Introduction to Map Projections

Every flat map of the Earth is a compromise. Because the planet is a three-dimensional spheroid, any attempt to flatten its surface onto a two-dimensional sheet inevitably introduces distortion. This fundamental challenge has driven cartographers for centuries to develop mathematical transformations known as map projections. A map projection is a systematic method of translating latitudes and longitudes from the curved Earth onto a flat plane. No projection can preserve all spatial properties simultaneously; each projection type prioritizes one or more of three key attributes: distances, areas, and directions. Understanding these trade-offs is essential for selecting the right projection for a given purpose—whether for navigation, statistical analysis, or general reference.

The choice of projection can dramatically affect how we perceive the world. For instance, the familiar Mercator projection exaggerates the size of high-latitude regions, while the Gall-Peters projection preserves area but distorts shapes. The following sections break down the three main preservation goals and the projections that serve them.

Types of Map Projections

Map projections are broadly categorized by the geometric property they preserve, but they can also be classified by their construction method (cylindrical, conic, azimuthal, or pseudocylindrical) or by the aspect of the globe used to develop the projection (normal, transverse, or oblique). The most common classification system groups projections into three categories based on preservation: conformal (preserving angles and local shapes), equal-area (preserving area), and equidistant (preserving distances from one or two points). A fourth category, compromise projections, balances distortion across all properties without strictly preserving any single one.

Each type has strengths and weaknesses that make it suitable for particular applications. For example, conformal projections are ideal for navigation, equal-area for thematic mapping of density or distribution, and equidistant for measuring radial distances. The next sections explore each preservation property in detail.

Preserving Distances: Equidistant Projections

Equidistant projections maintain true distances along specific lines or from a central point. No flat projection can preserve distances between every pair of points on Earth, so equidistant projections restrict accurate measurement to one or two reference lines. The most common characteristic is that distances from a center point (or along a meridian) are represented to scale.

How Equidistant Projections Work

In an equidistant projection, the scale is constant along one or more lines. For example, the Equidistant Conic projection preserves distances along all meridians and along one or two standard parallels. The Azimuthal Equidistant projection preserves distances from the center point to any other point on the map. This makes it useful for radio-wave range maps or for displaying the region around a specific city.

Common Equidistant Projections

  • Equidistant Cylindrical (Plate Carrée): Simple projection where the equator and all meridians are equally spaced. Distances along meridians are true, but areas and shapes are heavily distorted toward the poles.
  • Azimuthal Equidistant: Often used for polar regions, this projection shows true great-circle distances from the center point. The United Nations emblem uses an azimuthal equidistant projection centered on the North Pole.
  • Equidistant Conic: Standard for regional maps of mid-latitude areas like the United States, because it preserves distances along the meridians and provides reasonable area and shape accuracy near the standard parallels.

Trade-Offs and Use Cases

Equidistant projections sacrifice shape and area fidelity to maintain distance accuracy. For example, the Plate Carrée projection produces severe area distortion near the poles, making Antarctica appear as wide as the equator. However, for applications that require measuring distances from a hub (e.g., aviation range rings, emergency response zones), equidistant projections are indispensable. They are also used in plane surveying and small-scale maps of individual countries where distance fidelity along meridians is critical.

External resource: The ArcGIS Pro documentation offers detailed explanations of equidistant projection properties and usage.

Preserving Areas: Equal-Area Projections

Equal-area (or equivalent) projections ensure that any region on the map has the same area relative to the globe as it does in reality. This property is vital for thematic mapping where comparing the size of geographic units is essential, such as population density, crop yields, or land cover distribution. The trade-off is that shapes, angles, and distances are usually distorted, especially near the edges of the projection.

The Mathematics of Equal-Area

Equal-area projections maintain a constant ratio between the area on the map and the corresponding area on the globe. This is achieved by carefully controlling scale distortion along meridians and parallels. For instance, in the Mollweide projection, the meridians are compressed near the poles to correct for the area exaggeration seen in cylindrical projections. The Gall-Peters projection uses a cylindrical approach but contracts the spacing of parallels toward the poles to preserve area, resulting in a map where Africa and South America appear stretched vertically but are correctly sized relative to North America and Europe.

Prominent Equal-Area Projections

  • Mollweide: A pseudocylindrical projection that creates an oval-shaped world map. It preserves area globally while keeping the central meridian straight. Shapes are most accurate near the center and become increasingly distorted toward the edges.
  • Gall-Peters: A cylindrical equal-area projection that became controversial for replacing the Mercator projection in many educational contexts. It accurately shows the relative sizes of continents but severely distorts shapes, especially at high latitudes.
  • Albers Equal-Area Conic: Often used for mapping large countries with an east-west extent, such as the United States or China. It uses two standard parallels to minimize distortion across the mapped region and is widely used in statistical mapping.
  • Lambert Azimuthal Equal-Area: Commonly applied to continental-scale maps, especially of polar regions or individual continents. It preserves area while providing a more visually balanced shape than cylindrical equal-area projections.

Applications and Limitations

Equal-area projections are the standard for choropleth maps, dot density maps, and any visualization where area comparisons are primary. For instance, the UN Population Division uses equal-area projections to display global population distributions. However, the distortion of shapes can mislead viewers who expect familiar outlines. The Gall-Peters projection, for example, shows Africa as very tall and skinny, which can be disorienting. Equally, the Mollweide projection's elliptical shape makes it difficult to align compass directions (meridians curve). Despite these trade-offs, cartographers agree that for quantitative comparisons of geographic regions, an equal-area projection is the only fair choice.

For a deeper dive into equal-area principles, refer to the British Library's guide on map projections.

Preserving Directions: Conformal Projections

Conformal projections preserve local angles and shapes, meaning that at any point on the map, the intersection of latitude and longitude lines forms a right angle, and small features retain their correct form. This property is essential for navigation because a straight line drawn on a conformal map (a rhumb line) represents a constant compass bearing. However, conformality comes at the cost of area distortion—features far from the standard line or point become greatly exaggerated in size.

How Conformal Projections Achieve Accuracy

Conformal projections maintain scale along all directions from any given point, but the scale changes from point to point. For example, the Mercator projection is conformal but its scale increases dramatically with latitude, making Greenland appear larger than South America even though South America is nearly eight times larger. The key feature is that shapes of small objects (e.g., islands, coastlines) are locally correct, but the size of those objects is not true.

Notable Conformal Projections

  • Mercator: Developed in 1569 by Gerardus Mercator, this cylindrical projection was revolutionary for navigation because any straight line is a line of constant bearing (rhumb line). It remains widely used for nautical charts and web maps (e.g., Google Maps uses a variant called Web Mercator).
  • Lambert Conformal Conic: Used for aeronautical charts and regional maps of mid-latitude areas. It preserves shape well over the mapped region, with distortion minimized along two standard parallels.
  • Transverse Mercator: A variant where the cylinder is rotated 90 degrees so that the line of tangency is a meridian. This forms the basis of the Universal Transverse Mercator (UTM) coordinate system, widely used for topographic mapping and GPS coordinates.
  • Oblique Mercator: Useful for mapping elongated regions that are not aligned with the equator or a meridian, such as the Alaskan panhandle or the long arc of a satellite ground track.

Conformal Projections in the Modern World

The Mercator projection, despite its severe area distortion, dominated world maps for centuries because it provided a useful navigation aid. Today, its most pervasive use is in web mapping applications. The Web Mercator projection is the default for Google Maps, Bing Maps, OpenStreetMap, and most slippy map interfaces. This choice is driven by computational convenience (simple math, good for tile caching) and the fact that users expect north to be always up. However, this means that near the poles, areas are wildly exaggerated. For example, on a standard Web Mercator map, Greenland appears the same size as Africa, when in reality Africa is 14 times larger. Many educators and cartographers advocate for alternative projections in classroom and atlas contexts.

For navigational and military mapping, the UTM system based on the Transverse Mercator provides extremely accurate local representation of shapes and angles, making it the gold standard for ground operations. Pilots rely on Lambert Conformal Conic charts to plot routes because small angles remain correct.

For more on conformal projections and their history, see the USGS Professional Paper 1395, "Map Projections: A Working Manual".

Compromise and Hybrid Projections

No single projection perfectly preserves distances, areas, and directions. Compromise projections attempt to balance these distortions without excelling in any one property. They are often used for general-reference world maps where viewers need a visually pleasing representation with relatively low overall distortion.

Robinson Projection

Developed by Arthur H. Robinson in 1963, this projection was designed to create a visually appealing world map that reduces exaggeration of polar regions while keeping shapes recognizable. It is neither conformal nor equal-area, but its distortions are moderate across the entire map. The National Geographic Society used the Robinson projection for its world maps from 1988 to 1998, before switching to the Winkel Tripel.

Winkel Tripel Projection

Created by Oswald Winkel in 1921, this average of the equidistant cylindrical and Aitoff projections yields a map with low distortion in both area and shape. It has become the standard for many reference atlases, including the National Geographic Society from 1998 onward. The Winkel Tripel offers an excellent balance: distances are reasonably accurate away from the edges, shapes are less distorted than in equal-area projections, and area distortions are less severe than in conformal projections.

Other Compromise Options

  • Eckert IV: A pseudocylindrical equal-area projection that also provides fairly low shape distortion across most of the map.
  • Equal Earth projection: A relatively new projection (2018) that aims to combine equal-area properties with a more aesthetically pleasing shape, closely resembling the Robinson projection while maintaining true area.
  • Goode Homolosine: An interrupted projection that "cuts" the map in the oceans to reduce distortion. It preserves both area and shape within each lobe, but is discontinuous.

Compromise projections are the default choice for most world maps in textbooks and news media because they provide a recognizable and intuitive picture of the Earth without the extreme distortions of Mercator or Gall-Peters.

How to Choose a Projection

Selecting the right projection depends on the map's purpose, scale, region, and audience. Here are key decision criteria:

  • Navigation or directional analysis: Use a conformal projection like Mercator (for constant bearing) or Lambert Conformal Conic (for regional charts).
  • Area comparisons (thematic mapping): Use an equal-area projection such as Albers Equal-Area Conic or Mollweide.
  • Distance measurement from a point: Use an equidistant projection like Azimuthal Equidistant.
  • General reference or classroom maps: Use a compromise projection like Winkel Tripel or Robinson.
  • Interactive web maps: Must use a projection that tiles efficiently; Web Mercator is the de facto standard, but suppliers often provide alternative projections for visualization purposes.
  • Polar regions: Use stereographic (conformal) or azimuthal equidistant/equal-area projections centered on the pole.

In modern GIS software (e.g., QGIS, ArcGIS Pro), users can easily reproject data on the fly. The key is to select a projection that minimizes distortion for the specific area and analytical goal. For local or regional maps, conic projections (Lambert Conformal Conic or Albers Equal-Area) usually perform best.

Historical Context and Evolution

The study of map projections dates back to the ancient Greeks. Thales of Miletus is credited with one of the first projections (gnomonic), and Ptolemy's Geography described conic and cylindrical projections. The Age of Exploration spurred demand for navigational charts, leading to Mercator's 1569 projection. The 19th and 20th centuries saw an explosion of new projections, with mathematicians and cartographers seeking to reduce specific distortions. Today, with computer algorithms, we can create custom projections that minimize distortion for any given set of points, a technique known as least-areal projections or optimized projections. The National Geographic Society's adoption of the Winkel Tripel illustrates how evolving cartographic standards shift toward balance and accuracy for a global audience.

Conclusion: The Art of Compromise

All flat maps lie. The cartographer's task is to choose which lies are most acceptable for the map's intended use. Projections that preserve distances sacrifice shape and area; those that preserve areas distort distances and directions; and conformal projections exaggerate size. Understanding these trade-offs empowers map users to interpret spatial information critically and select the appropriate tool for each task.

In an age of digital mapping, where users can zoom across the planet on their phones, the underlying projection is often invisible. Yet the choice of projection influences everything from the perceived size of countries to the accuracy of distance measurements. By learning the principles of equidistant, equal-area, and conformal projections, you gain the ability to read maps with a discerning eye and to create maps that honestly represent the data they convey.