What is a Map Projection? A complete visual guide

A map projection is the math that turns the round Earth into a flat picture. Every projection lies about something — area, angle, distance, or direction. This is the complete visual guide to what each one preserves, what it distorts, and which to use when.

SimpleMapLab editorial teamPublished 21 May 2026~14 min read

The short version.You cannot flatten a sphere without stretching, compressing, or tearing it (Gauss's Theorema Egregium, 1827). Every projection chooses what to preserve and what to give up. The four properties: area, angle (shape), distance, and direction. No projection preserves all four. Picking the right projection means knowing what your map is trying to communicate.

What a projection actually is

Take a tomato. Cut it in half. Press one half flat against a cutting board. Notice what happens: the edges curl, the skin tears, the centre flattens out. You cannot get a flat tomato-half without changing something about it.

The Earth is a tomato. A flat map is the cutting board. A projection is the choice of how to deal with the tearing.

Mathematically: a map projection is a function that maps points on the surface of a sphere (specified by latitude φ and longitude λ) to points on a flat plane (specified by x and y). There are an infinite number of such functions. The interesting ones — the ones used in real maps — have nice mathematical properties.

The four things a projection can preserve

Cartographers think about projections in terms of four properties. Some projections preserve one or two; none preserve all four.

Area (equivalence).A country that's 5× larger than another country looks 5× larger on the map. Equal-Earth, Albers Conic Equal-Area, and Mollweide are equal-area projections.

Angle (conformality). The angle between two intersecting lines on the map equals the actual angle on the sphere. Locally, shapes are preserved — a small region looks the right shape. Mercator and Lambert Conformal Conic are conformal projections.

Distance (equidistance). Distances from a chosen central point (or along a chosen line) are correct. Azimuthal Equidistant preserves distance from the centre point; equirectangular preserves distance along meridians.

Direction (azimuth). The compass bearing from a chosen central point to any other point is correct. Azimuthal projections preserve direction from the centre.

The fundamental theorem. Carl Friedrich Gauss's 1827 Theorema Egregiumproves that no projection can preserve both area and angle. A sphere has positive Gaussian curvature; a plane has zero. The two can't be reconciled without distortion. Every projection is a choice about which distortion to accept.

The projection tour — six views of the same world

Every map below is rendered from the same source data — the Natural Earth 1:50m countries dataset — through SimpleMapLab's shared d3-geo renderer. Each highlights the same four regions (Africa, Greenland, USA, Australia) and includes Tissot's indicatrix: a 6×6 grid of circles that are all the same area on the sphere. The way each circle distorts reveals what the projection is doing to area.

1. Mercator — the famous conformal cylindrical

Designed by Gerardus Mercator in 1569 for marine navigation. Preserves angles perfectly — a straight line on a Mercator chart is a constant compass bearing. The trade-off is severe area distortion at high latitudes (Greenland appears ~14× larger than reality).

Mercator with Tissot indicatrix. Polar circles balloon. Preserved: angle. Distorted: area (badly), distance. Used for: marine navigation, web maps zoomed in.

2. Equirectangular (Plate Carrée) — the simplest projection

Attributed to Marinus of Tyre around 100 AD. The simplest possible projection: latitude becomes y, longitude becomes x, both with constant scaling. The world becomes a perfect 2:1 rectangle. Used in video games, raster data, and any context where the underlying lat/lng grid is more important than visual accuracy.

Equirectangular projection. The graticule is a uniform grid. Preserved: distance along meridians. Distorted: area, angle near poles. Used for: video games, raster data, climate databases.

3. Equal-Earth — modern equal-area

Designed in 2018 by Bojan Šavrič, Tom Patterson, and Bernhard Jenny as a modern replacement for Mercator on data-driven world maps. Preserves area perfectly; continent shapes remain recognisable. The Tissot circles below are all the same visible size — area is being faithful — but they stretch ellipse-shape near the poles because Equal-Earth gives up angle to keep area.

Equal-Earth projection. Tissot circles are visibly equal area; they elongate near the poles because shape is sacrificed. Preserved: area. Distorted: shape (mildly). Used for: data maps, statistical visualisations, modern atlases.

4. Orthographic — the world as a globe

The world seen from infinite distance — like looking at a billiard ball. Used for space-imagery contexts, NASA-style visualisations, and any time you want the planet to feel like a planet. Only half the sphere is visible at once; the back half is invisible. Centered here on Africa/Europe.

Orthographic projection centred near Africa. Preserves the visual feel of a sphere at the cost of seeing only half the world. Used for: globes, space imagery, intro pages, "blue marble" visuals.

5. Polar Azimuthal Equal-Area — Arctic-centred

The North Pole sits at the centre; latitude lines become concentric circles. Useful for anything involving the Arctic — sea ice, polar climate, polar flight paths, the UN logo (which uses the closely-related Azimuthal Equidistant). Preserves area, sacrifices distance and shape.

Polar Azimuthal Equal-Area, centred on the North Pole. Greenland, Russia, and Canada are now unambiguously the same size relative to each other. Used for: Arctic studies, polar flight planning, polar climate maps.

6. Albers Conic Equal-Area — the workhorse for continental maps

Imagine a paper cone resting on the globe along two parallels of latitude (here 20°N and 60°N). Project the globe onto the cone, then unroll the cone flat. The result is an equal-area projection that's accurate along a band of mid-latitudes. This is the projection most used for US continental maps (the geoAlbersUsa variant), Canadian maps, and any country whose bulk sits in a single hemisphere.

Albers Conic Equal-Area, parallels 20°N and 60°N. Accurate along that band; distorts away from it. Used for: USA / Canada / continental Europe maps, statistical atlases for one country.

The cheat-sheet — projection × property

Reading this table top-to-bottom is the quickest way to choose a projection for a specific purpose. ✓ = preserved exactly; ◐ = approximately preserved or compromise; ✗ = distorted.

Projection	Area	Angle	Distance	Best for
Mercator	✗	✓	✗	Marine navigation, web maps
Equirectangular	✗	✗	◐ (meridians)	Raster grids, video games
Equal-Earth	✓	✗	✗	Statistical world maps
Mollweide	✓	✗	✗	Science publications (CMB, sky)
Robinson	◐	◐	◐	Compromise atlas / school wall
Winkel-Tripel	◐	◐	◐	National Geographic default
Orthographic	✗	✗	✗	Globe / Earth visuals
Azimuthal Equal-Area	✓	✗	✗	Polar studies, hemispheric data
Azimuthal Equidistant	✗	✗	✓ (from centre)	UN logo, flight planning from one point
Albers Conic Equal-Area	✓	✗	✗ (good along parallels)	USA / Canada / continental maps
Lambert Conformal Conic	✗	✓	✗	Aeronautical charts
Gnomonic	✗	✗	✗	Great-circle flight routes (lines = geodesics)

How to choose a projection

The right projection depends entirely on what your map is communicating. A short decision guide:

Showing area-based data (population, GDP, biodiversity, election results, wildfires) — use Equal-Earth, Mollweide, or Goode Homolosine. Whatever you do, don't use Mercator for area data.

Navigation — use Mercator at sea, Lambert Conformal Conic in the air. Both preserve angle.

Showing one country or continent— use a Conic Equal-Area tuned to that country's latitude band. Albers for the USA. Lambert Conformal for European aeronautical.

Showing the Arctic or Antarctic — use a polar azimuthal projection. The Mercator world map literally cannot show the poles.

Showing the planet as a planet — use Orthographic. The slight inaccuracy of only seeing half is exactly the point.

A general-purpose world wall map — Robinson, Winkel-Tripel, or Equal-Earth. These compromise projections give up perfect accuracy on any one property to keep the world looking like the world.

Web mapping at street zoom— Web Mercator (Google's, OpenStreetMap's default). At local scale the area distortion is invisible; the angular accuracy and tile alignment are valuable.

A brief history of map projections

~100 AD. Marinus of Tyre is credited with the Equirectangular (Plate Carrée) projection — the first systematic flat-map of the known world. Ptolemy refined the same approach.

1569. Gerardus Mercator publishes his eponymous projection. Designed for marine navigation, it becomes the standard for nautical charts and, over the following two centuries, the de-facto standard for all world maps.

1772-1805. Johann Heinrich Lambert develops Lambert Conformal Conic and seven other projections. Heinrich Albers publishes Albers Equal-Area Conic. Karl Mollweide publishes his equal-area projection.

1827. Carl Friedrich Gauss proves the Theorema Egregium, establishing the mathematical impossibility of preserving all properties simultaneously.

1859.Nicolas Tissot introduces his indicatrix — the visual tool we've used on every map in this article.

1921, 1923, 1963. Compromise projections emerge: Winkel-Tripel (1921), Goode Homolosine (1923), Robinson (1963). These accept small distortions in every property to keep the world looking right.

1973-1980s.Arno Peters publicises the Gall-Peters equal-area projection and argues that Mercator's area distortion has serious cultural consequences. The Peters debate brings projection choice into public consciousness for the first time.

2005.Google Maps launches with Web Mercator as the default global projection. Over the following decade, hundreds of millions of people internalise a Mercator view of the world without realising it's a choice.

2018. Šavrič, Patterson, and Jenny publish Equal-Earth. The same year, Google Maps switches the fully-zoomed-out view to a globe.

Glossary

Conformal. Preserves local angles. Shapes look right at small scales; relative country sizes distort.

Equivalent / Equal-Area. Preserves area ratios across the entire map. Country sizes are honest; shapes distort.

Equidistant. Preserves distance — usually only from a single central point or along certain lines.

Azimuthal. Centred on a single point, with directions from that point preserved. Polar maps are azimuthal.

Cylindrical. Projects onto an imagined cylinder wrapped around the equator. Mercator and Equirectangular are cylindrical. Meridians become straight vertical lines.

Conic. Projects onto an imagined cone touching the globe at one or two parallels of latitude. Albers and Lambert Conformal Conic are conic.

Pseudocylindrical. Like cylindrical but with curved meridians. Equal-Earth, Mollweide, Robinson, and Winkel-Tripel are pseudocylindrical.

Rhumb line / loxodrome. A line of constant compass bearing. On a Mercator map, rhumb lines are straight — the property that made Mercator essential for sailors.

Great circle / geodesic.The shortest path between two points on a sphere. On most projections, geodesics curve. On a Gnomonic projection, they're straight lines — which is why aviation route-planning tools use gnomonic.

Tissot's indicatrix.Visual distortion-measurement tool: a grid of equal sphere-area circles overlaid on the projected map. The deformation of each circle reveals the projection's distortion pattern.

Theorema Egregium.Gauss's 1827 theorem proving that no projection can preserve both area and angle. The mathematical reason every projection is a compromise.

Related on SimpleMapLab

Why does Greenland look bigger than Africa? — the focused worked example of Mercator's area-distortion problem. Same renderer, deeper case study.
Size Comparisons cluster — 23 articles using equal-area overlay maps to compare countries, US states, and continents at honest scale.
The seven Geographic Lines tools — visualisations of the latitude and longitude framework all projections are built on: Equator, Tropic of Cancer, Tropic of Capricorn, Arctic Circle, Antarctic Circle, Prime Meridian, International Date Line.
External: TheTrueSize.com — drag-and-drop projection-distortion visualiser. Shows the same Mercator effect this article explains.

Methodology and sources

All six maps in this article are server-rendered from a single source dataset — the Natural Earth 1:50m countries TopoJSON — passed through six different d3-geo projections. The Tissot's indicatrix on each is a 6×6 grid of 4° geodesic-radius circles, generated by d3.geoCircle and projected through the same projection as the rest of the map.

Projection histories are cross-referenced against John Snyder's "Flattening the Earth: Two Thousand Years of Map Projections" (University of Chicago Press, 1993) — the definitive scholarly reference. Theorema Egregium statement follows Gauss's original 1827 paper (Disquisitiones generales circa superficies curvas). Modern projection summaries follow the Equal-Earth original paper (Šavrič, Patterson, Jenny, 2018, International Journal of Geographical Information Science).

Frequently asked questions

A map projection is the mathematical rule that turns latitude and longitude on the round Earth into x and y coordinates on a flat map. Because you can't flatten a sphere without stretching, compressing, or tearing it, every projection trades off between preserving area, angle, distance, or direction. Different projections make different trade-offs — and so each is useful for different purposes.

Because the sphere and the plane have different intrinsic geometry. Carl Friedrich Gauss proved this in 1827 — it's known as the Theorema Egregium ("remarkable theorem"). The Gaussian curvature of a sphere is positive; the Gaussian curvature of a plane is zero. No mapping can equate them without distortion. The corollary: you can preserve one or two properties but not all four (area, angle, distance, direction).

There is no universally "most accurate" projection. The accurate one depends on what you're measuring. For area, an equal-area projection like Equal-Earth or Albers Conic. For angle and shape, a conformal projection like Mercator or Lambert Conformal. For distance from a single point, an azimuthal equidistant projection. For looking at the world as a globe, orthographic. The question "which is most accurate" usually has a hidden second clause: "for X".

Gauss's 1827 theorem stating that Gaussian curvature is an intrinsic property of a surface — it cannot be changed by bending the surface without stretching. Since a sphere has positive curvature and a plane has zero curvature, no map from sphere to plane can preserve all distance ratios. This is the mathematical foundation for why every projection distorts something. The name (Latin for "remarkable theorem") reflects Gauss's own awareness of how fundamental the result is.

Google Maps uses a variant called Web Mercator. It was chosen because Mercator preserves angles at every zoom level — every map tile, regardless of zoom, has true compass directions. This is essential for street-level navigation where you need to know which way to turn. The trade-off is that Mercator distorts area at high latitudes; Greenland looks 14× larger than it actually is. Google switched the fully-zoomed-out world view to a globe in 2018 to mitigate this.

A visual tool invented in 1859 by Nicolas Tissot for measuring map projection distortion. A grid of identical sphere-area circles is placed across the globe; the projection is then applied. The way the circles change size and shape on the resulting flat map reveals the projection's distortion pattern. On Mercator, polar circles balloon huge. On Equal-Earth, all circles are the same size but elongate near the poles. On an equirectangular projection, near-polar circles widen east-west by a factor of 1/cos(lat).

A conformal projection preserves angles — at every point on the map, the angle between two intersecting lines equals the actual angle on the sphere. Mercator and Lambert Conformal Conic are the famous examples. An equal-area (or equivalent) projection preserves area ratios — a country that's 5× larger than another country looks 5× larger on the map. Equal-Earth and Albers Conic Equal-Area are the famous examples. Theorema Egregium tells you that no projection can be both conformal and equal-area.

For population, election, GDP, climate, biodiversity — anything area-based — use an equal-area projection: Equal-Earth for world, Albers Conic for North America, Mollweide for science journals. For navigation: Mercator. For showing the polar regions: Azimuthal Equal-Area. For "the world as a globe" visuals: Orthographic. For school wall maps where shape recognition matters more than absolute accuracy: Robinson or Winkel-Tripel (the National Geographic default).

Equirectangular (Plate Carrée) — attributed to Marinus of Tyre, ~100 AD. Mercator — 1569 by Gerardus Mercator. Lambert Conformal Conic — 1772. Albers Equal-Area Conic — 1805. Mollweide — 1805. Robinson — 1963 (Arthur Robinson). Winkel-Tripel — 1921 (Oswald Winkel). Goode Homolosine — 1923 (J. Paul Goode). Equal-Earth — 2018 (Bojan Šavrič, Tom Patterson, Bernhard Jenny).

The maps are server-rendered SVGs — they render as static images. They're interactive in the sense that browsers honour SVG's native scaling and accessibility (alt text, ARIA labels), but they're not pan-and-zoom maps. For interactive exploration of projection distortion, try thetruesize.com (drag countries between latitudes) or SimpleMapLab's Size Comparisons cluster (23 articles, each an equal-area side-by-side overlay).

The companion piece to this guide is "Why does Greenland look bigger than Africa?" — a focused worked example of the Mercator area-distortion problem. Both articles are part of the Map Projections cluster, which links into SimpleMapLab's seven Geographic Lines tools (Equator, Tropics, Polar Circles, Prime Meridian, IDL) and the 23-article Size Comparisons cluster.

Last reviewed: 21 May 2026. Maintained by the SimpleMapLab editorial team. Corrections welcome at hello@simplemaplab.com.