Coordinate Reference Systems

Estimated time: 45 minutes

Overview

Questions

• What is a coordinate reference system, and why does every layer need one?
• What is the difference between geographic and projected coordinate systems?
• What are EPSG codes, and which ones will I meet most often?
• Why do layers sometimes appear in the wrong place, and how do I fix it?

Objectives

• Explain the parts of a coordinate reference system: datum, coordinate system and units
• Distinguish geographic from projected coordinate systems and know when to use each
• Recognize common EPSG codes for work in the United States
• Distinguish defining a coordinate system from reprojecting data, and avoid the classic mistakes

Coordinates need context

---

The numbers 507575, 4474900 and -86.9107, 40.4247 describe the same place: the Purdue Memorial Union. The first pair is in meters in one system; the second is in degrees in another. Coordinates only mean something together with their coordinate reference system (CRS), which says how the numbers relate to locations on Earth.

The same tracts in two coordinate reference systems.

Managing the CRS of every layer is one of the most important, and most often neglected, parts of managing geospatial data.

The parts of a CRS

---

Part	What it does	Examples
Datum	A model of the Earth’s shape (an ellipsoid) and how it is anchored to the real Earth	WGS 84 (used by GPS), NAD83 (the official datum for North America)
Coordinate system	How positions are expressed: angles on the ellipsoid, or x and y on a flat projection	Latitude and longitude; UTM easting and northing
Units	The units of the coordinates	Degrees, meters, U.S. survey feet
Projection (projected systems only)	The mathematical method for flattening the curved Earth	Transverse Mercator, Albers Equal Area, Lambert Conformal Conic

Different datums place the same point at slightly different coordinates. In the contiguous United States, NAD83 and WGS 84 differ by about one to two meters: irrelevant for a state map, but important for surveying or precise field data.

Geographic and projected systems

---

	Geographic CRS	Projected CRS
Coordinates	Latitude and longitude	x (easting) and y (northing)
Units	Degrees	Usually meters or feet
Shape of Earth	Curved (a 3D ellipsoid)	Flat (a 2D plane)
Good for	Storing and exchanging data, global datasets, GPS	Measuring distances and areas, analysis, local mapping
Example	EPSG:4326 (WGS 84)	EPSG:26916 (NAD83 / UTM zone 16N)

A degree of longitude is about 111 km at the equator but only about 85 km in Indiana, and it shrinks to zero at the poles. So distances and areas calculated in degrees are meaningless. Before measuring anything, reproject to a suitable projected CRS.

Every projection distorts something: area, shape, distance or direction. Choose one that preserves what your analysis needs:

• Equal-area projections (such as Albers) for comparing areas and densities across a large region
• Conformal projections (such as UTM or Lambert Conformal Conic) for local shapes and angles
• UTM zones and State Plane zones for accurate local measurements

Choosing a projection for a finished map, and seeing how projections distort the world, is covered in the Data Visualization module’s Fundamentals of Map Design episode.

EPSG codes

---

Every common CRS has a numeric code in the EPSG registry (originally compiled by the European Petroleum Survey Group). Using codes avoids ambiguity: “UTM” alone is not enough, but EPSG:26916 is exact.

EPSG code	Name	Use
4326	WGS 84 (latitude and longitude)	GPS, GeoJSON, most web data, global datasets
4269	NAD83 (latitude and longitude)	U.S. federal data, including Census TIGER/Line files
3857	WGS 84 / Pseudo-Mercator	Web map tiles (Google, OpenStreetMap, Esri). For display only: areas are badly distorted
5070	NAD83 / Conus Albers	Equal-area maps and analysis of the contiguous United States
26916	NAD83 / UTM zone 16N	Accurate local measurement in Indiana and neighboring states
32616	WGS 84 / UTM zone 16N	The same zone on the WGS 84 datum

You can look up any code, and find the right one for an area, at https://epsg.io/.

How the CRS is stored

---

• In a shapefile, the CRS is in the separate .prj file.
• In a GeoPackage or GeoTIFF, it is stored inside the file.
• GeoJSON (RFC 7946) is always in WGS 84 longitude and latitude.
• A CSV of coordinates stores no CRS at all: you must document it, for example in a column name (lon_wgs84) and in the README.

Defining versus reprojecting

---

These two operations sound similar but do very different things:

	Defining (assigning) a CRS	Reprojecting (transforming)
What it does	Tells the software which CRS the coordinates are already in	Calculates new coordinates in a different CRS
Changes the numbers?	No	Yes
When to use	The CRS is missing or wrong, and you know the correct one	You need the data in another CRS for analysis or to match other layers
In QGIS	Layer Properties > Source > Assigned Coordinate Reference System, or the Assign projection tool	Reproject layer tool, or Export > Save Features As… with a new CRS

The classic mistake is to define a CRS when you meant to reproject. The numbers stay the same, but the software now believes they mean something else, and the layer jumps to the wrong place (or the wrong continent).

Callout

On-the-fly reprojection can hide problems

QGIS reprojects every layer on the fly to the project’s CRS, so layers in different systems still draw in the right place. That is convenient, but it can hide the fact that your layers differ. Tools that combine layers (clip, join by location, distance and network tools) work best, and sometimes only work correctly, when the layers share one projected CRS. Some tools also report results in the project’s units. Before analysis, reproject every layer to the same projected CRS and set the project to it.

Troubleshooting checklist

---

Symptom	Likely cause	Fix
Layer appears near 0° latitude, 0° longitude (off West Africa)	Projected coordinates (meters) read as degrees, or a missing CRS	Find the correct CRS and define it
Layer is shifted by a meter or two	Datum mismatch (for example NAD27 and NAD83, or NAD83 and WGS 84 with no transformation)	Use the right datum transformation when reprojecting
Areas or distances are tiny numbers such as 0.0002	Calculated in degrees	Reproject to a projected CRS first
Areas look far too large near the poles	Calculated in Web Mercator (EPSG:3857)	Use an equal-area projection
Layer will not appear at all	Coordinates in the wrong order (latitude, longitude swapped)	Check which column is x and which is y

Challenge

Define or reproject?

For each situation, should you define (assign) the CRS or reproject the data?

1. You receive a shapefile with no .prj, and the metadata says the data is in NAD83 / UTM zone 16N.
2. Your census tracts are in NAD83 latitude and longitude, and you need to calculate their areas in square kilometers.
3. Your field points were collected in WGS 84, and the rest of the project is in EPSG:26916.

Show me the solution

1. Define EPSG:26916. The coordinates are already in that system; the software just does not know it.
2. Reproject to an equal-area projected CRS (such as EPSG:5070) or a local one (EPSG:26916), then calculate areas.
3. Reproject the points to EPSG:26916 so every layer shares one projected CRS.

Challenge

Read the coordinates

Without opening a GIS, which CRS is each of these coordinate pairs probably in?

1. (-86.91, 40.42)
2. (507575, 4474900)
3. (-9675000, 4928000)

Show me the solution

1. Geographic (latitude and longitude, such as EPSG:4326 or 4269): small numbers within -180 to 180 and -90 to 90.
2. UTM (here zone 16N): eastings around 500,000 m and northings in the millions of meters.
3. Web Mercator (EPSG:3857): coordinates in meters from the equator and the prime meridian, with large negative x values in the Western Hemisphere.

Key Points

• Coordinates are meaningless without their coordinate reference system: datum, coordinate system, units and projection
• Store and exchange data in geographic systems; measure and analyze in projected ones
• Use EPSG codes to name CRSs exactly; 4326, 4269, 3857, 5070 and 26916 are common in U.S. work
• Defining a CRS labels existing coordinates; reprojecting calculates new ones. Confusing the two moves data to the wrong place
• Before analysis, put every layer, and the project, in the same projected CRS