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Try pressing an orange peel flat: it splits, buckles, or leaves gaps. Mapping Earth has the same basic challenge. A map projection is the mathematical method used to transfer locations on Earth’s curved surface to a flat map. Every whole-Earth flat map changes some aspect of the globe, so the right projection depends on what the map needs to show.
Why can’t a round Earth be flattened perfectly?
A sphere curves in two directions; a plane is flat. When a broad area of the sphere is represented on a plane, something has to give: shapes, areas, distances, or directions change. A projection is a set of rules for making that conversion, whether the result is printed on paper or displayed on a screen.
As the U.S. Geological Survey (USGS) puts it in its FAQ, “No flat map can rival a globe in truly representing the surface of the entire Earth, so every flat map misrepresents the surface of the Earth in some way.” The FAQ was updated February 21, 2023. Read the USGS explanation of how map projections are used.
How does a map projection work?
One way to picture the process is to imagine transferring points from a globe onto a cylinder, cone, or plane, then unfolding that surface. The surface can be made flat, but the method used to transfer the globe’s locations determines where and how the map is distorted. This is a useful visualization, not a claim that map projections are simply literal shadows.
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A surface that can be cut and laid flat without stretching or creasing is called a developable surface. Making that surface flat does not remove the challenge of representing a curved Earth on it; the projection still determines the trade-offs. MathWorks explains map projections and developable surfaces, and DePaul’s course notes discuss the underlying geometry.
Which properties can a projection preserve?
“Accurate” is not a single quality in mapmaking. Projections may preserve one or more useful properties, but none preserves every property across the entire Earth.
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| What matters | What to look for | Trade-off to understand |
|---|---|---|
| Relative area | An equal-area projection | Other properties, such as shape, may be distorted. |
| Local shape and angles | A conformal projection | Preserving local angles does not preserve area or distance everywhere. |
| Distance | An equidistant projection suited to a specified center or line | “Equidistant” does not mean every distance between every pair of places is true. |
| Direction | A projection suited to the relevant navigation task | Direction may be useful while area and distance are significantly distorted elsewhere. |
For example, Mercator preserves direction in a particular sense, but greatly enlarges distances and areas near the poles. Equidistant projections preserve distances only from a selected center or along specified lines. Those qualifications matter when deciding whether a map is appropriate for a task. The USGS outlines these projection trade-offs.
How should you choose a projection?
- Define the map’s purpose. A map for comparing the sizes of countries has different needs from one intended to support navigation.
- Identify the property that matters most. Decide whether area, local shape, distance, or direction is the priority, and specify which distances or directions need to be useful.
- Consider the region and extent. A projection suitable for a small region may not suit a whole-world map. Distortion becomes more consequential as the map covers more of the globe; the USGS notes Transverse Mercator as an example for mapping a small high-latitude area.
- Make the choice visible. For a world map, state the projection or make its purpose clear so readers can interpret the apparent sizes and shapes appropriately.
Try the orange-peel demonstration
To see the problem for yourself, use an orange, a marker, scissors, and tape. National Geographic’s classroom activity also uses globes and maps to help students observe distortion. See National Geographic’s flattening-the-globe activity.
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- Draw a rough grid or a few simple continent shapes on the orange.
- Peel the orange, then try to press the peel flat. Notice where it tears, overlaps, buckles, or leaves gaps.
- Compare the peel with a globe and several flat maps. Look for changes in the shapes and apparent sizes of places.
This is a visual demonstration, not a precision measurement or proof of a particular projection. A globe is useful for comparison, but you do not need to buy one to understand the basic idea.
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