A system for mapping the round Earth onto a flat surface is called a map projection. Every map you’ve ever seen uses one, because there’s no way to perfectly flatten a sphere without stretching, squishing, or tearing something. Map projections use mathematical formulas to convert locations on the globe into points on a flat plane, and each projection makes different trade-offs about what it gets right and what it distorts.
Alongside projections, coordinate systems like latitude and longitude give every spot on Earth a precise numerical address. Together, these tools form the foundation of everything from paper atlases to GPS navigation to Google Maps.
Why a Flat Map Can’t Be Perfect
Peel an orange and try to press the skin flat. It tears. That’s the fundamental problem cartographers face: a curved surface can’t be laid flat without distortion. When positions on a globe are transformed to positions on a flat grid, four types of distortion can occur: distortion of sizes, angles (shapes), distances, and directions. No single projection can preserve all four at once, so every map projection is a deliberate choice about which property matters most for the task at hand.
Cartographers visualize these trade-offs using a tool called the Tissot indicatrix, developed by French cartographer Nicolas Auguste Tissot in the nineteenth century. The idea is simple: imagine drawing identical circles all over the globe. Then project those circles onto the flat map. If they stay circular but change size, the map preserves shape but not area. If they become stretched ellipses that all cover the same area, the map preserves area but not shape. The pattern of circles and ellipses across the map reveals exactly where and how distortion creeps in.
Latitude, Longitude, and the Grid That Covers the Globe
Before you can project the Earth, you need a way to describe locations on it. That’s the job of the geographic coordinate system built from latitude and longitude. Latitude measures how far north or south you are from the equator, which sits naturally at the halfway point between the poles. Longitude measures how far east or west you are from the prime meridian, a line running pole to pole through Greenwich, England.
The equator has a physical basis, but the prime meridian is arbitrary. In 1884, representatives at the International Meridian Conference in Washington, D.C. chose a line running through the telescope at the Royal Observatory in Greenwich, largely because many nautical charts and time zones already used it as a starting point. Coordinates are measured in degrees, minutes, and seconds. Lines of latitude are always equally spaced, but lines of longitude are widest apart at the equator and converge until they meet at the poles.
Modern GPS relies on a refined version of this system called WGS84 (World Geodetic System 1984). It models the Earth not as a perfect sphere but as a slightly squished ellipsoid with a radius at the equator of 6,378,137 meters and a flattening ratio of about 1/298. That extra precision matters when you need accuracy down to centimeters rather than miles.
The Mercator Projection and Navigation
The Mercator projection, created in 1569, is probably the most famous map projection in history. Its defining feature: a straight line drawn anywhere on the map shows a true compass direction. That property made it indispensable for sailors, who could draw a line between two ports and read off the bearing they needed to follow.
The cost is severe size distortion near the poles. Greenland appears roughly the same size as Africa on a Mercator map, even though Africa is about 14 times larger. The U.S. Geological Survey notes that distances and areas on Mercator maps are “grossly distorted near the map’s polar regions.” This distortion fueled decades of criticism that Mercator maps make Europe and North America look disproportionately large compared to equatorial regions in Africa and South America.
Equal-Area Projections
Equal-area projections solve the size problem by ensuring that every region on the map occupies the correct proportion of space relative to every other region. If Brazil is 15 times the size of France in reality, it will be 15 times the size on the map too. The trade-off is that shapes get distorted, especially toward the edges. Landmasses can look stretched or compressed in unfamiliar ways.
The most prominent example is the Gall-Peters projection, which gained attention in 1973 when Arno Peters argued it was a fairer alternative to the Mercator. By showing countries at their true relative sizes, he contended, it corrected a visual bias that made wealthier northern nations look larger than poorer equatorial ones. The projection was endorsed by UNESCO, the National Council of Churches, and other organizations. Boston Public Schools began integrating Gall-Peters maps into classrooms in 2017. The shapes of continents look noticeably elongated near the equator and squashed near the poles, but every country’s area is accurate.
Compromise Projections
Rather than perfectly preserving one property, compromise projections aim to keep all four types of distortion at tolerable levels. Nothing is exactly right, but nothing is badly wrong either. These projections are popular for world maps in textbooks and atlases, where the goal is a balanced, visually appealing picture of the whole planet.
The most widely used compromise projection today is the Winkel Tripel. In 1995, National Geographic adopted it to replace the Robinson projection on its signature world maps, calling it “one of the most accurate representations of the round globe on flat paper.” It handles angles well across most of the map, though areas near the poles still show some distortion. If you’ve seen a world map in a classroom or magazine in the past three decades, there’s a good chance it was a Winkel Tripel.
Conic Projections for Mid-Latitude Regions
Not every map needs to show the whole world. When cartographers map a single country or region, they can pick a projection optimized for that area’s shape and location. Conic projections, which mathematically wrap a cone around the globe and unroll it, work especially well for mid-latitude regions that stretch primarily east to west. The Lambert conformal conic projection is the standard choice for mapping the contiguous United States, and it’s also used for other wide, mid-latitude landmasses like Russia and China. Distortion stays low along the latitudes where the cone contacts the globe and increases as you move north or south from that band.
UTM: A Grid System for Precise Measurement
For tasks that demand precise distance and position measurements, like military operations, engineering, and land surveys, the Universal Transverse Mercator (UTM) system divides the world into 60 north-south zones, each 6 degrees of longitude wide. The zones are numbered 1 through 60, starting at 180 degrees longitude and increasing eastward. Within each narrow zone, distortion is minimal because you’re only projecting a small slice of the Earth at a time.
UTM coordinates use meters rather than degrees, which makes it straightforward to calculate distances and areas. If you’ve ever seen a grid reference on a topographic map from the U.S. Geological Survey, you were looking at UTM coordinates.
How Web Maps Handle Projection
Google Maps, Bing Maps, and OpenStreetMap all use a variant called Web Mercator (technically EPSG:3857). It’s a simplified version of the classic Mercator projection, optimized for the way digital maps work: square tiles that load quickly and snap together seamlessly as you zoom in and out. NASA’s Earthdata system also provides imagery in this projection for integration with these platforms.
Web Mercator inherits the same size distortions as the original Mercator. Zoom out to see the whole world, and Antarctica looks enormous. But at the street level, where most people actually use these apps, distortion is negligible. The projection’s real advantage is computational efficiency: it makes the math behind panning, zooming, and routing fast enough to feel instant on your phone. When you pinch to zoom on a map app, you’re interacting with a projection system designed in 1569, adapted for a world its creator never imagined.