Equal-Area vs Conformal vs Equidistant Projections

Equal-area projections preserve relative area. Conformal projections preserve local angles. Equidistant projections preserve specified distances. The crucial word in each definition is different—and, for equidistant projections in particular, the promise is narrower than the name may suggest.

No flat projection can preserve all three properties everywhere. Choosing among them means deciding which geometric relationship the map must communicate most reliably.

Property · What is preserved · What is not guaranteed · Typical purpose

Equal area — Area ratios across the map — Local shape, angle, direction or distance — Thematic maps where visible region size matters
Conformal — Angles and infinitesimal shape at each point — Area or constant scale across a large extent — Navigation, topographic mapping and local orientation
Equidistant — Distance from particular points or along particular lines — Every distance between arbitrary locations — Range or distance-from-origin maps

Equal area: honest size, altered shape

On an equal-area map, equal amounts of the Earth's surface occupy equal amounts of map space. A country with twice the ground area of another will be represented with twice the mapped area, wherever the two countries lie.

This is valuable for choropleths and other filled-area maps because the visual footprint of a polygon contributes to its prominence. Global land cover, habitat extent, agricultural area and population totals are all themes for which systematic area enlargement can distort the visual argument.

Area preservation is achieved by stretching shapes. Equal Earth produces a continuous and familiar-looking world, Mollweide has an elliptical outline, and interrupted equal-area projections can reduce distortion over continents by breaking continuity elsewhere. They share the preserved property, not the same appearance or best use.

For a regional map, a projection such as Albers Equal Area or Lambert Azimuthal Equal Area can be configured around the study area. A global equal-area CRS is not automatically the best analytical CRS for a small country.

Conformal: correct local angles, changing scale

A conformal projection preserves the angle at which curves meet. In an infinitesimally small neighbourhood, it applies the same scale in every direction, so local shapes are retained. This supports orientation and bearing work: Mercator makes a line of constant compass bearing straight, while Transverse Mercator and Lambert Conformal Conic are widely used for regional mapping.

Conformality does not keep a continent's overall shape or area correct. If scale changes considerably from one side of a large feature to the other, the feature can still look stretched. On a Mercator world map, the local scale increases towards the poles; the angle property survives precisely because both map directions are enlarged together.

The term is therefore best read as locally shape-preserving, not simply “shape-preserving”. It is a differential property, not a guarantee about every outline visible at world scale.

Equidistant: a defined set of distances

An equidistant projection never makes all distances between all pairs of places correct on a world map; instead, it preserves a specified family of distances.

An azimuthal equidistant projection centred on London, for example, preserves distance and direction from London to every other point. It does not preserve the distance between Tokyo and Cape Town. A two-point equidistant projection preserves distances from two chosen control points. Other methods maintain scale along selected meridians or parallels.

This makes equidistant maps useful when one origin structures the question, as with radio range from an antenna, flight distance from a hub or proximity to a pole. Because the centre is part of the claim, moving it changes the set of distances that remain correct.

The same map can need more than one property

Real mapping tasks often contain competing needs: a reference map should keep the world recognisable, a flow map should not make routes unnecessarily confusing, and a statistical layer may need correct area. No projection label resolves those tensions on its own.

A compromise projection such as Winkel Tripel or Robinson can distribute several forms of distortion so that none dominates the overall world view. That is often useful for general reference, but it is not a fourth preserved property. Neither projection makes area, angle or distance exact everywhere.

The display and analytical needs can also be separated. A map may calculate polygon areas geodesically, present a global thematic overview in Equal Earth and use a Web Mercator local view for interaction. The important discipline is to avoid carrying a projection's valid property into a stage where it does not apply.

How to read projection claims critically

Before relying on a projection description, ask four questions:

What exactly is preserved? “Shape” may mean local angle; “distance” may mean distance only from a centre.
Where is it preserved? Some properties apply everywhere, others along standard lines or near a central meridian.
Over what extent? A projection can have negligible distortion within a city and severe distortion across a continent.
For which operation? A visually suitable display may still be a poor space for calculating area or distance.

Tissot's indicatrix makes these distinctions visible. Projected infinitesimal circles stay circular on a conformal map but change size; they keep equal area on an equal-area map but often become ellipses. On an equidistant map, their behaviour depends on location because the preserved distance applies in specified directions.

A practical selection rule

Choose the property by identifying the mistake that would be hardest for the reader to recover from.

If unequal area on the map would change the apparent importance of the data, use an equal-area projection.
If local bearings, angles or orientation are central, evaluate a conformal projection over the intended area of use.
If the map communicates range from a known centre or line, consider an equidistant projection designed around it.
If the map is primarily general reference, compare compromise projections as well as property-preserving options.

Then test the specific projection—not just its family—with the actual extent and content. “Equal area”, “conformal” and “equidistant” narrow the search; they do not finish it.

References

Map Projections: A Working Manual. US Geological Survey reference on preserved properties and distortion.
PROJ projection catalogue. Technical documentation for projection methods and their parameters.