# Coordinate systems, projections, and transformations

Data usually comprises an array of numbers. Spatial data is similar, but it also carries numerical information that allows you to position it somewhere on earth. These numbers are part of a coordinate system that gives you a frame of reference for your data, to locate features on the surface of the earth, to align your data relative to other data, to perform spatially accurate analysis, and to make maps.

All spatial data is created in some coordinate system, whether it is points, lines, polygons, rasters, or annotation. The coordinates themselves can be specified in many different ways, such as decimal degrees, feet, meters, or kilometersâ€”in fact, any form of measurement can be used as a coordinate system. Identifying this measurement system is the first step to choosing a coordinate system that displays your data in its correct position in ArcGIS Pro, in relation to your other data.

## Coordinate systems

Data is defined in both horizontal and vertical coordinate systems. Horizontal coordinate systems locate data across the surface of the earth, and vertical coordinate systems locate the relative height or depth of data.

Horizontal coordinate systems can be of three types: geographic, projected, and local. You can find out what coordinate system your data is in by examining the layer's properties. Geographic coordinate systems (GCS) most commonly have units in decimal degrees measuring degrees of longitude (x-coordinates) and degrees of latitude (y-coordinates). The location of data is expressed as positive or negative numbers: positive x- and y-values for north of the equator and east of the prime meridian, and negative values for south of the equator and west of the prime meridian.

Spatial data can also be expressed using projected coordinate systems (PCS). Coordinates are expressed using linear measurements rather than angular degrees. Finally, some data may be expressed in a local coordinate system with a false origin (0, 0 or other values) in an arbitrary location that can be anywhere on earth. Local coordinate systems are often used for large-scale (small area) mapping. The false origin may be aligned to a known real-world coordinate or not, but for the purposes of data capture, bearings and distances may be measured using the local coordinate system rather than global coordinates. Local coordinate systems are usually expressed in feet or meters.

Vertical coordinate systems are either gravity-based or ellipsoidal. Gravity-based vertical coordinate systems reference a mean sea level calculation. Ellipsoidal coordinate systems reference a mathematically derived spheroidal or ellipsoidal volumetric surface.

## Projections

A projection is the means by which you display the coordinate system and your data on a flat surface, such as a piece of paper or a digital screen. Mathematical calculations are used to convert the coordinate system used on the curved surface of earth to one for a flat surface. Since there is no perfect way to transpose a curved surface to a flat surface without some distortion, many different map projections exist that provide different properties. Some preserve shape, while some preserve distance. Others preserve area or direction. The extent, location, and property you want to preserve must inform your choice of map projection. There are over 4000 coordinate systems in the ArcGIS platform, so it is likely that you can find one to match your data. In the event that you cannot, you can create a custom coordinate system to display the data.

ArcGIS Pro reprojects data on the fly so any data you add to a map adopts the coordinate system definition of the first layer added. As long as the first layer added has its coordinate system correctly defined, all other data that has correct coordinate system information reprojects on the fly to the coordinate system of the map. This approach facilitates exploring and mapping data, but it should not be used for analysis or editing, because it can lead to inaccuracies from misaligned data between different layers. Data is also slower to draw when it is projected on the fly. If you intend to perform analysis or edit the data, then first project it into a consistent coordinate system and the same coordinate system shared by all your layers. This creates a new version of your data.

## Transformations

After defining the coordinate system that matches your data, you may still find you want to use data in a different coordinate system. This is where transformations are useful. Transformations are required to convert data between different geographic coordinate systems or between different vertical coordinate systems. Unless your data lines up, you'll face difficulties and inaccuracies in any analysis and mapping you perform on the mismatched data.