Mercator’s Map: The Projection That Shaped How We See the World

A flat map of a round planet must lie somewhere. The map you probably know best, the one on classroom walls and in your phone, keeps compass directions true but makes places near the poles look huge. Greenland looks as big as Africa, even though Africa is about fourteen times larger. This guide explains why Gerardus Mercator drew his map in 1569, how the stretching works, and what it means for the way we see the world.

The problem every map has

Peel an orange and try to press the skin flat. It will tear or stretch. The surface of a sphere cannot be flattened without distorting something: shape, area, distance or direction. Mapmakers choose which one to keep and which to give up. That choice is called a projection.

Why sailors wanted Mercator’s map

In the 1500s, European ships crossed oceans using a compass. A ship that keeps a steady compass bearing sails along a curve on a globe called a rhumb line. On older flat maps that curve was hard to draw and hard to follow. Mercator found a way to stretch the map so that every rhumb line becomes a straight line. A navigator could now draw a line between two ports, read the angle against the compass rose, and sail that bearing.

The price was area. To keep angles correct, the map stretches east-west and north-south by the same amount at each latitude, and that stretch grows quickly toward the poles. The poles themselves can never be shown, because the stretch becomes infinite.

Try it: how much does the map stretch

Move the slider to a latitude. The circle shows a circle of the same real size drawn on a Mercator map at that latitude. The numbers show how many times larger lengths and areas look.

The maths is short. At latitude φ the stretch in length is 1 divided by cos φ, called secant φ. Area grows by the square of that. Here is the table in Python, with output I actually ran.

import math
for lat in (0, 13, 28, 45, 60, 72, 80, 85):
    p = math.radians(lat)
    y = math.log(math.tan(math.pi/4 + p/2)) + 0.0
    s = 1/math.cos(p)
    print(f"{lat:>3}  y={y:5.2f}  length x{s:5.2f}  area x{s*s:6.1f}")

  0  y= 0.00  length x 1.00  area x   1.0
 13  y= 0.23  length x 1.03  area x   1.1
 28  y= 0.51  length x 1.13  area x   1.3
 45  y= 0.88  length x 1.41  area x   2.0
 60  y= 1.32  length x 2.00  area x   4.0
 72  y= 1.84  length x 3.24  area x  10.5
 80  y= 2.44  length x 5.76  area x  33.2
 85  y= 3.13  length x11.47  area x 131.6

Greenland sits mostly between 60 and 83 degrees north, where areas are exaggerated roughly four to over thirty times. Africa straddles the equator, where stretch is almost nothing. That is why they look alike on the map even though Africa’s real area, about 30.4 million square kilometres, is about fourteen times Greenland’s 2.2 million.

The history of the map

Mercator also gave us the word atlas for a book of maps. His son Rumold published a collection after his death in 1594. The map for sailors, though, remained his best-known work.

Which projection should you use

India and the mapping of the subcontinent

Mapping India was one of the largest scientific projects of the 19th century. The Great Trigonometrical Survey began in 1802 under William Lambton, using a chain of precise triangles measured across the land. Later George Everest led it, and Indian surveyors such as Radhanath Sikdar did the maths and fieldwork. Sikdar is credited with recognising that Peak XV was the highest mountain in the world, a result announced in 1856. The mountain was later named after Everest.

On a Mercator map India sits near the equator, so it is only mildly stretched: Chennai is about 3 percent longer in length, and Delhi about 14 percent. Himalayan ranges around 35 degrees north are stretched more, about 22 percent in length. Today the Survey of India issues official maps, and maps published in India must follow its outer boundary.

Mind map: maps and projections

Myths worth correcting

• Myth: Mercator wanted to make Europe look big. Fact: he designed it for navigation. The side effect on size was a known cost.
• Myth: The Mercator map is wrong. Fact: it is correct for angles. It is just not the right tool for comparing area.
• Myth: Equal-area maps are always better. Fact: they distort shapes, so each map suits a job.

Frequently asked questions

Keep reading

Sources

• Mercator projection, Encyclopaedia Britannica, overview of the projection
• Gerardus Mercator, Encyclopaedia Britannica, life and the 1569 map
• Great Trigonometrical Survey, Britannica, survey of India
• Radhanath Sikdar, Wikipedia, Peak XV calculation

Facts were cross-checked against these pages and rewritten in our own words. Stretch figures are calculated from the standard formulas.