Equirectangular: properties, uses, and limitations
The plainest projection there is: longitude as x, latitude as y. Neither conformal nor equal-area, and the only one of the five whose two distortion rows are identical - both are sec(latitude).
Description
The equirectangular projection, also called plate carree, plots longitude straight onto x and latitude straight onto y. Ptolemy credits it to Marinus of Tyre around AD 100, which makes it one of the oldest projections on record.
It gets mistaken for raw coordinates rather than a projection, because an array of longitude-latitude pairs drawn as-is lands exactly here. It is still a projection, and it still makes a trade: the only thing it guarantees is distance along a meridian.
Projection properties
- Family
- Equidistant cylindrical
- Frame ratio
- 2.000:1
- Latitudes drawn
- The whole world
- Pole line
- As long as the equator
- True-shape parallel
- The equator
- Area distortion doubles
- 60.0°
- Shape distortion doubles
- 60.0°
- Held at 1.00 by definition
- Neither
Meridians are evenly spaced vertical lines, parallels are evenly spaced horizontal lines, and the two spacings are equal, so the graticule is a grid of squares. The frame is exactly 2:1 - measured here at 2.000.
It is neither conformal nor equal-area. Area distortion and shape distortion are both sec(latitude), so the two curves lie on top of each other: 1.15 at 30 degrees, exactly 2 at 60, 9.57 at 84. No other projection here has two identical rows.
The only place shapes come out undistorted is the equator itself. Each pole is stretched into a line as long as the equator.
Measured distortion
| Latitude | 0° | 30° | 45° | 60° | 72° | 84° |
|---|---|---|---|---|---|---|
| Area distortion | 1.00 | 1.15 | 1.41 | 2.00 | 3.24 | 9.57 |
| Shape distortion | 1.00 | 1.15 | 1.41 | 2.00 | 3.24 | 9.57 |
Both rows are measured against this projection's own equator, taken as 1. They compare with each other and with nothing on another projection's page - every projection is normalised to itself.
Uses
Its commonest use is not a map for reading but a storage format: a raster sampled at even steps of longitude and latitude is already in this projection. Global elevation, climate and satellite grids are mostly shipped this way.
As an index map, a thumbnail, or anywhere a fixed pixel-to-degree relationship is worth more than accuracy, it is the least effort available.
Limitations
It preserves nothing, so no area comparison or angle measured off it has any standing. The 'equidistant' in the name is only about meridians: east-west distance is already stretched twofold by 60 degrees.
As a world map its high-latitude distortion is visible but not lurid. That is the risk - it is easier to mistake for an honest map than Mercator is.
Parameters
How this site builds it (w and h are the canvas; sphere is the whole globe):
geoEquirectangular().fitExtent([[0, 0], [w, h]], sphere)d3-geo's geoEquirectangular takes no standard parallel, which makes it the standard-parallel-zero case: plate carree proper. Only the central meridian can move.
The family at large is parameterised by a standard parallel: east-west scale is multiplied by cos of it, and the frame goes from 2:1 to 2cos(f0):1. Setting it to zero returns the map drawn here.