Map projection

A map projection converts locations on a curved surface, described by a coordinate system such as latitude and longitude, into positions on a plane. The term covers mathematical and geometric methods used to make paper maps and digital maps. A globe represents the whole Earth without flattening it, but is cumbersome and shows little detail at small scale; a flat map is easier to carry, print, display and combine with other data.

No flat map can represent the entire Earth's surface with every spatial property true at once. A projection may preserve one or more qualities—such as area, local angles and shapes, direction, or distance—while distorting others. The pattern and amount of distortion depend on the projection, its scale, and the area shown. There is therefore no single best projection for every map: the choice depends on what information the map is meant to communicate.

Many projections are grouped by the geometric surface used in their construction: cylindrical, conic, or planar (often called azimuthal). These families describe a way of constructing the projection, not the property it preserves. A conformal projection preserves local angles and the shapes of very small areas, but can greatly distort area. An equal-area projection represents relative surface areas correctly but distorts shapes. Equidistant projections preserve distances only along particular lines or from a chosen center, not all distances everywhere. Projection families may also include compromise methods that balance several kinds of distortion rather than eliminating one.

Cartographers consider a map's purpose, geographic extent, orientation, scale and the properties users need to compare. The Mercator projection, introduced by Gerardus Mercator in 1569, is conformal and represents constant-bearing rhumb lines as straight lines, a useful feature in some navigation. It is not equal-area: scale and the apparent area of places increase markedly toward high latitudes, so a world map in this projection can mislead comparisons of land area. Equal-area projections are often preferable when the map's purpose is to compare the relative sizes or distribution of regions. The same projection may behave differently at different scales, so projection choice is part of a map's design rather than a neutral finishing step.