How map projections distort the world

Map projections distort the world because you cannot flatten a curved surface onto a plane without changing some geographic property. Different projection families trade off area, shape, distance and direction in predictable ways; the right projection depends on what you want to measure or show. This article explains how those trade-offs work, how distortion looks in practice, and how to pick a projection for common mapping tasks.

Why distortion is unavoidable

The Earth is roughly a curved surface. When you try to represent that surface on a flat map, geometry forces compromises: you can preserve some properties but not all at once. For example, a projection that keeps angles local (conformal) will necessarily distort areas, while an equal-area projection will change shapes to preserve relative surface sizes.

That trade-off is not a matter of bad design but of mathematics. Every projection introduces distortion; cartographers choose which distortions are acceptable for the map's purpose.

What usually changes: the four basic properties

Mapmakers talk about four properties that projections can preserve or distort. Understanding these helps you read and choose maps.

• Area - whether regions keep their relative sizes. Equal-area projections preserve this.
• Shape - local angles and the appearance of small features. Conformal projections preserve shape locally.
• Distance - whether true distances are preserved from point to point. Only some projections preserve distances along particular lines or from a center point.
• Direction - whether bearings are accurate. Some projections preserve azimuths from a point.

Common projection families and how they trade area and shape

Different families make different choices about which property to prioritize. Here are the families you will encounter most often.

Conformal projections

Conformal projections preserve local angles and shapes of small features. This is useful when you need accurate local geometry, for example in navigation or some types of urban planning. The familiar Mercator is conformal and keeps compass bearings easy to plot on a straight line; read more about that in Mercator explained.

Equal-area projections

Equal-area projections preserve the relative sizes of areas. They are the right choice when you want fair comparisons of land area, population density, or resource distribution. Read a focused comparison in Area vs shape.

Equidistant and azimuthal

Equidistant projections preserve distances from certain points or along certain lines, while azimuthal projections preserve direction from a central point. These are useful for radio-planning, flight routes from a hub, or polar maps.

How distortion appears: patterns you can spot

Distortion is not uniform; projection families produce characteristic patterns. You will see systematic stretching, compression, or skewing across the map.

One useful tool to visualise these changes is Tissot's indicatrix: a grid of small circles projected onto the map that become ellipses showing local distortion. That tool makes distortion visible at a glance; see an explanation in Visualising distortion.

Typical examples

• Mercator-style projections stretch high latitudes, making Greenland and Antarctica look much larger than they are.
• Some equal-area projections look squashed near the equator and expanded near the poles to keep areas correct.
• Azimuthal maps centred on a point preserve direction from that point but distort shape farther away.

A practical workflow: choose a projection in 6 steps

This step-by-step process helps you pick a projection for a concrete mapping task.

1. Define the map's primary purpose: comparison of area, navigation, distance measurements, or general reference.
2. Decide the geographic extent: global, continental, national, regional, or local. Extent changes which distortions are tolerable.
3. If area comparison matters, prioritise an equal-area projection; if preserving local shape and angles matters, pick a conformal option.
4. Consider the map's audience and conventions: some domains expect a certain projection (for example, navigation charts often use Mercator-like projections).
5. Test two candidate projections with your actual data. Use Tissot indicatrices or overlay a grid to inspect distortion visually.
6. Document your choice and why you made it. Always show the projection name in the map's metadata or legend.

For web maps and interactive applications, follow practical guidance in Choosing projections.

Worked example: mapping population density for a country

Suppose you need a choropleth that fairly compares population density across regions within a country. Here is a short worked example of the decision process.

1. Goal: compare area-normalised quantities (people per km2). Preserve area to avoid misleading region sizes.
2. Extent: national. Large-scale equal-area projections or locally tuned projections reduce distortion across the country.
3. Pick an equal-area projection appropriate for the latitude band or use a national government standard if one exists.
4. Render your choropleth and overlay a graticule or Tissot indicatrices to verify that areas look proportional.
5. Include projection information in the map caption so readers understand the choice.

Common mistakes and how to avoid them

Beginners often make predictable errors. Avoid these to keep your maps honest and useful.

• Choosing Mercator for a thematic map of area comparisons - this exaggerates high-latitude regions.
• Using a global projection for a small, local dataset which introduces unnecessary distortion - switch to a local projection.
• Failing to state the projection - readers cannot judge distortion without that metadata.
• Presuming "visually pleasing" equals "geographically correct" - some designs sacrifice accuracy for aesthetics without disclosure.

Quick reference checklist before publishing a map

• Have I stated the projection and its EPSG or common name?
• Does the projection preserve the property most important for my message (area, shape, distance, or direction)?
• Have I inspected distortion visually, for example with Tissot indicatrices or a graticule?
• Would a different projection change the map's interpretation? If yes, note that in the caption.

Closing: read projections with intent

Projections change what a map communicates. They do not "lie" so much as prioritise certain truths over others. Learn the basic trade-offs—area, shape, distance, direction—inspect distortion visually, and choose the projection that supports your map's purpose. When in doubt, document the choice and test at least one alternative so readers can judge whether the map is fit for the task.