What is a map projection in simple terms?

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.

Why can't one map projection preserve everything?

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).

Which projection is most accurate?

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".

What is the Theorema Egregium?

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.

Why does Google Maps use Mercator?

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.

What is Tissot's indicatrix?

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).

What's the difference between a "conformal" and "equal-area" projection?

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.

Which projection should I use for my data?

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).

When was each major projection invented?

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).

Are the maps on this page interactive?

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).

Where can I read more on SimpleMapLab?

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.

What is a Map Projection? A complete visual guide

By Marko Visic · Published May 21, 2026 · Updated Sep 26, 2026

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.

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 Egregium proves 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.