Map Projection Overview
Peter H. Dana
These materials may be used for study, research, and education in not-for-profit
applications. All commercial rights are reserved. Please credit the author,
Peter H. Dana, The Geographer's Craft Project, Department of Geography,
The University of Texas at Austin. Copyright © 1999 Peter H. Dana.
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version. For convenience, a Full
Table of Contents is provided.
- Map projections are attempts to portray the surface of the earth or
a portion of the earth on a flat surface. Some distortions of conformality,
distance, direction, scale, and area always result from this process. Some
projections minimize distortions in some of these properties at the expense
of maximizing errors in others. Some projection are attempts to only moderately
distort all of these properties.
- When the scale of a map at any point on the map is the same in any
direction, the projection is conformal. Meridians (lines of longitude)
and parallels (lines of latitude) intersect at right angles. Shape is preserved
locally on conformal maps.
- A map is equidistant when it portrays distances from the center of
the projection to any other place on the map.
- A map preserves direction when azimuths (angles from a point on a line
to another point) are portrayed correctly in all directions.
- Scale is the relationship between a distance portrayed on a map and
the same distance on the Earth.
- When a map portrays areas over the entire map so that all mapped areas
have the same proportional relationship to the areas on the Earth that
they represent, the map is an equal-area map.
- Different map projections result in different spatial relationships
- Map projections fall into four general classes.
- Cylindrical projections result from projecting a spherical surface
onto a cylinder.
- When the cylinder is tangent to the sphere contact is along a great
circle (the circle formed on the surface of the Earth by a plane passing
through the center of the Earth)..
- In the secant case, the cylinder touches the sphere along two lines,
both small circles (a circle formed on the surface of the Earth by a plane
not passing through the center of the Earth).
- When the cylinder upon which the sphere is projected is at right angles
to the poles, the cylinder and resulting projection are transverse.
- When the cylinder is at some other, non-orthogonal, angle with respect
to the poles, the cylinder and resulting projection is oblique.
- Conic projections result from projecting a spherical surface onto a
- When the cone is tangent to the sphere contact is along a small circle.
- In the secant case, the cone touches the sphere along two lines, one
a great circle, the other a small circle.
- Azimuthal projections result from projecting a spherical surface onto
- When the plane is tangent to the sphere contact is at a single point
on the surface of the Earth.
- In the secant case, the plane touches the sphere along a small circle
if the plane does not pass through the center of the earth, when it will
touch along a great circle.
- Miscellaneous projections include unprojected ones such as rectangular
latitude and longitude grids and other examples of that do not fall into
the cylindrical, conic, or azimuthal categories
Selected Map Projections
- Cylindrical Equal Area
- Cylindrical Equal-Area projections have straight meridians and parallels,
the meridians are equally spaced, the parallels unequally spaced. There
are normal, transverse, and oblique cylindrical equal-area projections.
Scale is true along the central line (the equator for normal, the central
meridian for transverse, and a selected line for oblique) and along two
lines equidistant from the central line. Shape and scale distortions increase
near points 90 degrees from the central line.
- Behrmann Cylindrical Equal-Area
- Gall's Stereographic Cylindrical
- Gall's stereographic cylindrical projection results from projecting
the earth's surface from the equator onto a secant cylinder intersected
by the globe at 45 degrees north and 45 degrees south. This projection
moderately distorts distance, shape, direction, and area.
- The Peters projection is a cylindrical equal-area projection that de-emphasizes
area exaggerations in high latitudes by shifting the standard parallels
to 45 or 47 degrees.
- The Mercator projection has straight meridians and parallels that intersect
at right angles. Scale is true at the equator or at two standard parallels
equidistant from the equator. The projection is often used for marine navigation
because all straight lines on the map are lines of constant azimuth.
- Miller Cylindrical
- The Miller projection has straight meridians and parallels that meet
at right angles, but straight lines are not of constant azimuth. Shapes
and areas are distorted. Directions are true only along the equator. The
projection avoids the scale exaggerations of the Mercator map.
- Oblique Mercator
- Oblique Mercator projections are used to portray regions along great
circles. Distances are true along a great circle defined by the tangent
line formed by the sphere and the oblique cylinder, elsewhere distance,
shape, and areas are distorted. Once used to map Landsat images (now replaced
by the Space Oblique Mercator), this projection is used for areas that
are long, thin zones at a diagonal with respect to north, such as Alaska
State Plane Zone 5001.
Mercator (Alaska State Plane Zone 5001)
- Transverse Mercator
- Transverse Mercator projections result from projecting the sphere onto
a cylinder tangent to a central meridian. Transverse Mercator maps are
often used to portray areas with larger north-south than east-west extent.
Distortion of scale, distance, direction and area increase away from the
- Many national grid systems are based on the Transverse Mercator projection
- The British National Grid (BNG) is based on the National Grid System
of England, administered by the British Ordnance Survey. The true origin
of the system is at 49 degrees north latitude and 2 degrees west longitude.
The false origin is 400 km west and 100 km north. Scale at the central
meridian is 0.9996. The first BNG designator defines a 500 km square. The
second designator defines a 100 km square. The remaining numeric characters
define 10 km, 1 km, 100 m, 10 m, or 1 m eastings and northings.
National Grid 100 km Squares
- The Universal Transverse Mercator (UTM) projection is used to define
horizontal, positions world-wide by dividing the surface of the Earth into
6 degree zones, each mapped by the Transverse Mercator projection with
a central meridian in the center of the zone. UTM zone numbers designate
6 degree longitudinal strips extending from 80 degrees South latitude to
84 degrees North latitude. UTM zone characters designate 8 degree zones
extending north and south from the equator.
- Eastings are measured from the central meridian (with a 500km false
easting to insure positive coordinates). Northings are measured from the
equator (with a 10,000km false northing for positions south of the equator).
- Pseudocylindrical projections resemble cylindrical projections, with
straight and parallel latitude lines and equally spaced meridians, but
the other meridians are curves.
- The Mollweide projection, used for world maps, is pseudocylindrical
and equal-area. The central meridian is straight. The 90th meridians are
circular arcs. Parallels are straight, but unequally spaced. Scale is true
only along the standard parallels of 40:44 N and 40:44 S.
- Eckert Projections
- Eckert IV Equal Area
- The Eckert IV projection, used for world maps, is a pseudocylindrical
and equal-area. The central meridian is straight, the 180th meridians are
semi-circles, other meridians are elliptical. Scale is true along the parallel
at 40:30 North and South.
IV Equal Area
- Eckert VI Equal Area
- The Eckert VI projection , used for maps of the world, is pseudocylindrical
and equal area. The central meridian and all parallels are at right angles,
all other meridians are sinusoidal curves. Shape distortion increases at
the poles. Scale is correct at standard parallels of 49:16 North and South.
VI Equal Area
- The Robinson projection is based on tables of coordinates, not mathematical
formulas. The projection distorts shape, area, scale, and distance in an
attempt to balance the errors of projection properties.
- Sinusoidal Equal Area
- Sinusoidal equal-area maps have straight parallels at right angles
to a central meridian. Other meridians are sinusoidal curves. Scale is
true only on the central meridian and the parallels. Often used in countries
with a larger north-south than east-west extent.
- Albers Equal Area Conic
- A conic projection that distorts scale and distance except along standard
parallels. Areas are proportional and directions are true in limited areas.
Used in the United States and other large countries with a larger east-west
than north-south extent.
- Equidistant Conic
- Direction, area, and shape are distorted away from standard parallels.
Used for portrayals of areas near to, but on one side of, the equator.
- Lambert Conformal Conic
- The polyconic projection was used for most of the earlier USGS topographic
quadrangles. The projection is based on an infinite number of cones tangent
to an infinite number of parallels. The central meridian is straight. Other
meridians are complex curves. The parallels are non-concentric circles.
Scale is true along each parallel and along the central meridian.
- Azimuthal Equidistant
- Azimuthal equidistant projections are sometimes used to show air-route
distances. Distances measured from the center are true. Distortion of other
properties increases away from the center point.
- Lambert Azimuthal Equal Area
- The Lambert azimuthal equal-area projection is sometimes used to map
large ocean areas. The central meridian is a straight line, others are
curved. A straight line drawn through the center point is on a great circle.
Azimuthal Equal Area
- Orthographic projections are used for perspective views of hemispheres.
Area and shape are distorted. Distances are true along the equator and
Aspect Orthographic Projection
- Stereographic projections are used for navigation in polar regions.
Directions are true from the center point and scale increases away from
the center point as does distortion in area and shape.
- Unprojected Maps
- Texas State-Wide Projection
- In 1992, the Cartographic Standards Working Group proposed a Texas
State-Wide Map Projection Standard for the GIS Standards Committee of the
GIS Planning Council for the Department of Information Sciences.
- Earlier maps had often used projections designed for the continental
- The new projection was designed to allow state-wide mapping with a
minimum of scale distortion. A Lambert Conformal Conic Projection was proposed
with an origin at 31:10 North, 100:00 West and with standard parallels
at 27:25 North and 34:55 North. For plane coordinate use a false Easting
and Northing of 1,000,000 meters were defined for the origin.
- Space Oblique Mercator
- The Space Oblique Mercator is a projection designed to show the curved
ground-track of Landsat images. There is little distortion along the ground-track
but only within the narrow band (about 15 degrees) of the Landsat image.
- Muehrcke, Phillip C. 1986. Map use: reading, analysis, interpretation.
Madison, WI: JP Publications.
- Snyder, John P. 1987. Map projections: a working manual.USGS
Professional Paper 1395. Washington, DC: United States Government Printing
- Many of the maps on this page were produced using MapInfo's MapInfo
and Golden Software's MapViewer and Surfer for Windows.