# Map Projections

The Earth is a spheroid - it is round like a ball or sphere but flattened by slightly by the centrifugal force of rotation. The Earth has a circumference of around 24,900 miles, but is around 27 miles wider than it is tall.

The Earth exists in three-dimensions but, other than globes, most representations of the earth, such as printed maps or web maps, are two dimensional. A projection is a set of mathematical transformations used to represent the three-dimensional world in two dimensions.

This tutorial introduces some fundamental concepts about projections that will be useful when choosing projections for your GIS projects.

## Coordinate Systems

The process of representing the three-dimensional world as two-dimensional visualizations requires a sequence of steps.

1. The lumpy surface of the earth is approximated with a simplified representation called a geoid.
2. A smooth mathematical ellipsoid or spheroid representation of that geoid that is used as the reference for latitude and longitude degrees. This reference system is called a geodetic datum, often just called a datum for convenience.
3. A datum defines a geographic coordinate system of latitudes and longitudes that indicates where locations are on the surface of the planet. Because different datums place their ellipsoids in slightly different places, a single latitude and longitude can refer to different places depending on which datum is used.
4. Finally, a set of mathematical transformations are performed on the three-dimensional latitudes and longitudes to indicate two-dimensional X and Y locations where features are drawn on the paper map or computer display. Those X and Y locations make up a projected coordinate system.

The science of creating geoids is called geodesy or geodetics. Geodetic engineers measure three fundamental properties of the earth. Because these properties are constantly changing (albeit in often subtle ways), geodetic engineers always have something to do in support of the earth sciences.

• Geometric shape
• Orientation in space
• Gravity field

There are dozens of different datums that have been developed over the past century to best fit a datum to specific parts of the earth using the technology of the time. In the United States you will commonly encounter these datums:

• The World Geodetic System from 1984 (WGS 84) is used by the Global Positioning System (GPS), and is the datum you will encounter most frequently.
• The North American Datum of 1983 (NAD 83) is commonly used with state and local data in the US.
• The North American Datum of 1927 (NAD 27) is an older version of NAD83 that you may encounter with old maps.

GIS software can transform data created with one geographic coordinate system into another, and when you are just visualizing data on a simple map, geographic coordinate systems are generally not a concern. However, there are times you need to pay attention to geographic coordinate systems:

• When selecting projections from multiple variants
• When combining data with different / uncertain geographic coordinate systems on the same map and the data doesn't overlay correctly
• When working on engineering or surveying projects where high accuracy is required.

## Coordinate System ID Numbers

Projections are often named after the cartographers that developed them. While some common projections have names that are generally understood (like spherical mercator), a name is usually not specific enough to indicate exactly which projection you want to use.

For example, although the Mercator is a well known general type of projection, different Mercator projections have different parameters depending on how they wrap the world in different ways (transverse, oblique) at different places (central meridian) and use different coordinate units.

Most coordinate systems can be specifically identified with a WKID (well-known identifier). There are two different sets of WKID numbers, so you need both the WKID and the name of the authority that defines what those numbers means:

• EPSG: The European Petroleum Survey Group created a numbered registry of projections starting in 1985. While the EPSG became part of the International Association of Oil and Gas Producers in 2005, the EPSG name was retained for convenience. One issue with this numbering system is that there is not a clear structure to the numbering scheme, the same projection can have different numbers.
• ESRI is the maker of ArcGIS Pro software and, arguably, the dominant GIS company in the world. For projections that do not have EPSG ID numbers, ESRI defines its own set of numbers for use in its software.

You can look up WKID numbers at:

For example: the details for the Robinson projection listed in ArcGIS Pro show that projection is based on a WGS 1984 geographic coordinate system (EPSG ID 4326) and the projected coordinate system is ESRI ID 54030.

## Common World Projected Coordinate Systems

There are dozens of different types of projections. When you consider that many of those projections have parameters that can be varied depending on the part of the earth you wish to focus on, the number of possible projections is infinite.

However, there are a much more limited number of projections that are commonly used. The following are some North-America-centric suggestions that can give you a good starting point in seeking an appropriate projection for your map. A much longer list of world projections is available here.

### World Mercator

Mercator is one of the oldest and most commonly seen projections. It was devised by the Flemish cartographer Gerardus Mercator (1512-1594) during the great age of European exploration, and as such it is conformal (preserves direction) in order to facilitate naval navigation.

The primary disadvantage of the Mercator is that it makes areas close to the poles like Greenland look much larger than they really are. This is called the "Greenland Problem."

The Mercator projection is a cylindrical projection, with a developable surface equivalent to wrapping the map as a cylinder around the earth.

### Spherical Mercator (Web Mercator)

Spherical Mercator is a variation of the Mercator projection that mathematically represents the world as a sphere rather than an ellipsoid to make calculations easier. This is the projection used by almost all web maps.

Because the world is slightly flattened, this spherical representation causes the map to be inaccurate when mapping large areas closer to the poles. However, that is not usually a major problem with a web mapping app like Google Maps that is used in lower latitudes for mundane tasks like finding sushi restaurants.

### Robinson Projection

The Robinson projection is a compromise projection developed by Arthur Robinson in 1964. The Robinson projection solved the "Greenland Problem" by representing the country closer to its actual size than the Mercator projection. The Robinson projection is considered by many to be visually appealing and in 1988 was adopted by the National Geographic Society for some of its world maps in place of the older Van der Grinten projection.

### Winkel Tripel

Winkel Tripel is another compromise projection devised by Oswald Winkel in 1921 that strives to represent the whole world while minimizing distortion of area, direction and distance (tripel means three in German). This is the projection used for maps by the National Geographic Society and many educational publishers.

### McArthur's Universal Corrective Map

McArthur's Universal Corrective Map is one of a number of alternative projections intended to provoke viewers to critically examine assumptions about maps. It is a variant on a Mercator projection by Australian cartographer Stuart McArthur that debuted in 1979 with a reversal of north and south.

There is, of course, no geological or astrophysical reason why north should be up, and the reversal of the poles asks us to call into question the biases inherent to a traditional north-up orientation.

### Unprojected Longitude / Latitude

Since longitude and latitude represent x/y coordinates, they can be directly graphed on a grid, and this is the default when you open an unprojected feature class in ArcGIS Pro. However, because longitudes are closer together the further you move away from the equator, the shapes of areas are flattened and expanded the further you move away from the equator.

Equirectangular (unprojected) longitude and latitude is useful for diagnosing problems with data, but should not be used in any professional presentation, as it implies carelessness or ignorance of cartographic principles and standards.

## Common Large Country and Continent Projected Coordinate Systems

### Albers Equal Area Conic

Albers Equal Area Conic is a common projection for maps of the continental United States that has historically been used by the United States Geological Society (USGS). It was developed by Heinrich C. Albers in 1805.

This is an example of a conic projection that is equivalent to wrapping the developable surface as a cone around the planet in a way that intersects the surface of the earth in one or two places, which are called standard parallels. This projection is an equal-area projection preserves area while slightly distorting shape. The selection of standard parallels can be based on which part of the earth is the point of focus.

### Lambert Conformal Conic

The Lambert Conformal Conic is another conic projection commonly used for the continental United States. While it distorts area, it preserves shapes better, and since it preserves angles (conformal) it is commonly used for aeronautical charts since a straight line on the map approximates the shortest-path great-circle distance between two points. It was first developed an published by Swiss cartographer Johann Heinrich Lambert in 1772.

## Common Local Projected Coordinate Systems

While projections for world or country maps are primarily focused on presentation or navigation, projections at the local level are more important for the ability to accurately find specific locations and measure distances, such as when surveying property lines or engaging in military activity.

### State Plane Coordinate System

The State Plane Coordinate System is a set of projections commonly used by local and state governments in the USA.

There are 124 different zones in different parts of the US. These zones are based on the shapes of the states and are designed to maximize the amount of area in each zone while minimizing distortion. The small size of these zones means that distortion of distance can be greatly minimized to 1 part in 10,000. You can measure a distance of two miles within around a foot of accuracy

See this tutorial for more information on how to select a projection from the state plane coordinate system.

### Universal Transverse Mercator

Universal Transverse Mercator (UTM) is a coordinate system based on the Mercator projection and used as an alternative to latitude and longitude. It was devised by the US Army Corps of Engineeers in the 1940s to make land navigation easier and is still used as the basis for the military's Military Grid Reference System.

Unlike the State Plane Coordinate System, this set of projections covers the world, as befits an organization like the US military that has operations all over the world.

The world is divided into zones and the coordinates within each zone are specified in meters. Because the projection preserves distance (conformal) and the distortions of distance within small areas on a Mercator are minimal, distance calculations are easier when conducting military operations within fairly small areas.

Transverse Mercator is based on a cylindrical wrapping of the developable surface around the planet like the Mercator. However, the wrapping is around the poles (transverse) rather than around the equator (equatorial), so the zones of minimal distortion cover broad swaths of area that can be used as battle spaces.