How much does the Mercator projection distort size?

Why Mercator stretches

Mercator was designed so that any compass heading plots as a straight line. To keep angles true, the map must stretch north to south by the same amount it stretches east to west. On a globe, meridians converge at the poles. On the Mercator map they are parallel, so every parallel is drawn as long as the equator. The parallel at latitude φ is really cos φ times the equator's length, so the map stretches it by 1/cos φ, and stretches north-south distance by the same factor.

Web maps, including the interactive maps on this site, use Web Mercator, which has the same scale behavior. That is why Greenland, Alaska and northern Canada look enormous on a phone.

Scale factor by latitude

Worked example: Alaska vs Texas

Census land area gives Alaska 571,242 square miles and Texas 261,259, a ratio of 2.19. Averaging each state's county internal points, weighted by land area, puts Alaska's land at about 63.7° N and Texas at about 31.4° N.

Mercator inflates area by 5.10× at 63.7° and by 1.37× at 31.4°. Multiply the true ratio by the ratio of those factors and Alaska appears about 8.1 times the size of Texas on the map. The result is approximate, since each state spans many latitudes, but it shows why Alaska looks larger than it is. The county size comparison tool moves outlines on the sphere, so shapes keep their true size as you drag them.

Scale at five capitals

Projections that keep area

Equal-area projections keep sizes true and give up shape or angle. The Albers equal-area conic is a common choice for maps of the contiguous states, and the state and county maps on this site are drawn with it, with Alaska and Hawaii moved into insets. On those maps, a county twice as large on the ground covers twice the paper.

No flat map keeps both area and shape everywhere. Pick the property the map needs. For navigation keep angles, for comparing sizes keep area, and for measuring distances use the globe: see great circle vs rhumb line.

Why a Mercator scale bar only works at one latitude

A scale bar on a Mercator map is true only along the latitude it was drawn for. A ruler length that covers 100 miles at Honolulu covers only 56 miles at Juneau, because the map stretches Juneau's latitude by 1.90× and Honolulu's by 1.07×. Web maps usually recompute the scale bar as you pan, but on a zoomed out view it is still wrong for most of the screen. For distance, trust the measuring tools rather than the ruler.

See the distortion yourself

Drag a county in the county size comparison tool from Texas toward Alaska. The outline grows on screen as it moves north, even though the tool keeps its true size on the sphere. The growth you see is exactly the area scale factor in the table above. The country size comparison does the same for countries.