Map Projections

Explore the 15 most popular map projections. Learn how they distort the Earth, their unique properties, and their applications.

What is a map projection?

A map projection is a mathematical method used to represent the three-dimensional curved surface of the Earth on a flat map plane. Because a sphere cannot be flattened without tearing, stretching, or compressing it, every flat map must contain distortions.

The Cartographer's Trilemma

In 1827, mathematician Carl Friedrich Gauss proved (in his Theorema Egregium) that a sphere cannot be projected onto a flat plane without deformation. Cartographers must choose which of the three main properties to preserve at the expense of others:

πŸ“ Conformal (Orthomorphic)

Preserves local angles and shapes (e.g., Mercator). Vital for navigation (as it keeps compass bearings straight), but drastically inflates areas near the poles.

πŸ—ΊοΈ Equal-Area (Equiareal)

Preserves the relative sizes of landmasses (e.g., Gall-Peters or Mollweide). Countries have the correct relative surface areas, but their local shapes become heavily stretched or distorted.

βš–οΈ Compromise Projections

Do not perfectly preserve area or shapes, but instead balance both distortions to produce a natural, visually pleasing map of the world (e.g., Robinson or Winkel Tripel).

Mercator Projection

Conformal Cylindrical
Gerardus Mercator(1569)

Designed in 1569 by the Flemish geographer and cartographer Gerardus Mercator. It became the standard projection for marine navigation because rhumb lines (lines of constant bearing) are represented as straight line segments.

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Robinson Projection

Compromise Pseudocylindrical
Arthur H. Robinson(1963)

Created in 1963 by Arthur Robinson at the request of Rand McNally. Robinson developed it through trial and error, adjusting coordinates in a table until the world map looked visually balanced and natural to the human eye.

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Gall-Peters Projection

Equal-Area Cylindrical
James Gall / Arno Peters(1855 / 1973)

First described by James Gall in 1855, and independently popularized in 1973 by German historian Arno Peters. Peters promoted it as a politically fair alternative to Mercator, correctly portraying the size of Global South countries.

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Mollweide Projection

Equal-Area Pseudocylindrical
Karl Brandan Mollweide(1805)

Developed in 1805 by the German mathematician and astronomer Karl Mollweide. It was created to satisfy the need for an equal-area projection showing the entire globe inside an aesthetically pleasing ellipse.

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Winkel Tripel Projection

Compromise Modified Azimuthal
Oswald Winkel(1921)

Designed in 1921 by German cartographer Oswald Winkel. The name 'Tripel' (triple) refers to Winkel's goal of minimizing three types of distortion simultaneously: area, direction, and distance.

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Equal Earth Projection

Equal-Area Pseudocylindrical
B. Šavrič, T. Patterson, B. Jenny(2018)

Created in 2018 by a team of cartographers in response to criticism of the Gall-Peters projection. The objective was to design an equal-area projection that avoids the severe elongation of equatorial landmasses.

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Peirce Quincuncial

Conformal Polyhedral
Charles Sanders Peirce(1879)

Developed in 1879 by the American philosopher and mathematician Charles Sanders Peirce. Utilizing elliptic functions, it projects the sphere onto a square, placing the North Pole at the center and dividing the South Pole into the four corners.

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Berghaus Star Projection

Star-like Azimuthal-Conic
Hermann Berghaus(1879)

Designed in 1879 by German cartographer Hermann Berghaus. It was initially created as a logo for the cover of Stieler's Handatlas and gained recognition due to its distinctive and artistic star shape.

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August Epicycloidal

Conformal Two-Sheeted
Franz August(1874)

Designed in 1874 by the German mathematician Franz August. It is a conformal projection (preserving angles) that maps the entire sphere inside a heart-shaped boundary (epicycloid).

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Plate CarrΓ©e

Equirectangular / Plate CarrΓ©e
Marinus of Tyre(ok. 120 n.e.)

One of the oldest known projections, credited to Marinus of Tyre around 120 AD. The French name 'Plate CarrΓ©e' translates to 'flat square', as lines of latitude and longitude form a simple square grid.

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Globe (Orthographic)

Perspective Azimuthal
Ancient Greeks (Apollonius)(III w. p.n.e.)

Known since antiquity, described by Greek mathematician Apollonius of Perga in the 3rd century BC. It represents a perspective view of the globe projected onto a plane from an infinite distance (like from outer space).

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Waterman Butterfly

Polyhedral (butterfly), interrupted
Steve Waterman(1996)

Created in 1996 by Steve Waterman from the geometry of the Waterman polyhedra (a dense sphere packing). It builds on Bernard J. S. Cahill's earlier 1909 "butterfly map", which unfolded the globe into eight triangular octahedral lobes. Waterman arranged the cuts to run through the oceans and spare the continents.

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Dymaxion (Airocean) Projection

Polyhedral (icosahedral), interrupted, near-equal-area
Richard Buckminster Fuller (and Shoji Sadao)(1943)

Developed in 1943 by the famous American architect and inventor Buckminster Fuller (with cartographic work finalized by Shoji Sadao in 1954). Fuller aimed to create a map representing the Earth as "one island in one ocean" (One Island, One Ocean), without splitting any major landmasses (like Asia and North America) and without distorting their relative sizes. Unlike most maps, it has no top or bottom, nor a preferred North-up orientation.

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Werner Cordiform Projection

Pseudoconical equal-area (cordiform)
Johannes Werner (based on Johannes Stabius' design)(1514)

Developed and popularized in 1514 by the German parish priest and mathematician Johannes Werner of Nuremberg. Werner refined an earlier design proposed around 1500 by the Viennese humanist Johannes Stabius (Stab). During the 16th and 17th centuries, it was widely used for world maps and maps of Asia, before eventually being replaced by newer, less distorted projections.

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Spilhaus Ocean Map Projection

Oblique conformal in a square (ocean-centric)
Athelstan Spilhaus (designed based on Adams' projection)(1942)

Designed in 1942 by the South African-American geophysicist and oceanographer Athelstan Spilhaus. Spilhaus aimed to create a map depicting the world ocean as a single, continuous body of water to better visualize marine currents and global water circulation. This projection is an oblique aspect of the Adams World in a Square II projection, rotated and centered on Antarctica.

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Summary of Map Projection Properties

A comprehensive side-by-side comparison of all projections across their main geometric characteristics.

ProjectionAreaShapeDistancesAngles & DirectionsContinuity
Mercator Projection❌ Distortedβœ… Preserved❌ Distortedβœ… Preservedβœ… Preserved
Robinson Projectionβš–οΈ Compromiseβš–οΈ Compromiseβš–οΈ Compromiseβœ… Preservedβœ… Preserved
Gall-Peters Projectionβœ… Preserved❌ Distorted❌ Distorted❌ Distortedβœ… Preserved
Mollweide Projectionβœ… Preserved❌ Distorted❌ Distorted❌ Distortedβœ… Preserved
Winkel Tripel Projectionβš–οΈ Compromise❌ Distorted❌ Distortedβš–οΈ Compromiseβœ… Preserved
Equal Earth Projectionβœ… Preservedβš–οΈ Compromise❌ Distorted❌ Distortedβœ… Preserved
Peirce Quincuncial❌ Distortedβœ… Preserved❌ Distortedβœ… Preservedβœ… Preserved
Berghaus Star Projection❌ Distorted❌ Distortedβœ… Preserved❌ Distorted❌ Interrupted
August Epicycloidal❌ Distortedβœ… Preserved❌ Distortedβœ… Preservedβœ… Preserved
Plate CarrΓ©e❌ Distorted❌ Distortedβœ… Preserved❌ Distortedβœ… Preserved
Globe (Orthographic)❌ Distorted❌ Distorted❌ Distorted❌ Distorted❌ Interrupted
Waterman Butterfly❌ Distorted❌ Distorted❌ Distortedβœ… Preserved❌ Interrupted
Dymaxion (Airocean) Projection❌ Distorted❌ Distorted❌ Distortedβœ… Preserved❌ Interrupted
Werner Cordiform Projectionβœ… Preserved❌ Distortedβœ… Preserved❌ Distortedβœ… Preserved
Spilhaus Ocean Map Projectionβœ… Preservedβœ… Preservedβœ… Preservedβœ… Preserved❌ Interrupted

Mercator Projection

Area:❌ Distorted
Shape:βœ… Preserved
Distances:❌ Distorted
Angles & Directions:βœ… Preserved
Continuity:βœ… Preserved

Robinson Projection

Area:βš–οΈ Compromise
Shape:βš–οΈ Compromise
Distances:βš–οΈ Compromise
Angles & Directions:βœ… Preserved
Continuity:βœ… Preserved

Gall-Peters Projection

Area:βœ… Preserved
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:❌ Distorted
Continuity:βœ… Preserved

Mollweide Projection

Area:βœ… Preserved
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:❌ Distorted
Continuity:βœ… Preserved

Winkel Tripel Projection

Area:βš–οΈ Compromise
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:βš–οΈ Compromise
Continuity:βœ… Preserved

Equal Earth Projection

Area:βœ… Preserved
Shape:βš–οΈ Compromise
Distances:❌ Distorted
Angles & Directions:❌ Distorted
Continuity:βœ… Preserved

Peirce Quincuncial

Area:❌ Distorted
Shape:βœ… Preserved
Distances:❌ Distorted
Angles & Directions:βœ… Preserved
Continuity:βœ… Preserved

Berghaus Star Projection

Area:❌ Distorted
Shape:❌ Distorted
Distances:βœ… Preserved
Angles & Directions:❌ Distorted
Continuity:❌ Interrupted

August Epicycloidal

Area:❌ Distorted
Shape:βœ… Preserved
Distances:❌ Distorted
Angles & Directions:βœ… Preserved
Continuity:βœ… Preserved

Plate CarrΓ©e

Area:❌ Distorted
Shape:❌ Distorted
Distances:βœ… Preserved
Angles & Directions:❌ Distorted
Continuity:βœ… Preserved

Globe (Orthographic)

Area:❌ Distorted
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:❌ Distorted
Continuity:❌ Interrupted

Waterman Butterfly

Area:❌ Distorted
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:βœ… Preserved
Continuity:❌ Interrupted

Dymaxion (Airocean) Projection

Area:❌ Distorted
Shape:❌ Distorted
Distances:❌ Distorted
Angles & Directions:βœ… Preserved
Continuity:❌ Interrupted

Werner Cordiform Projection

Area:βœ… Preserved
Shape:❌ Distorted
Distances:βœ… Preserved
Angles & Directions:❌ Distorted
Continuity:βœ… Preserved

Spilhaus Ocean Map Projection

Area:βœ… Preserved
Shape:βœ… Preserved
Distances:βœ… Preserved
Angles & Directions:βœ… Preserved
Continuity:❌ Interrupted