Map Projection Overview
Peter H. Dana
These materials were developed by Peter H. Dana, Department of
Geography, University of Texas at Austin, 1995. These materials
used for study, research, and education in not-for-profit
If you link to or cite these materials, please credit the
H. Dana, The Geographer's Craft Project, Department of
Geography, The University
of Colorado at Boulder. These materials may not be copied to or
from another Web server without the author's express permission.
© 1999 Peter H. Dana. All commercial rights are reserved. If you
comments or suggestions, please contact the author or Kenneth E.
This page is available in a framed
version. For convenience, a Full
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
direction, scale, and area always result from this process. Some
minimize distortions in some of these properties at the expense
errors in others. Some projection are attempts to only
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)
(lines of latitude) intersect at right angles. Shape is
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
have the same proportional relationship to the areas on the
they represent, the map is an equal-area map.
Different map projections result in different spatial
Map projections fall into four general classes.
Cylindrical projections result from projecting a spherical
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
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
to the poles, the cylinder and resulting projection are
When the cylinder is at some other, non-orthogonal, angle
to the poles, the cylinder and resulting projection is
Conic projections result from projecting a spherical surface
onto a cone.
When the cone is tangent to the sphere contact is along a
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 a
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
latitude and longitude grids and other examples of that do not
the cylindrical, conic, or azimuthal categories
Selected Map Projections
Cylindrical Equal Area
Cylindrical Equal-Area projections have straight meridians and
the meridians are equally spaced, the parallels unequally
are normal, transverse, and oblique cylindrical equal-area
Scale is true along the central line (the equator for normal,
meridian for transverse, and a selected line for oblique) and
lines equidistant from the central line. Shape and scale
near points 90 degrees from the central line.
Behrmann Cylindrical Equal-Area
Gall's Stereographic Cylindrical
Gall's stereographic cylindrical projection results from
earth's surface from the equator onto a secant cylinder
the globe at 45 degrees north and 45 degrees south. This
distorts distance, shape, direction, and area.
The Peters projection is a cylindrical equal-area projection
area exaggerations in high latitudes by shifting the
to 45 or 47 degrees.
The Mercator projection has straight meridians and parallels
at right angles. Scale is true at the equator or at two
equidistant from the equator. The projection is often used for
because all straight lines on the map are lines of constant
The Miller projection has straight meridians and parallels
that meet at
right angles, but straight lines are not of constant azimuth.
areas are distorted. Directions are true only along the
equator. The projection
avoids the scale exaggerations of the Mercator map.
Oblique Mercator projections are used to portray regions along
Distances are true along a great circle defined by the tangent
by the sphere and the oblique cylinder, elsewhere distance,
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
Mercator (Alaska State Plane Zone 5001)
Transverse Mercator projections result from projecting the
a cylinder tangent to a central meridian. Transverse Mercator
often used to portray areas with larger north-south than
Distortion of scale, distance, direction and area increase
away from the
Many national grid systems are based on the Transverse
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
The false origin is 400 km west and 100 km north. Scale at
meridian is 0.9996. The first BNG designator defines a 500
km square. The
second designator defines a 100 km square. The remaining
define 10 km, 1 km, 100 m, 10 m, or 1 m eastings and
Grid 100 km Squares
The Universal Transverse Mercator (UTM) projection is used to
positions world-wide by dividing the surface of the Earth into
zones, each mapped by the Transverse Mercator projection with
meridian in the center of the zone. UTM zone numbers designate
longitudinal strips extending from 80 degrees South latitude
to 84 degrees
North latitude. UTM zone characters designate 8 degree zones
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
(with a 10,000km false northing for positions south of the
Pseudocylindrical projections resemble cylindrical projections,
and parallel latitude lines and equally spaced meridians, but
meridians are curves.
The Mollweide projection, used for world maps, is
equal-area. The central meridian is straight. The 90th
meridians are circular
arcs. Parallels are straight, but unequally spaced. Scale is
along the standard parallels of 40:44 N and 40:44 S.
Eckert IV Equal Area
The Eckert IV projection, used for world maps, is a
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.
Eckert VI Equal Area
The Eckert VI projection , used for maps of the world, is
and equal area. The central meridian and all parallels are
at right angles,
all other meridians are sinusoidal curves. Shape distortion
the poles. Scale is correct at standard parallels of 49:16
North and South.
The Robinson projection is based on tables of coordinates, not
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
only on the central meridian and the parallels. Often used in
with a larger north-south than east-west extent.
Albers Equal Area Conic
A conic projection that distorts scale and distance except
parallels. Areas are proportional and directions are true in
Used in the United States and other large countries with a
than north-south extent.
Direction, area, and shape are distorted away from standard
Used for portrayals of areas near to, but on one side of, the
Lambert Conformal Conic
The polyconic projection was used for most of the earlier USGS
quadrangles. The projection is based on an infinite number of
to an infinite number of parallels. The central meridian is
meridians are complex curves. The parallels are non-concentric
Scale is true along each parallel and along the central
Azimuthal equidistant projections are sometimes used to show
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
A straight line drawn through the center point is on a great
Azimuthal Equal Area
Orthographic projections are used for perspective views of
Area and shape are distorted. Distances are true along the
Aspect Orthographic Projection
Stereographic projections are used for navigation in polar
are true from the center point and scale increases away from
point as does distortion in area and shape.
Texas State-Wide Projection
In 1992, the Cartographic Standards Working Group proposed a
Map Projection Standard for the GIS Standards Committee of the
Council for the Department of Information Sciences.
Earlier maps had often used projections designed for the
The new projection was designed to allow state-wide mapping
with a minimum
of scale distortion. A Lambert Conformal Conic Projection was
with an origin at 31:10 North, 100:00 West and with standard
at 27:25 North and 34:55 North. For plane coordinate use a
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
ground-track of Landsat images. There is little distortion
along the ground-track
but only within the narrow band (about 15 degrees) of the
Bugayevskiy, Lev M. and John P. Snyder. 1995. Map
Projections: A Reference
Manual. London: Taylor and Francis.
Muehrcke, Phillip C. and Juliana O. Muehrcke. 1998. Map Use:
4th ed. Madison, WI: JP Publications.
Snyder, John P. 1987. Map projections: a working manual. USGS
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
Last revised 2014.9.11. References updated. KEF.