The Mercator Projection
Mercator projection explained — Gerardus Mercator's 1569 conformal cylindrical chart, the sec(φ) scale factor that inflates Greenland, and Web Mercator differences.
By Steve K.. Published . Last updated .
The Mercator projection is a conformal cylindrical map projection published by Gerardus Mercator in 1569. Its defining property is that any course of constant compass bearing (a rhumb line) plots as a straight line; the cost is sec(φ) scale-factor inflation toward the poles, with area distortion sec²(φ).
The Mercator projection is the most consequential map projection in history. It revolutionised marine navigation in the 16th century, dominated geography classrooms through the 20th, and underlies every slippy-map tile in the 21st via its spherical Web Mercator descendant. The wider projection landscape lives on /learn/what-is-a-map-projection; the transverse-cylindrical sibling on /learn/utm-coordinate-system. Its mathematics is also the canonical example of how map projections trade one property for another: Mercator perfectly preserves angles at every point on Earth, and in exchange brutally inflates area toward the poles. This article runs the numbers behind that trade-off, distinguishes classical (EPSG:3395) from Web Mercator (EPSG:3857), and covers the navigation properties that keep Mercator in operational use on every modern marine chart. The companion pillar /learn/what-is-a-map-projection covers projections in general.
The defining property: rhumb lines plot as straight lines
A rhumb line (also called a loxodrome) is a path on Earth's surface that crosses every meridian at the same angle. A ship setting a constant compass bearing and holding it follows a rhumb-line course. On a Mercator chart, every rhumb line is a straight line, which is why a 16th-century captain could draw a single straight pencil mark between two ports and read off the compass bearing to follow.
| Property | Mercator chart | Globe surface |
|---|---|---|
| Rhumb line | Straight line | Spiral toward the pole |
| Great circle (shortest path) | Curved arc | Straight line on the sphere |
| Meridians | Parallel vertical lines | Great circles converging at poles |
| Parallels | Parallel horizontal lines (uneven spacing) | Circles of decreasing circumference |
| Angles | Preserved exactly (conformal) | (reference) |
| Areas | Distorted by sec2(φ) | (reference) |
Mercator's rhumb-line property required the y-spacing of parallels
to increase with latitude in exact proportion to the cylindrical
projection's east-west stretching. The formula on the sphere is
y(φ) = R × ln(tan(π/4 + φ/2)); the ellipsoidal form (used by
EPSG:3395) substitutes the isometric latitude. Both formulas diverge
to infinity as latitude approaches ±90°, which is why no Mercator
map shows the geographic poles — they sit infinitely far from the
equator on the projection.
The Mercator distortion table
The scale factor at latitude φ is exactly sec(φ) for the spherical Mercator (the conformal property requires the same scale factor in both x and y at every point). Area-scale is sec2(φ).
| Latitude | Scale factor sec(φ) | Area distortion sec²(φ) | Visual effect |
|---|---|---|---|
| 0° (equator) | 1.000 | 1.0× | Truthful (the contact line) |
| 10° | 1.015 | 1.03× | Imperceptible |
| 20° | 1.064 | 1.13× | Slight |
| 30° | 1.155 | 1.33× | Slight enlargement (Cuba, India) |
| 40° | 1.305 | 1.70× | Noticeable (Iberia, Korea) |
| 45° | 1.414 | 2.0× | 2× area distortion |
| 50° | 1.556 | 2.42× | Strong (UK, Mongolia) |
| 60° | 2.000 | 4.0× | 4× distortion (Scandinavia, southern Greenland) |
| 70° | 2.924 | 8.55× | Severe (most of Greenland) |
| 80° | 5.759 | 33.16× | Greenland looks like a continent |
| 85° | 11.474 | 131.6× | Web Mercator clip latitude |
| 89° | 57.299 | 3,283× | Approaching infinity |
| 90° (pole) | ∞ | ∞ | Pole maps to infinity (never shown) |
The "Greenland looks like Africa" observation is sec2(70°) ≈ 8.6 doing its job: Greenland's 2.166 million km2 inflated 8.6× becomes ~18.6 million km2, comparable to South America's 17.84 million km2 — or roughly the area Africa occupies on the same Mercator world map (Africa is at much lower latitudes and barely distorted). On the actual globe, Africa is ~14× larger than Greenland by area.
Classical Mercator vs Web Mercator
The Mercator on a navigation chart and the Web Mercator on Google Maps are almost the same projection but differ on three operational points.
| Property | Classical Mercator (EPSG:3395) | Web Mercator (EPSG:3857) |
|---|---|---|
| Reference surface | WGS-84 ellipsoid | Sphere of radius a = 6,378,137 m |
| Projection formula | Ellipsoidal Mercator (isometric latitude) | Spherical Mercator (treats lat/lon as if on a sphere) |
| North-south displacement vs ellipsoidal | 0 m (reference) | Up to ~21 km at 85° latitude |
| Latitude clip | No fixed clip | ±85.0511287798° (= atan(sinh(π))) |
| Tile pyramid friendliness | Less so | Each zoom level is a square 2n × 2n grid |
| Use case | Official marine charts (IHO), high-accuracy work | Slippy-map tiles (Google, Mapbox, OSM, Bing) |
| Adopted by | IHO S-4 charts, NOAA charts | OGC TMS, Web Map Tile Service (WMTS) |
The ±85.0511° latitude clip is not arbitrary — it is the latitude at which the projected y-coordinate equals π times the equatorial radius (in unitless terms), producing a square map that divides cleanly into 2n × 2n tiles at zoom level n. Polar regions above that latitude are simply not visible on Web Mercator-based maps; every web mapping interface inherits the clip.
Why marine charts still use Mercator after 450 years
The Mercator projection has survived four centuries on operational marine charts despite the area distortion because the rhumb-line property is exactly what a magnetic-compass-equipped vessel needs.
| Navigation task | Why Mercator excels | The alternative |
|---|---|---|
| Setting a compass course | Constant bearing = straight line on chart | On an equal-area chart, a constant bearing is a curve |
| Reading a course bearing | Direct angle measurement from chart | Other projections need bearing tables |
| Plotting GPS positions | Latitude/longitude grid is rectilinear | Distorted on non-cylindrical projections |
| Distance estimation | Use latitude scale (1 arcmin = 1 NM) at the latitude of interest | Need per-projection scale calibration |
| Great-circle approximation | Plot a few rhumb-line legs along the GC route | Direct great-circle plotting (gnomonic charts) |
Modern marine practice plots the great-circle route on a gnomonic projection (where great circles are straight lines), reads off waypoints at convenient intervals, then transfers those waypoints onto a Mercator chart for the actual rhumb-line legs the helmsman steers. The IHO maintains both as standard chart series under IHO S-4 Regulations for International Charts and IHO S-66.
The Greenland problem in numbers
The visual inflation of Greenland on a Mercator world map is the most visible example of conformal-cylindrical area distortion. The real numbers:
| Region | Actual area (M km²) | Centroid latitude | sec²(φ) at centroid | Apparent area on Mercator (M km²) |
|---|---|---|---|---|
| Greenland | 2.166 | ~72° N | ~10.5 | ~22.7 |
| Africa | 30.37 | ~5° N | ~1.01 | ~30.7 |
| South America | 17.84 | ~15° S | ~1.07 | ~19.1 |
| Antarctica | 14.20 | ~85° S | ~131 | ~1,860 (usually cropped) |
| Russia | 17.10 | ~60° N | ~4.0 | ~68.4 |
| Australia | 7.69 | ~27° S | ~1.26 | ~9.7 |
| Brazil | 8.52 | ~10° S | ~1.03 | ~8.8 |
The mathematics is unambiguous: every country's apparent area on Mercator is its actual area multiplied by sec2(φ) at its centroid. Tropical and equatorial countries look approximately truthful; mid-latitude countries are noticeably enlarged; polar landmasses are wildly inflated. Antarctica is typically cropped because at sec2(85°) ≈ 131 the projection would otherwise consume more than half the map.
When Mercator is the right (and wrong) choice
| Right choice for | Wrong choice for |
|---|---|
| Marine navigation (ellipsoidal Mercator on IHO charts) | World thematic / political maps |
| Web slippy-map tiles (Web Mercator + WMTS) | Polar regions above ~80° (use UPS) |
| Low-latitude regional maps (distortion minimal within 30° of equator) | Equal-area work (density, populations, biomes) |
| Conformal mapping of equatorial regions | Regional surveying / engineering (use UTM) |
| Local shipping/aviation lanes | Continental thematic maps (use Albers or LAEA) |
A typical practitioner sees Mercator daily on three surfaces: every Google/Mapbox/OSM web map tile (Web Mercator); every IHO marine chart (ellipsoidal Mercator); and historical world maps still in classrooms (classical Mercator, increasingly being replaced by Winkel Tripel or Equal Earth in current curricula).
Common misconceptions
Related
- What Is a Map Projection?— The pillar — what projections are and why they distort
- The UTM Coordinate System— Transverse Mercator applied to 60 zones
- Projected Coordinate Systems— The family Mercator belongs to
- Distance Calculator— Vincenty geodesic distance — accurate regardless of display projection
- Methodology— How content is sourced and verified
Frequently asked questions
What is the Mercator projection?
The Mercator projection is a conformal cylindrical map projection published by Gerardus Mercator in 1569. It maps the curved Earth onto a flat plane by wrapping a cylinder around the equator and projecting points outward, then unrolling. The defining property is that rhumb lines (paths of constant compass bearing) appear as straight lines on the map — designed specifically to make marine navigation possible with a ruler and a compass.
Why is Greenland so big on Mercator maps?
The Mercator projection's scale factor at latitude φ is sec(φ) = 1/cos(φ). At the equator the scale is 1.0; at 60° it is 2.0; at 80° it is 5.76. Because area scales with the square of the linear factor, areas are magnified by sec²(φ). Greenland spans roughly 60°N to 83°N — its area gets magnified by an average factor of ~14, making it appear roughly the same visual size as Africa, even though Africa is in fact ~14 times larger.
Why does the Mercator projection cannot show the poles?
The y-coordinate formula y = R·ln(tan(π/4 + φ/2)) diverges to infinity as φ approaches ±90°. The poles are at infinite distance on a Mercator map. Practical Mercator maps truncate at some latitude near the poles — typically ±85.06° for Web Mercator (the exact value at which the projection becomes square) — and use Universal Polar Stereographic for polar coverage.
What is a rhumb line and why does Mercator preserve it?
A rhumb line — also called a loxodrome — is a path on the Earth that crosses every meridian at the same angle. Following a constant compass bearing produces a rhumb line. On a Mercator projection, rhumb lines appear as straight lines, which is the property that made the projection essential for pre-GPS marine navigation: a navigator could draw a straight line between two ports, read the bearing once, and steer that bearing all the way. The trade-off is that rhumb lines are not the shortest path (great-circle arcs are), so Mercator routes are slightly longer than optimal.
Is Mercator still used today?
Yes — for marine navigation (the original use case), for some weather maps in the tropical and mid-latitude bands, and as the basis of Web Mercator (EPSG:3857), the projection of every major web map. The classical ellipsoidal Mercator (EPSG:3395) is now mostly historical; Web Mercator is everywhere. For most other use cases — thematic mapping, polar work, equal-area display — Mercator is the wrong choice.
What is the difference between Mercator and Web Mercator?
Classical Mercator (EPSG:3395) uses the ellipsoidal Mercator math on the WGS-84 ellipsoid. Web Mercator (EPSG:3857) applies the spherical Mercator math to WGS-84 lat/lon as if they were spherical coordinates on a sphere of radius 6,378,137 m. The two differ by up to ~21 km of north-south displacement at 85° latitude. Web Mercator is what every web slippy-map tile uses; classical Mercator is what marine charts use.
Who invented the Mercator projection?
Gerardus Mercator (Gerhard Kremer), a Flemish cartographer, published the original Mercator world chart in 1569 as "Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata" — a 132 × 198 cm engraved map designed for marine navigation. The mathematical formulation of the projection wasn't fully published until Edward Wright did so in 1599. The original 1569 chart is preserved at the Maritime Museum Rotterdam.
Why does Mercator distort area but not shape?
Mercator is a *conformal* projection, meaning the scale factor at every point is the same in all directions — angles are preserved (small shapes stay shapes). To achieve this while flattening the convergent meridians, Mercator stretches the y-axis at the same rate as the x-axis at every latitude. The x-axis stretches by sec(φ); the y-axis must too. Both stretches multiply to give the sec²(φ) area distortion that inflates polar landmasses.
Sources
- USGS — Map Projections — A Working Manual (Snyder, 1987, PP 1395) · https://pubs.usgs.gov/pp/1395/report.pdf · Accessed .
- Library of Congress — Mercator’s 1569 world map — Nova et Aucta Orbis Terrae Descriptio · https://www.loc.gov/item/2003683482/ · Accessed .
- EPSG — EPSG:3395 — WGS 84 / World Mercator · https://epsg.org/crs_3395/WGS-84-World-Mercator.html · Accessed .
- NOAA NGS — NGS projection references · https://geodesy.noaa.gov/ · Accessed .
Cite this article
APA format:
Steve K. (2026). The Mercator Projection. Coordinately. https://coordinately.org/learn/mercator-projection
BibTeX:
@misc{coordinately_themercatorprojection_2026,
author = {K., Steve},
title = {The Mercator Projection},
year = {2026},
publisher = {Coordinately},
url = {https://coordinately.org/learn/mercator-projection},
note = {Accessed: 2026-06-05}
}