff
variations: Briesemeister; Nordic
Pseudoazimuthal Equal-area Ernst Hammer 1892 Modified from azimuthal equal-area equatorial map. Boundary is 2:1 ellipse. Variants are oblique versions, centred on 45°N.
Winkel tripel Pseudoazimuthal Compromise Oswald Winkel 1921 Arithmetic mean of the equirectangular projection and the Aitoff projection. Standard world projection for the NGS 1998–present.
Van der Grinten Other Compromise Alphons J. van der Grinten 1904 Boundary is a circle. All parallels and meridians are circular arcs. Usually clipped near 80°N/S. Standard world projection of the NGS 1922–88.
Equidistant conic projection
= simple conic
Conic Equidistant Based on Ptolemy’s 1st Projection 100 (c.) Distances along meridians are conserved, as is distance along one or two standard parallels[2]
Lambert conformal conic Conic Conformal Johann Heinrich Lambert 1772
Albers conic Conic Equal-area Heinrich C. Albers 1805 Two standard parallels with low distortion between them.
Werner Pseudoconical Equal-area Johannes Stabius 1500 (c.) Distances from the North Pole are correct as are the curved distances along parallels.
Bonne Pseudoconical, cordiform Equal-area Bernardus Sylvanus 1511 Parallels are equally spaced circular arcs and standard lines. Appearance depends on reference parallel. General case of both Werner and sinusoidal
Bottomley Pseudoconical Equal-area Henry Bottomley 2003 Alternative to the Bonne projection with simpler overall shape

Parallels are elliptical arcs
Appearance depends on reference parallel.

American polyconic Pseudoconical Ferdinand Rudolph Hassler 1820 (c.) Distances along the parallels are preserved as are distances along the central meridian.
Azimuthal equidistant
=Postel
zenithal equidistant
Azimuthal Equidistant Abū Rayḥān al-Bīrūnī 1000 (c.) Used by the USGS in the National Atlas of the United States of America.

Distances from centre are conserved.
Used as the emblem of the United Nations, extending to 60° S.

Gnomonic Azimuthal Gnomonic Thales (possibly) 580 BC (c.) All great circles map to straight lines. Extreme distortion far from the center. Shows less than one hemisphere.
Lambert azimuthal equal-area Azimuthal Equal-area Johann Heinrich Lambert 1772 The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points.
Stereographic Azimuthal Conformal Hipparchos (deployed) 200 BC (c.) Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres. Maps all small circles to circles, which is useful for planetary mapping to preserve the shapes of craters.
Orthographic Azimuthal Hipparchos (deployed) 200 BC (c.) View from an infinite distance.
Vertical perspective Azimuthal Matthias Seutter (deployed) 1740 View from a finite distance. Can only display less than a hemisphere.
Two-point equidistant Azimuthal Equidistant Hans Maurer 1919 Two "control points" can almost be arbitrarily chosen. The two straight-line distances from any point on the map to the two control points are correct.
Peirce quincuncial Other Conformal Charles Sanders Peirce 1879
Guyou hemisphere-in-a-square projection Other Conformal Émile Guyou 1887
B.J.S. Cahill's Butterfly Map Polyhedral Compromise Bernard Joseph Stanislaus Cahill 1909 Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements
Cahill-Keyes projection Polyhedral Compromise Gene Keyes 1975 Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses
Waterman butterfly projection Polyhedral Compromise Steve Waterman 1996 Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various arrangements
Quadrilateralized spherical cube Polyhedral Equal-area F. Kenneth Chan, E. M. O’Neill 1973
Dymaxion map Polyhedral Compromise Buckminster Fuller 1943 Also known as a Fuller Projection.
Myriahedral projections Polyhedral Compromise Jarke J. van Wijk 2008 Projects the globe onto a myriahedron: a polyhedron with a very large number of faces.[3][4]
Craig retroazimuthal
= Mecca
Retroazimuthal James Ireland Craig 1909
Hammer retroazimuthal, front hemisphere Retroazimuthal Ernst Hammer 1910
Hammer retroazimuthal, back hemisphere Retroazimuthal Ernst Hammer 1910
Littrow Retroazimuthal Joseph Johann Littrow 1833 Also conformal
Armadillo Other Compromise Erwin Raisz 1943

## Key

Main article: Map projection

The designation "deployed" means popularisers/users rather than necessarily creators. The type of projection and the properties preserved by the projection use the following categories:

### Type of projection

• Cylindrical: In standard presentation, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.
• Pseudocylindrical: In standard presentation, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels.
• 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. Listed here after pseudocylindrical as generally similar to them in shape and purpose.
• Conic: In standard presentation, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles.
• Pseudoconical: In standard presentation, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs.
• Azimuthal: 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.
• Other: Typically calculated from formula, and not based on a particular projection
• Polyhedral maps: Polyhedral maps can be folded up into a polyhedral approximation to the sphere, using particular projection to map each face with low distortion.
• Retroazimuthal: Direction to a fixed location B (by the shortest route) corresponds to the direction on the map from A to B.

### Properties

• Conformal: Preserves angles locally, implying that locally shapes are not distorted.
• Equal Area: Areas are conserved.
• Compromise: Neither conformal nor equal-area, but a balance intended to reduce overall distortion.
• Equidistant: All distances from one (or two) points are correct. Other equidistant properties are mentioned in the notes.
• Gnomonic: All great circles are straight lines.

## Notes

1. ^ Donald Fenna. "Cartographic Science: A Compendium of Map Projections, with Derivations". Section "The Ortelius Oval" p. 249.
2. ^ Carlos A. Furuti. Conic Projections: Equidistant Conic Projections
3. ^ Jarke J. van Wijk. "Unfolding the Earth: Myriahedral Projections". [1]
4. ^ Carlos A. Furuti. "Interrupted Maps: Myriahedral Maps". [2]