Understand projections

You will not find a projection that is suitable for all maps. All projections distort the earth in some way. Each one seeks to preserve some geometric property at the expense of others.

Projection types

Conformal projections preserve angles locally, so the shapes of features appear true. But the cost of this quality is the distortion of areas and distances. Equal area projections preserve area, at the expense of angles, so the shapes of some places appear skewed. Equidistant projections preserve distances, although only from certain points or along certain lines on the map.

Stereographic, Azimuthal Equidistant, and Lambert Azimuthal Equal Area projections, each centered on the equator
Three maps, drawn with examples of conformal, equal area, and equidistant projections, overlaid with geodesic circles that demonstrate geometric distortions.

Compromise projections provide a representation of the earth that is not perfectly correct in any way but not badly distorted in any way either. They are usually used for maps of the entire world.

There are dozens of projections available in ArcGIS that can be configured into countless projected coordinate systems. Your choice of a projected coordinate system depends on many factors, including the part of the world you are mapping, the scale of your map, and the purpose of your map. You want to choose a projected coordinate system in which the places and properties that are most important to your map are the least distorted.


Map global analysis results

Map projections distort the grid of latitude and longitude lines, which means they also distort your data. You've taken great care to conduct an analysis of future precipitation changes properly and precisely. Next you need to present your results on a map. You want to choose a projection that will allow you to present those results clearly, so they are not misinterpreted.

Find a global equal area projection

First, you'll explore a few traditional resources to help you find a suitable projection for your analysis results.

  1. Download the Projections project package.
  2. Locate the downloaded Projections.ppkx file on your computer. Double-click the file to open it in ArcGIS Pro. If prompted, sign in to your ArcGIS account.
    Note:

    If you don't have ArcGIS Pro or an ArcGIS account, you can sign up for an ArcGIS free trial.

    The project has three maps. The Precipitation Change map is active.

    Global precipitation data displayed in the Web Mercator projection

    The data on this map shows predicted precipitation anomalies for the years 2040 to 2059. You can learn more about how this data was created in the lesson Explore Future Climate Projections. The analysis—including distance and area measurements—that created this map was conducted properly, but the map presents the accurate results in an inaccurate way.

    First, you'll find out which projection this map is using.

  3. In the Contents pane, right-click Precipitation Change and choose Properties.

    Properties option in the map's context menu

  4. In the Map Properties window, click the Coordinate Systems tab.

    Under Current XY, you can see that the current coordinate system for this map is WGS 1984 Web Mercator (auxiliary sphere).

    Current XY coordinate system in the Map Properties window

    Web Mercator is a common projected coordinate system designed for web mapping applications. Most of Esri's basemaps are tiled in Web Mercator, so they can have the greatest compatibility. However, this projection does not preserve areas, distances, or angles.

  5. In the Map Properties window, click Cancel.

    Looking at this map, you may think that Greenland is many times larger than India. In fact, Greenland is smaller than India. If the Web Mercator projection distorts the relative sizes of countries so dramatically, you know that it must also be distorting your analysis results.

    This map suggests that the areas that will experience the most extreme change in precipitation are relatively small, just a narrow band along the equator. Web Mercator is not an appropriate choice for this map. Next, you'll consult a chart that compares projections to find one that is appropriate for your map.

  6. Open Quick Notes on Map Projections in ArcGIS.

    Part of the Quick Notes on Map Projections chart

    The property that is most important to preserve in your precipitation map is area. This is true for most maps presenting analysis results involving area, density, or distance comparisons.

  7. Use the chart to find a projection that meets the following criteria:
    • Properties: Equal Area
    • Suitable Extent: World
    • General Purpose: Thematic

    There are a few projections that are suitable for your map. One of them is Equal Earth.

    Highlighted columns in the map projections chart

  8. Go to the ArcGIS Pro help page for the Equal Earth projection. Scroll down and read the Usage section.

    You can read about any projection found in ArcGIS to help you decide which is best for your map.

Change the map's projected coordinate system

You've decided to use the Equal Earth projection. Next, you'll apply it to your Precipitation Change map.

  1. In ArcGIS Pro, in the Contents pane, double-click Precipitation Change to open the Map Properties window.
  2. Click the Coordinate Systems tab.
  3. In the search bar, type Equal Earth and press Enter.

    The list of available coordinate systems filters based on your search.

  4. Expand Projected Coordinate System and expand World. Click Equal Earth (world).

    The Current XY button updates to indicate that the map's coordinate system has changed.

    Current XY coordinate system set to Equal Earth (world)

    Tip:

    Changing the coordinate system in the Map Properties window affects only the map. It does not change the coordinate system of your data layers. These are projected on the fly to draw correctly on the map. To learn more about projection on the fly, read this blog article.

  5. In the Map Properties window, click OK.

    The new projected coordinate system is applied to your map.

    Global precipitation data displayed with the Equal Earth projection

    The analysis results are now presented in a form that preserves relative areas, so your map readers can accurately compare the sizes of precipitation anomalies.

  6. On the Quick Access Toolbar, click Save to save the project.

    Save button on the Quick Access Toolbar

Below is a comparison of the two projections. How might the Web Mercator projection mislead or hinder people from properly interpreting your analysis results?

Comparison of Atlantic Ocean, Africa, and Europe in the Equal Earth and Web Mercator projections

The Equal Earth projection is designed to show the entire world, but there are two parts of the world that it is unable to map effectively. Next, you'll try a projection designed to map polar regions.


Map polar data

A compass needle does not point to the true north pole. Instead it points to the magnetic north pole, a location that is constantly changing. Next, you'll make a map to show the wandering path the magnetic pole has taken over the past 400 years. You also want to use this map to show whether the magnetic pole is moving closer to, or farther away from, true north.

Find a polar equidistant projection

You'll search for a projected coordinate system that preserves distances from the north pole.

At the top of the map view, click the North Pole tab to activate that map.

Rectangular map of the world with point data along the top edge

The data in this map was provided by NOAA National Centers for Environmental Information (NCEI).

The map does a poor job of illustrating the changing location of the magnetic north pole. The points all appear to be far away from the true north pole, and they are also split up on either side of the map. Measurements made on this map would be meaningless.

For this map's projection, you have two criteria:

  • To display the arctic data more naturally, you need a projection designed for polar regions.
  • To determine how close magnetic north is to true north, you need an equidistant projection, which will preserve accurate distance measurements to the north pole.

Next, you'll find an appropriate projected coordinate system by searching for keywords.

  1. In the Contents pane, double-click North Pole to open the Map Properties window.
    Note:

    This map currently uses a geographic coordinate system, WGS 1984. When a geographic coordinate system is selected, your map will be projected using a pseudo Plate Carée projection. You can read more about the difference between geographic and projected coordinate systems in this blog article.

  2. On the Coordinate Systems tab, search for Equidistant.
  3. Expand the Projected Coordinate System list and expand Polar.

    The Polar group in the Projected Coordinate System list

    Tip:

    Drag the edges of the Map Properties window to make it larger.

    There are only two projected coordinate systems, one for the north pole and one for the south pole.

  4. Click North Pole Azimuthal Equidistant and click OK.

    This projection distorts both angles and areas. Distortion is extreme in the southern hemisphere.

    Circular map of the world with the north pole and point data in the center

    However, this projection is useful for mapping the area around the north pole. It preserves true distances and directions measured from the pole.

  5. In the Contents pane, right-click HistoricalMagneticPoleTrack and choose Zoom To Layer.

    Map of the point data in the Canadian arctic with a white circle surrounding the north pole

    There are some problems with the Topographic basemap. This basemap is tiled using the Web Mercator projection, so it becomes distorted when it is drawn on the Azimuthal Equidistant map. Additionally, Web Mercator is unable to show the poles, so the basemap is cut off past 85° latitude, leaving a blank hole in your map.

    The Topographic basemap is not suitable for your polar map, so you'll find one that is.

  6. In the Contents pane, right-click Topographic and choose Remove.
  7. In the Catalog pane, click the Portal tab and click the Living Atlas tab.

    The Portal and Living Atlas tabs in the Catalog pane

  8. In the Search bar, type Polar Basemap and press Enter.
  9. From the search results, right-click Arctic Ocean Base and choose Add To Current Map.

    Arctic Ocean Base tile layer in the Catalog pane search results

    The map updates to display the new basemap, which covers the portion of the earth north of 50° latitude.

    Circular map with the Arctic Ocean basemap

Find the northernmost magnetic pole

Next, you'll use your map to measure distances between true north and the wandering magnetic north pole, to determine the year when they were closest.

  1. On the ribbon, click the Map tab. In the Inquiry group, click Measure.

    The Measure Distance window appears on top of the map.

    Measure Distance window set to Metric

  2. Click the point labeled North Pole, and click the point labeled 2020.

    Measurement between the North Pole and 2020 points

    The tool reports a distance of 403.1 kilometers (250.47 miles).

  3. On your keyboard, press Esc to clear the measurement.
  4. Measure the distance between the true north pole and some previous locations of the magnetic north pole.

    Magnetic north was nearest to true north in 2018, when it was 394.16 kilometers (244.92 miles) away. It is now heading south, toward Russia.

You can make true distance measurements on this map because it uses an equidistant projection. However, no projection can preserve all distances. The Azimuthal equidistant projection preserves distance and direction from the central point only. So measurements from the north pole are true. But measurements between any other locations on this map will be inaccurate.

Measure geodesic and planar distances

The measurements you've made so far have been planar. Planar distances are like measuring with a ruler on a paper map. Geodesic distances are like measuring with a string over the surface of a globe. Next, you'll compare planar and geodesic measurements between the magnetic north poles of 1590 and 2020.

  1. Press Esc to clear your current measurement.
  2. Measure between the point labeled 1590 and the point labeled 2020.

    Measurement between the 1590 and 2020 points

    The distance reported between these two locations is 1,758.73 kilometers (1092.82). However, the only accurate planar distances that can be made on this map are from the center point. To find accurate distances between other locations, you need to make geodesic measurements.

  3. Press Esc. In the Measure Distance window, click the Mode button and choose Geodesic.

    Mode set to Geodesic in the Measure Distance window

  4. Measure the distance between the poles of 1590 and 2020 again.

    This time the reported distance is 1,866.63 kilometers (1,159.87 miles). The geodesic distance is over 100 kilometers longer than the planar distance.

  5. Close the Measure Distance window and save the project.

Geodesic distances ignore the map's projection and provide a true distance. Planar distances are only true if the map uses a distance-preserving projection and only to certain points or along certain lines.

In ArcGIS, you can choose between planar or geodesic measurements. But your map reader will not have this choice; they will only see a flat map on a screen or piece of paper. An equidistant projection is the right choice for this map to allow everyone to assess distance correctly from the north pole.

The projected coordinate system you chose for this map was already centered on the north pole, which happened to be the location you wanted to measure from. But what if you wanted to measure from a different point? Next, you'll learn how to adjust a projection to be centered over the best location for your map.


Map the border of two UTM zones

Sometimes you won't find a projected coordinate system that is ready-made for your map's purpose. ArcGIS Pro allows you to customize any coordinate system to have parameters that better suit your needs.

Universal Transverse Mercator (UTM) is a system that is commonly used for large scale maps. If your map is narrower than 6° of longitude, you can map it with a UTM projected coordinate system. The map you'll make next is narrow enough but doesn't fit properly into an existing UTM zone, so you'll create a custom projected coordinate system.

Find the correct UTM zone

You want to map the border between Finland and Russia. This will be a reference map, meant to give descriptive context to the border region. You want to use a conformal projection to show the shapes of features in their most recognizable forms.

  1. At the top of the map view, click the Border tab to activate that map.

    Map with a white rectangle surrounding the Finland-Russia border

    This map currently uses the Web Mercator projection. While the Mercator projection is conformal, Web Mercator (Mercator Auxiliary Sphere) is not. In addition, this projection distorts area and distances dramatically in higher latitudes.

    The white rectangle represents the area you want to map. Because this is a narrow piece of the earth—within 6° of longitude—you can use a UTM zone. UTM projected coordinate systems are conformal and their distortion of other map properties is minimal.

    UTM divides the earth into 60 zones. Next, you'll use a spatial filter to determine which UTM zone to use for your map.

  2. In the Contents pane, double-click Border to open the Map Properties window.
  3. On the Coordinate Systems tab, next to the search bar, click Spatial Filter and click Set spatial filter.

    Set spatial filter in the Coordinate Systems window

  4. In the Spatial Filter Extent window, click Map Neatline.

    The values under Selected extent update to match the extent of the Map Neatline layer.

    Map Neatline highlighted in the Spatial Filter Extent window

  5. Click Apply.

    The XY Coordinate Systems Available list is filtered to only contain coordinate systems with extents that overlap with your map.

  6. In the list, expand Projected Coordinate System, UTM, WGS 1984, and Northern Hemisphere.

    Expanded groups in the list of available coordinate systems

    There are two UTM zones for the area that you want to map, 35N and 36N, and you can't tell from this list which zone is best.

  7. Click Cancel to close the Map Properties window.

    Next, you'll add an online layer to your map to visualize the UTM grid.

  8. In the Catalog pane, click the Portal tab and click Living Atlas.
  9. In the search bar, type UTM Grid and press Enter.
  10. In the search results, right-click the World UTM Grid feature layer and choose Add To Current Map.

    World UTM Grid feature layer in the Catalog pane search results

  11. In the Contents pane, right-click World_UTM_Grid and choose Label.

    The Finland-Russia border lies on the border of two UTM zones: 35 and 36.

    Map of the Finland-Russia border overlaid with transparent labeled UTM zones

    UTM projected coordinate systems minimize distortion to reasonable levels, but only within their zone areas. Neither zone 35 nor 36 will provide this benefit for your map area.

  12. In the Contents pane, right-click World_UTM_Grid and choose Remove.

The World_UTM_Grid layer confirmed that the best choice for this map is a custom projected coordinate system. Next, you'll use an online tool to create one for this region.

Create a custom projected coordinate system

Projection Wizard is an online tool that designs custom projection parameters based on two criteria: distortion property and map extent.

  1. Go to projectionwizard.org.
  2. On the map, drag the corners of the extent box to roughly match the one in ArcGIS Pro.
  3. For Distortion Property, choose Conformal.

    Projection Wizard with Distortion Property set to Conformal and extent drawn around the Finland-Russia border

    A suggested projection and some notes are listed below the map. Projection Wizard recommends the Transverse Mercator projection with a central meridian of 29º 53' E.

    Tip:

    If the suggested projection is Oblique Stereographic, try making the extent rectangle narrower.

  4. Next to Transverse Mercator, click the PROJ.4 link.

    PROJ.4 link next to Transverse Mercator in Projection Wizard

    A pop-up window appears, containing the central meridian in decimal degree form.

  5. In the pop-up window, copy the number after the equal sign to the clipboard and click Cancel.

    Highlighted number in the Projection Wizard PROJ.4 window

  6. In ArcGIS Pro, on the Border map, open Map Properties.
  7. On the Coordinate Systems tab, click the Add Coordinate System button and choose New Projected Coordinate System.

    New Projected Coordinate System in the Coordinate System window

    The New Projected Coordinate System window appears. Here you can construct a custom coordinate system with parameters that match your needs.

  8. For Name, type Finland-Russia Border.

    The Projection is already set to Transverse Mercator, the same one that was recommended by Projection Wizard.

    Note:

    A projection and a projected coordinate system are not the same thing. A projection is one parameter in a projected coordinate system. Other parameters include a geographic coordinate system, a linear unit, and a set of parameters that depend on the selected projection (central meridian, scale factor, and so on).

    Learn more in the blog article Coordinate Systems: What's the Difference?.

  9. For Central Meridian, paste the value you copied from Projection Wizard, or 29.88402778.

    New Projected Coordinate System window with modified values for Name, Projection, and Central Meridian

  10. Click Save.

    Finland-Russia Border is now set as the Current XY coordinate system for your map. It is also listed in the Custom category of available coordinate systems.

    Finland-Russia Border set as the Current XY coordinate system and listed in the Custom category

    Coordinate systems in the Custom category are not saved. Next, you'll add it to a favorites folder so you can use it in future maps.

  11. Under Custom, right-click Finland-Russia Border and choose Add to Favorites.

    Add to Favorites in the Finland-Russia Border context menu

  12. Scroll to the top of the coordinate systems list and expand the Favorites group to ensure that Finland-Russia Border is listed there.
    Note:

    Favorite coordinate systems are stored as .prj files in C:\Users\<your user name>\AppData\Local\ESRI\ArcGISPro\Favorites.

  13. In the Map Properties window, click OK to commit the change.

    The map redraws with the new projected coordinate system.

  14. In the Contents pane, right-click National Geographic World Map and choose Zoom To Layer.

    The Transverse Mercator projection has a gore shape, showing only part of the world.

    Gore-shaped map of part of the world

    It is not possible in this projection to map areas outside of this gore shape, and it is only appropriate to map areas in the middle—within 3° of its central meridian.

  15. Zoom to the Map Neatline layer.

    The image below shows a comparison of the map in the new custom projected coordinate system and in Web Mercator.

    Comparison of the white extent shape in the Transverse Mercator and Web Mercator projections

In the custom coordinate system, the shape of the neatline polygon is now a trapezoid instead of a rectangle. Its northern edge is shorter than its southern edge. The rectangle in Web Mercator is misleading: on the earth, these lines are not the same length. The new projection represents them more accurately.

The two maps shown above are drawn at the same scale: 1 to 20 million. But that scale is meaningless in the Web Mercator map, since its area distortions are so extreme. Distortion in the Transverse Mercator map is small enough to be unnoticeable, and more precise measurements can be made on that map.

Modify a projected coordinate system

You've built a custom Transverse Mercator projected coordinate system, but it is missing a few of the properties that are offered by a true UTM zone. Next, you'll modify an existing coordinate system to match your map's location.

  1. On the map, hover the pointer over the middle of the Map Neatline shape.

    The coordinates of the pointer location are reported below the map. The center of the neatline shape is roughly 29.9° east. This is close to the value that you found using Projection Wizard earlier.

    Pointer hovering over center of white neatline shape with longitude value highlighted

    Next, you'll modify an existing UTM coordinate system. You'll shift it sideways so it is centered over this longitude.

  2. Open the Map Properties window and click the Coordinate Systems tab.
  3. In the XY Coordinate Systems Available list, expand Projected Coordinate System, UTM, WGS 1984, and Northern Hemisphere.
  4. Scroll down and right-click WGS 1984 UTM Zone 1N. Choose Copy and Modify.

    Copy and Modify in the WGS 1984 UTM Zone 1N context menu

    The Modify Projected Coordinate System window appears. It looks similar to the New Projected Coordinate System window you worked in previously.

    UTM is a set of projected coordinate systems. All of them use the Transverse Mercator projection. This is the same projection that you used earlier, but the UTM coordinate system defines a few additional parameters: False Easting and Scale Factor.

    Modify Projected Coordinate System window with False Easting and Scale Factor highlighted

    False Easting shifts the origin point of the coordinate system far away from your map area to ensure that no coordinates have negative values. Scale Factor minimizes distortion across the entire 6° zone.

  5. For Name, type Finland-Russia Border UTM.
  6. For Central Meridian, type 29.9.

    Modify Projected Coordinate System window with modified values for Name and Central Meridian

  7. Click Save.
  8. Right-click the new custom coordinate system and choose Add to Favorites.
  9. In the Map Properties window, click OK.

    You won't see a visual difference between this projected coordinate system and the previous one. However, the addition of the scale factor makes your map more accurate for direct measurements over the entire zone.

  10. Save the project.

Now that you know how to modify projections, how could you modify the Equal Earth projection from the start of this lesson to better show the Pacific Ocean? How could you modify the Azimuthal Equidistant projection to center on your city instead of the north pole?

Tip:

Copy and modify the Equal Earth (world) coordinate system. Change the central meridian to 160°W or a similar value.

Copy and modify the North Pole Azimuthal Equidistant coordinate system. Change the central meridian and the latitude of origin to match the location of your city.

In this lesson, you learned some techniques and explored resources that will help you choose an appropriate map projection:

Take a closer look at the maps you see on the internet, in the news, or in apps. Do they use a projection that is well suited to their purpose? Are their distance and area measurements accurate?

The consequences of ignoring your choice of map projection include distorting your data and misleading your map readers. However, if you spend some time to find an appropriate projected coordinate system, you'll create a map that presents your data and your message clearly and accurately.

You can find more lessons in the Learn ArcGIS Lesson Gallery.