For very small study areas, it is sometimes acceptable to ignore projection, and to assume that the region of interest is comprised of a flat, two-dimensional surface. However, if the study region is larger than a few kilometres, or if information is to be included from data sources, e.g. mapsheets, which have been constructed with different projections, then a GIS needs to understand the projection used for each layer in order to avoid inaccuracies.

Projection consists of two main stages: first the surface of the earth is estimated through the use of a geometric description called an ellipsoid (sometimes, though not always correctly, referred to as a spheroid), and secondly the surface of this ellipsoid is projected on to a flat surface to generate the map. Ellipsoids are defined in terms of their equatorial radius (the semi-major axis of the ellipse) and by another parameter, such as the flattening, reciprocal flattening or eccentricity. However, as a user of GIS, the ellipsoid definition is usually uncomplicated to incorporate. Most of the ellipsoids which have been used to generate maps have names such as the 1830 'Airy' spheroid (used by the Ordnance Survey) or the 'International' or 'Hayford' ellipsoid of 1909, and it should be sufficient to provide the full name of the ellipsoid used (for a simple introduction to ellipsoids see Defence Mapping Agency 1984).

There are a huge variety of methods available for undertaking the projection itself. Since by their very nature projections are a compromise, each method produces a map with different properties. In a cylindrical projection, for example, the lines of latitude (parallels) of the selected ellipsoid are simply drawn as straight, parallel lines. In the resulting map the parallels become shorter with distance from the equator, and to maintain the right-angled intersections of the lines of latitude and longitude, the lines of longitude (meridians) are also drawn as parallel lines. This maintains the correct length of the meridians, at the expense of areas close to the poles which become greatly exaggerated in an east-west direction. A transverse cylindrical projection is created in the same manner, but the cylinder is rotated with respect to the parallels and is then defined by the meridian at which the cylinder touches the spheroid rather than the parallel.

The Mercator projection exaggerates the distance between meridians by the same degree as the lengths of the parallels, in order to obtain an orthomorphic projection. A transverse Mercator is similar, but based on the transverse cylindrical projection. There are also many other forms of projection which are not based on the cylinder, including conical projections (based on the model of a cone, placed with its vertex immediately above one of the poles) and entirely separate families of projections such as two-world equal area projections and zenithal projections.

Depending on the projection used, different parameters will need to be specified in order to define it. Basic projections are often modified through the use of correction factors. In transverse projections, for example, it is not uncommon for a scaling factor to be applied to the central meridian to correct for the east-west distortion of the projection itself. A projection may also use a false origin, which arbitrarily defines a point on the projection plane to be the point 0,0. False origins are normally used to ensure that all co-ordinates in the area of the projection have positive values.

All projections have limits beyond which one or more of their attributes will become too distorted. For example, the Transverse and Universal Transverse Mercator projections work well only for a narrow east-west width - around 6 degrees of longitude - beyond this limit the distortion increases rapidly. When choosing a map projection it is essential to check the details of both the capabilities and the limitations of any given projection method against the nature of the area of interest: size, extents, nature of use, etc.

Details of projection procedures can be found in a variety of standard texts, for example Bugayevsky and Snyder 1995; Snyder 1987; Evenden 1983; 1990. Standard software for specifying and undertaking cartographic projection is available for a variety of platforms. Probably the most flexible is the PROJ 4 product of the USGS discussed by Evenden 1990.

Geographical co-ordinates, expressed in angles of latitude and longitude are used to locate features upon the globe whereas planar Cartesian co-ordinate systems are used to locate features upon projected maps.

In a planar co-ordinate system, the relative positions of objects represented upon a given mapsheet can be specified using standard units of distance measured with respect to a fixed origin point. The precise characteristics of a given co-ordinate system depend heavily upon the projection used to generate the 2-dimensional representation; as a result coordinate systems are as numerous as projection systems.

For example, there are five primary coordinate systems in use in the US, a country with a very broad east-west extent. Some of these are based upon the properties of specific map projections and others on historical land division strategies (DeMers 1997: 63).

By contrast, a single planar co-ordinate system based upon the transverse Mercator projection is used for all recent mapping for Great Britain, which is elongated north-south but narrow east-west. The British National Grid uses the Airy spheroid for its datum, and its origin is located at 49 degrees North, 2 degrees West. There is a false origin defined at 400,000, -100,000 such that the central meridian is the Zero easting of the National Grid - which is also aligned to the 2 degree West meridian of Longitude. Additionally, the scale along the central meridian is 0.9996012717 (as opposed to the more normal scale of 0.9996 for the Transverse Mercator projection): this results in distances along the northing 180,000, almost exactly half way across Great Britain, being to true scale. The units of the National Grid are metres measured east and north from the origin. A similar Transverse Mercator projection, but with an origin further to the west, is used for Ireland.

It is important to realise that projections and the resultant planar co-ordinate systems vary across nations and through time. The British National Grid has only been in use since the 1940s. British mapping prior to this time was based upon the Cassini projection and used an independent datum for each county. This mapping is often termed the County Series. A problem common to all situations where multiple datums are in use for any one country is that features which cross the borders of the different datums may not match when the respective map sheets are brought together. This problem certainly exists in the pre-war British mapping and is also present in the State-Plane system in use in the US today.

As with the British Ordnance Survey, many national mapping agencies use local projections designed to suit the size and shape of the area covered by their maps.

The Universal Transverse Mercator (UTM) system is a planar projection where degrees of longitude and latitude form a rectangular grid. Since distortion tends to increase most markedly on either side of the central meridian with this projection, UTM is used for narrow north-south oriented zones.

The world is divided into zones each covering 6 degrees of longitude and numbered in an easterly direction from 1, centred on 177 degrees west, to 60, centred on 177 degrees east. Within each zone, a transverse Mercator projection is established with its origin at the intersection of the central meridian with the equator. The false origin is offset so that the central meridian is at 500,000 metres east. The false Northing is zero metres in the northern hemisphere and 10,000,000 metres in the southern hemisphere. The scaling factor on the central meridian is 0.99960.

Despite its world-wide applicability, UTM has some disadvantages. Different ellipsoids may be required in different parts of world, and transformations between zones are required when the area of interest covers more than one zone. The UK, for example, is mostly in zone 30, but areas east of the Greenwich meridian fall into zone 31. The US State-Plane co-ordinate system is an application of UTM.

The use of three-dimensional absolute co-ordinates from satellite positioning systems introduces further complications. These systems measure the relative positions of receiver and satellites using an 'Earth-Centred, Earth-Fixed' Cartesian co-ordinate system (ECEF). This system, which is aligned with the World Geodetic System 1984 (WGS 84) reference ellipsoid, has its origin close to the earth's centre of mass, its z axis parallel with the direction of the conventional terrestrial pole and its x axis passing through the intersection of the equator and the Greenwich meridian. Fortunately most receivers convert ECEF co-ordinates to WGS 84 latitude, longitude and height for output, and some will also perform transformations to other datums and co-ordinate systems, for example to the Great Britain National Grid.