What is a Map Projection? Types, Distortion, Examples

A map projection is a set of formulas that turns positions on the curved Earth, given as latitude and longitude, into x and y positions on a flat map. A globe cannot be flattened without stretching or tearing, so every projection distorts something. This article tests one claim: no flat map keeps both area and shape. An equal-area projection keeps area and stretches shapes. A conformal projection keeps local shapes and inflates area. A compromise projection such as Robinson gets both wrong, by smaller amounts.

Key takeaways

• A map projection converts latitude and longitude into x and y on a plane. It distorts area, shape, distance or direction somewhere on every map.
• The four families are cylindrical, conic, azimuthal and pseudocylindrical. They are named for the surface the globe is projected onto, or for the pattern of the map's grid lines.
• In Wherobots, Mercator drew Greenland at 16.4 times its true area and kept 500 km circles round, with roundness of 0.961 or higher.
• Equal Earth and Gall-Peters kept every country's area exactly. They flattened the same circle at 75°N to roundness 0.217 and 0.132.
• Robinson drew eight countries at 0.823 to 1.599 times their true area. Its circle at 75°N fell to roundness 0.337.
• An azimuthal equidistant map centered on Chicago matched the true distance to seven cities to the kilometer. Area and shape away from its center were distorted.
• Choose by task: equal-area to compare sizes, conformal for navigation, azimuthal equidistant for distance from one place, a compromise for a general world map.

What is a map projection?

The meaning of projection in cartography is a rule that transfers the graticule from a globe onto a flat surface. The graticule is the grid of latitude and longitude lines. John P. Snyder's Map Projections: A Working Manual (US Geological Survey (USGS) Professional Paper 1395, 1987) is the standard reference for projection formulas. It notes that a few projections are geometric, like a light casting the globe's lines onto paper. Most are mathematical, with spacing chosen to keep a property such as area.

A projection is one part of a coordinate reference system, which also fixes the datum, units and axis order. That article covers datums, EPSG codes, the registry numbers for coordinate systems, and Universal Transverse Mercator (UTM) zones. This one covers the projection step and the distortion it causes.

Snyder defines a developable surface as one that can be turned into a plane without distortion. He names three: the cylinder, the cone and the plane. A globe is not developable. Snyder states the result: "no map projection shows scale correctly throughout the map". He also writes: "No map can be both equal-area and conformal."

Every geospatial dataset drawn or measured on a flat grid has passed through a projection. A GeoTIFF records the projection of its pixel grid in its tags. Landsat and Sentinel-2 scenes used in satellite imagery analysis arrive on UTM grids.

The four properties a projection can keep

Snyder lists the properties a mapmaker weighs when choosing a projection. Four of them describe distortion.

• Area. On an equal-area map, a coin placed anywhere covers the same area of the Earth. Snyder notes that shapes, angles and scale are distorted on most parts of such a map. Less common names for equal-area are equivalent and authalic.
• Shape. A conformal map shows the angles around every point correctly, so small features keep their shape. Snyder stresses that this holds at each point, while equal area holds across the whole map. Large areas on a conformal map are still distorted.
• Distance. No projection shows scale correctly everywhere. An equidistant projection shows true distance from one or two points to every other point, or along every meridian.
• Direction. An azimuthal map shows the direction from its center to every other point correctly.

A projection that keeps none of the four exactly is a compromise projection. Snyder's table of suggested world maps lists Miller Cylindrical and Robinson under "compromise distortion".

Tissot's indicatrix

Nicolas Auguste Tissot published his analysis of projection distortion in 1859 and 1881, as Snyder recounts. He showed that an infinitely small circle on the Earth projects as a perfect ellipse on any map. On a conformal map, that ellipse is a circle, larger or smaller than the original. On an equal-area map, the ellipse keeps the circle's area and changes its shape. The ellipse's longest and shortest axes measure the scale distortion and the largest angle error at that point. Mulcahy and Clarke's Symbolization of Map Projection Distortion: A Review (Cartography and Geographic Information Science, 2001) surveys this and other ways to draw distortion on a map.

The Wherobots test below uses a finite version of the indicatrix: a circle 500 km in radius, drawn on the ellipsoid and then projected.

Types of map projections

Snyder groups most projections by the developable surface they are built on. National Geographic's guide to selecting a map projection names the same three basic kinds: planar, conical and cylindrical.

• Cylindrical. A cylinder wraps the globe, touching it along the equator. Meridians become equally spaced straight lines, and parallels become straight lines at right angles to them. Mercator is the best-known example, and it keeps local shape.
• Conic. A cone sits over the globe and touches it along one parallel. Meridians become straight lines that radiate from the cone's tip, and parallels become circular arcs. The Lambert conformal conic keeps local shape, and the Albers equal-area conic keeps area.
• Azimuthal, or planar. A plane touches the globe at one point, often a pole. Meridians radiate from the center at their true angles, and parallels become circles around it. The azimuthal equidistant projection keeps true distance from the center.
• Pseudocylindrical. Parallels are straight and meridians are equally spaced, as on a cylindrical map. Every meridian except the central one curves. Snyder calls these "false cylindrical" projections.

A cylinder or cone can also cut through the globe along two parallels, which gives two standard parallels of true scale. Turning the surface sideways or tilting it gives transverse and oblique aspects.

Family	How the grid looks	Properties available	Examples	Typical use
Cylindrical	Straight meridians and parallels at right angles	Conformal, equal-area, or equidistant along meridians	Mercator, Gall-Peters, plate carrée	Navigation charts, regions along the equator
Conic	Straight meridians from one point, arcs for parallels	Conformal or equal-area	Lambert conformal conic, Albers	Mid-latitude regions wider east-west than north-south
Azimuthal (planar)	Meridians radiate from the center, circles for parallels	True direction from the center, plus conformal, equal-area or equidistant	Stereographic, Lambert azimuthal equal-area, azimuthal equidistant	Polar maps, hemispheres, distance from one place
Pseudocylindrical	Straight parallels, curved meridians	Equal-area or compromise	Mollweide, Equal Earth, Robinson, Goode homolosine	World maps

Equal-area projection

An equal-area projection draws every region at its true size relative to every other region, as defined in the four properties above. Common examples are the Albers equal-area conic for mid-latitude regions, the Mollweide and the Equal Earth projection for world maps, and the Gall-Peters cylindrical projection. Each keeps area by stretching shapes, since no map can be both equal-area and conformal.

Area calculations on projected x and y need an equal-area projection. ST_Area on projected coordinates returns the area the map draws. In the Wherobots test below, Mercator returned 16.4 times Greenland's true area and Robinson 1.599 times. Equal Earth (EPSG:8857) and the equal-area cylindrical projection returned exactly 1 for all eight countries. ST_AreaSpheroid measures on the ellipsoid and skips the projection step.

Map projection examples

The table lists what eight common projections keep and give up. The next section tests all of them except Goode homolosine.

Projection	Family	Keeps	Gives up
Mercator	Cylindrical	Local shape, straight compass courses	Area, increasingly toward the poles
Plate carrée	Cylindrical	Distance along meridians, on a sphere	Area and shape away from the equator
Robinson	Pseudocylindrical	None exactly	Some area and some shape
Equal Earth	Pseudocylindrical	Area	Shape toward the poles
Mollweide	Pseudocylindrical	Area	Shape toward the edges
Gall-Peters	Cylindrical	Area	Shape, stretched north-south near the equator and east-west near the poles
Goode homolosine	Pseudocylindrical, interrupted	Area	Continuity, since the oceans are cut
Azimuthal equidistant	Azimuthal	Distance and direction from the center	Area and shape away from the center

Mercator projection

Gerardus Mercator presented his projection in 1569 to aid navigation, according to Snyder. On a Mercator map, a rhumb line, a course of constant compass bearing, is a straight line. The poles lie at infinity. PROJ, the open-source projection library, calls Mercator "inappropriate for world maps because of the gross distortions in area" in its Mercator documentation. It gives Greenland as the example: drawn larger than South America, with one eighth of its area. The EPSG:3395 World Mercator record lists its scope as small-scale conformal mapping between 80°S and 84°N.

Many online maps use a variation of Mercator, as the National Geographic guide notes. Battersby, Finn, Usery and Yamamoto examined that choice in Implications of Web Mercator and Its Use in Online Mapping (Cartographica, 2014).

Robinson projection

The PROJ documentation for Robinson classes it as pseudocylindrical and implements it as a spherical projection only. Snyder lists it as a compromise projection for world maps. National Geographic used the Van der Grinten projection from 1922 until 1988. In 1995, the Winkel tripel replaced the Robinson projection on the Society's world maps, according to its guide.

Equal Earth

Bojan Šavrič, Tom Patterson and Bernhard Jenny introduced the Equal Earth map projection in the International Journal of Geographical Information Science in 2018. The PROJ documentation for Equal Earth says it was inspired by Robinson and keeps the relative size of areas. It has an ellipsoidal form. EPSG registered it as EPSG:8857 on WGS 84, the World Geodetic System 1984. Its stated scope is small-scale equal-area mapping.

Mollweide

Carl B. Mollweide presented his equal-area projection of the Earth inside an ellipse in 1805, Snyder records. National Geographic used an interrupted Mollweide for its September 2012 map of the ocean floors. The PROJ documentation for Mollweide lists only a spherical form.

Gall-Peters, the Peters projection

Johann Heinrich Lambert described the cylindrical equal-area projection in 1772. James Gall's version, with true scale along the 45th parallels north and south, dates from 1855. He described it in Use of cylindrical projections for geographical, astronomical, and scientific purposes (Scottish Geographical Magazine, 1885). Snyder reports that Arno Peters of Germany presented a near-identical projection in 1967 as an original concept. The PROJ documentation for the equal-area cylindrical projection lists Gall-Peters as the setting with true scale at 45°.

Goode homolosine projection

J. Paul Goode of the University of Chicago interrupted the sinusoidal projection in 1916 to reduce its distortion, Snyder writes. He then joined the sinusoidal projection between about 40°N and 40°S with the Mollweide projection beyond. He presented the result in The homolosine projection: a new device for portraying the earth's surface entire (Annals of the Association of American Geographers, 1925). The PROJ documentation for the interrupted Goode homolosine describes six sinusoidal and six Mollweide regions. They meet at 40° 44' 11.8", the latitude where the two scales are equal. The lobes are placed to show the land.

Azimuthal projection

An azimuthal projection keeps directions from its center. Snyder notes that of the common azimuthal projections, one is equal-area, one is conformal and one is equidistant. Lambert presented the azimuthal equal-area projection in 1772. On the azimuthal equidistant projection, distances measured from the center are true. Snyder adds that the center is its only point without distortion. Mercator's 1569 world map carried polar azimuthal equidistant insets.

Map projections in Wherobots

The test measures area and shape in the same projections, on the same reference.

• What would support the claim: equal-area projections read 1 for every country's area and flatten circles near the pole. Mercator inflates area with latitude and keeps circles round. Robinson misses both, by less.
• What would break it: any projection that reads close to 1 for area and keeps circles round at 75°N.

ST_Transform reprojects a geometry, with the target given as an EPSG code or a PROJ string. The reference is ST_AreaSpheroid and ST_DistanceSpheroid, which measure on the WGS 84 ellipsoid with no projection.

Source	Rows read	What the queries read
Overture division areas in the Havasu catalog	8	Land polygons of eight countries and territories, from the equator to Greenland
Four points typed into the SQL	4	Centers of 500 km circles at 20°E and 0°, 30°, 60° and 75°N
Eight city-center points typed into the SQL	8	Chicago and seven destinations

ST_Transform accepted every projection below. It rejected the interrupted Goode homolosine (+proj=igh) and the Winkel tripel (+proj=wintri) with "Unknown projection", so neither is in the test.

Query A: country areas in six projections

WITH c AS (
  SELECT country, subtype, geometry AS g
  FROM wherobots_open_data.overture_maps_foundation.divisions_division_area
  WHERE subtype IN ('country','dependency') AND class = 'land'
    AND country IN ('CD','BR','IN','AU','DZ','DE','CA','GL')
),
m AS (
  SELECT country, subtype, g,
    ST_AreaSpheroid(g) AS true_m2,
    ST_Area(ST_Transform(g, 'EPSG:4326', 'EPSG:3395')) AS merc,
    ST_Area(ST_Transform(g, 'EPSG:4326', '+proj=eqc +lon_0=0 +datum=WGS84 +units=m')) AS eqc,
    ST_Area(ST_Transform(g, 'EPSG:4326', '+proj=robin +lon_0=0 +datum=WGS84 +units=m')) AS robin,
    ST_Area(ST_Transform(g, 'EPSG:4326', 'EPSG:8857')) AS eqearth,
    ST_Area(ST_Transform(g, 'EPSG:4326', '+proj=moll +lon_0=0 +datum=WGS84 +units=m')) AS moll,
    ST_Area(ST_Transform(g, 'EPSG:4326', '+proj=cea +lat_ts=45 +lon_0=0 +datum=WGS84 +units=m')) AS gallpeters
  FROM c
)
SELECT country, subtype,
  ROUND(ST_Y(ST_Centroid(g)), 1) AS centroid_lat,
  ROUND(true_m2 / 1e6, 0) AS km2_ellipsoid,
  ROUND(merc / true_m2, 3) AS mercator,
  ROUND(eqc / true_m2, 3) AS plate_carree,
  ROUND(robin / true_m2, 3) AS robinson,
  ROUND(eqearth / true_m2, 4) AS equal_earth,
  ROUND(moll / true_m2, 4) AS mollweide,
  ROUND(gallpeters / true_m2, 4) AS gall_peters
FROM m ORDER BY ABS(ST_Y(ST_Centroid(g)))

Each value is the projected area divided by the area on the ellipsoid, so 1 means the projection kept area. The query ran in 30.2 seconds.

Country	Centroid latitude	km² on the ellipsoid	Mercator	Plate carrée	Robinson	Equal Earth	Mollweide	Gall-Peters
Democratic Republic of the Congo	-2.9	2,330,064	1.008	1.011	0.823	1	1.0066	1
Brazil	-10.8	8,507,733	1.058	1.034	0.836	1	1.0061	1
India	22.9	3,149,953	1.19	1.096	0.872	1	1.0047	1
Australia	-25.7	7,687,126	1.249	1.121	0.885	1	1.0042	1
Algeria	28.2	2,309,975	1.294	1.142	0.897	1	1.0037	1
Germany	51.1	357,630	2.533	1.591	1.075	1	0.9986	1
Canada	61.4	9,966,823	5.134	2.109	1.208	1	0.9971	1
Greenland	74.8	2,161,739	16.4	3.8	1.599	1	0.9946	1

Mercator's area ratio climbs with latitude, from 1.008 for the Democratic Republic of the Congo to 16.4 for Greenland. Overture lists Greenland as a dependency, so the query selects that subtype too. Plate carrée, which plots longitude and latitude directly as x and y, reaches 3.8. Robinson shrinks the tropics to 0.823 and enlarges Greenland to 1.599. Equal Earth and Gall-Peters read 1 for all eight.

Mollweide reads 0.9946 to 1.0066. PROJ implements Mollweide, and Robinson, as spherical projections. Applied to WGS 84 coordinates, which sit on a flattened ellipsoid, the Mollweide formulas come within 0.66% of equal area without reaching it. Equal Earth and the equal-area cylindrical projection have ellipsoidal forms in PROJ and read exactly 1.

Query B: one 500 km circle at four latitudes

Area alone does not show shape. This query draws a circle of 500 km radius on the ellipsoid with ST_Buffer(..., true) at four latitudes and projects it. Roundness is the shape's area divided by the area of the smallest circle that encloses it. A circle scores 1. An ellipse twice as wide as it is tall scores 0.5.

WITH pts AS (
  SELECT * FROM VALUES (0.0), (30.0), (60.0), (75.0) AS t(lat)
),
c AS (
  SELECT lat, ST_Buffer(ST_Point(20.0, lat), 500000, true) AS g FROM pts
),
p AS (
  SELECT lat, g, ST_AreaSpheroid(g) AS true_m2, proj, ST_Transform(g, 'EPSG:4326', code) AS pg
  FROM c
  LATERAL VIEW explode(map(
    'mercator', 'EPSG:3395',
    'plate_carree', '+proj=eqc +lon_0=0 +datum=WGS84 +units=m',
    'robinson', '+proj=robin +lon_0=0 +datum=WGS84 +units=m',
    'equal_earth', 'EPSG:8857',
    'gall_peters', '+proj=cea +lat_ts=45 +lon_0=0 +datum=WGS84 +units=m',
    'azimuthal_eqd_20E_0N', '+proj=aeqd +lat_0=0 +lon_0=20 +datum=WGS84 +units=m'
  )) e AS proj, code
)
SELECT proj, lat,
  ROUND(ST_Area(pg) / true_m2, 3) AS area_ratio,
  ROUND(ST_Area(pg) / ST_Area(ST_MinimumBoundingCircle(pg)), 3) AS roundness,
  ROUND((ST_XMax(pg) - ST_XMin(pg)) / (ST_YMax(pg) - ST_YMin(pg)), 3) AS width_to_height
FROM p ORDER BY proj, lat

The query ran in 2.2 seconds.

Projection	Latitude	Area ratio	Roundness	Width to height
Azimuthal equidistant (center 20°E, 0°N)	0	1	0.993	0.999
Azimuthal equidistant (center 20°E, 0°N)	30	1.047	0.95	1.046
Azimuthal equidistant (center 20°E, 0°N)	60	1.209	0.824	1.206
Azimuthal equidistant (center 20°E, 0°N)	75	1.354	0.749	1.331
Equal Earth	0	1	0.736	0.74
Equal Earth	30	1	0.843	0.864
Equal Earth	60	1	0.585	1.689
Equal Earth	75	1	0.217	4.568
Gall-Peters	0	1	0.499	0.502
Gall-Peters	30	1	0.664	0.667
Gall-Peters	60	1	0.497	1.999
Gall-Peters	75	1	0.132	7.441
Mercator	0	1.002	0.992	0.998
Mercator	30	1.334	0.991	0.997
Mercator	60	4.022	0.989	0.993
Mercator	75	15.515	0.961	0.97
Plate carrée	0	1.007	0.986	0.992
Plate carrée	30	1.16	0.867	1.147
Plate carrée	60	1.999	0.498	1.997
Plate carrée	75	3.884	0.257	3.861
Robinson	0	0.821	0.871	0.877
Robinson	30	0.907	0.936	0.972
Robinson	60	1.19	0.638	1.547
Robinson	75	1.648	0.337	2.946

Mercator keeps the circle round at every latitude, at 0.961 or higher, and inflates its area to 15.515 times at 75°N. Its roundness dips at 75°N because the circle spans about 70.5°N to 79.5°N. Mercator's scale changes across that span, and conformal maps keep shape only for small areas.

Equal Earth and Gall-Peters keep the area at 1 at all four latitudes. At 75°N, Equal Earth draws the circle 4.568 times wider than tall, and Gall-Peters 7.441 times. Gall-Peters also stretches the circle at the equator, to half as wide as tall.

Robinson's area runs from 0.821 to 1.648, and its roundness from 0.936 down to 0.337.

Query C: distance from Chicago

The third query checks distance. It compares the ellipsoidal distance from Chicago to seven cities with the straight-line distance in three projections. The azimuthal equidistant projection is centered on Chicago.

WITH cities AS (
  SELECT * FROM VALUES
    ('London', -0.1276, 51.5072), ('New York', -74.0060, 40.7128), ('Cairo', 31.2357, 30.0444),
    ('Tokyo', 139.6917, 35.6895), ('Sao Paulo', -46.6333, -23.5505), ('Sydney', 151.2093, -33.8688),
    ('Anchorage', -149.9003, 61.2181)
  AS t(city, lon, lat)
),
o AS (SELECT ST_Point(-87.6298, 41.8781) AS chicago)
SELECT city,
  ROUND(ST_DistanceSpheroid(chicago, ST_Point(lon, lat)) / 1e3, 0) AS km_ellipsoid,
  ROUND(ST_Distance(ST_Transform(chicago, 'EPSG:4326', '+proj=aeqd +lat_0=41.8781 +lon_0=-87.6298 +datum=WGS84 +units=m'),
                    ST_Transform(ST_Point(lon, lat), 'EPSG:4326', '+proj=aeqd +lat_0=41.8781 +lon_0=-87.6298 +datum=WGS84 +units=m')) / 1e3, 0) AS km_azimuthal_equidistant,
  ROUND(ST_Distance(ST_Transform(chicago, 'EPSG:4326', 'EPSG:3395'), ST_Transform(ST_Point(lon, lat), 'EPSG:4326', 'EPSG:3395')) / 1e3, 0) AS km_mercator,
  ROUND(ST_Distance(ST_Transform(chicago, 'EPSG:4326', 'EPSG:8857'), ST_Transform(ST_Point(lon, lat), 'EPSG:4326', 'EPSG:8857')) / 1e3, 0) AS km_equal_earth
FROM cities CROSS JOIN o
ORDER BY km_ellipsoid

The query ran in 1.9 seconds.

City	km on the ellipsoid	km, azimuthal equidistant	km, Mercator	km, Equal Earth
New York	1,147	1,147	1,526	1,104
Anchorage	4,598	4,598	7,776	3,843
London	6,371	6,371	9,865	7,416
Sao Paulo	8,384	8,384	9,033	8,672
Cairo	9,881	9,881	13,332	10,248
Tokyo	10,161	10,161	25,321	19,543
Sydney	14,871	14,871	28,102	22,679

The azimuthal equidistant map matches all seven distances to the kilometer. Mercator reads 25,321 km to Tokyo, against 10,161 km on the ellipsoid. Both world maps are cut at 180° longitude, so their straight line to Tokyo or Sydney runs east the long way round. Query B shows the cost of the azimuthal map away from its center. A circle 75° from the center reads 1.354 times its area, with roundness 0.749.

Verdict

The results support the claim. No projection in the test kept both area and shape at 75°N.

• Conformal: Mercator kept circles at roundness 0.961 or higher and drew Greenland at 16.4 times its true area.
• Equal-area: Equal Earth and Gall-Peters read exactly 1 for all eight countries. They flattened the 75°N circle to roundness 0.217 and 0.132.
• Compromise: Robinson's area ranged from 0.823 to 1.599 across the countries, and its roundness fell to 0.337. Its area error is smaller than Mercator's, and its shape error smaller than that of Equal Earth or Gall-Peters.
• Equidistant: azimuthal equidistant kept the distance from its center exactly and kept neither area nor shape.

How to choose a map projection

Snyder writes that "it cannot be said that there is one 'best' projection for mapping." The best map projection to use depends on what the map has to keep. His table of suggested projections gives a starting point:

• World maps: an equal-area projection such as Mollweide to compare sizes. Mercator when straight compass courses matter. A compromise such as Robinson for a general reference map.
• A hemisphere: Lambert azimuthal equal-area for area, stereographic for shape, azimuthal equidistant for distance from the center.
• A region wide east-west, away from the equator: Albers equal-area conic or Lambert conformal conic.
• A region long north-south: transverse Mercator or transverse cylindrical equal-area.

The International Cartographic Association's book Choosing a Map Projection (Springer, 2017) treats the same question at book length. Snyder and Voxland's An Album of Map Projections (USGS Professional Paper 1453, 1989) shows the candidates side by side.

For geospatial analysis, measure distance and area on the ellipsoid, as the test above did, and use a projection to draw the result. A spatial join needs both layers in the same coordinate system before it compares them. Reprojecting a raster such as a digital elevation model resamples its grid, which gives cells new values. Reprojecting vector data moves each vertex and resamples nothing, one of the differences between raster and vector data. Global grids face the same trade-off: H3 maps its hexagons from an icosahedron with a gnomonic projection, and their area varies by about a factor of two worldwide.

Map projection research history

According to Snyder, Mercator probably set the spacing of his parallels by drawing. Edward Wright published the tables that fix the spacing in 1599. Johann Heinrich Lambert's 1772 Beiträge added seven projections, including the conformal conic, the cylindrical equal-area and the azimuthal equal-area.

In 1962, Waldo Tobler classified projections by whether each map coordinate depends on latitude, longitude or both. In his scheme, a pseudocylindrical projection has y depending on latitude alone and x on both.

Goldberg and Gott's Flexion and Skewness in Map Projections of the Earth (Cartographica, 2007) proposed two more measures for scoring world maps. Flexion measures how much a map bends straight lines, and skewness how lopsided it makes them.

Conclusions

1. No flat map keeps both area and shape. In this test, the projections that kept area exactly flattened the 75°N circle to roundness 0.217 and 0.132. Mercator kept it round and inflated it 15.515 times.
2. If a map compares sizes or densities, use an equal-area projection with an ellipsoidal form, such as Equal Earth (EPSG:8857). It read 1 for all eight countries. As a hedge, PROJ's Mollweide is spherical and read 0.9946 to 1.0066. That suits a world map, and its errors of up to 0.66% matter where area must be exact.
3. If a world map must keep straight compass courses or local shapes, use Mercator, and never compare sizes on it. It read 16.4 times for Greenland and 1.008 for the Democratic Republic of the Congo.
4. If a world map is for general reference, a compromise projection such as Robinson keeps both errors moderate. It read 0.823 to 1.599 times true area, with roundness down to 0.337 at 75°N.
5. If the map shows distance from one place, center an azimuthal equidistant projection on that place. It matched all seven distances from Chicago. Mercator read 9,865 km to London, against 6,371 km on the ellipsoid.
6. If the result is a number, measure on the ellipsoid. ST_AreaSpheroid and ST_DistanceSpheroid gave the reference values here without choosing a projection. At 75°N, each projection matched them only for the property it was built to keep, if any.

Related terms

• Coordinate reference system: datums, EPSG codes and UTM zones, of which a projection is one part
• Geospatial data: the vector and raster data that projections flatten
• Geospatial analysis: methods whose distances and areas depend on the projection
• Spatial join: combining layers that must share a coordinate system
• H3: a global hexagonal grid built on an icosahedron projection
• GeoTIFF: the raster format that stores its projection in tags
• Raster vs vector data: how each data model is reprojected
• Havasu catalog: the open tables the test queries read

Read more from Wherobots

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Reproject and measure geometries in any of these projections with a Wherobots free trial at cloud.wherobots.com.