Geodesic or planar: which to use for distance analysis
Earth’s curvature impacts how we measure and calculate distances. For the distance analysis tools within ArcGIS Spatial Analyst, distance can be calculated as a planar distance or a geodesic distance. These two methods can produce vastly different results because they make different assumptions about the surface we are calculating distance over.
Planar vs. Geodesic
Planar distance is a distance between locations that is calculated in a 2D Cartesian coordinate system. While these projected coordinate systems do account for Earth’s curvature, they are limited. When projecting the Earth from 3D to a 2D representation, it is impossible to preserve distance, area, direction, and shape all at once. Each projected coordinate system is designed to preserve one or two of those at the expense of the others. Between the 2D representation and the inability to preserve all elements, planar distances are always inaccurate.
Geodesic distance, on the other hand, is the distance between two points connected along the curved surface of the world. It is calculated in a 3D spherical space rather than on a 2D plane. This is done using a geoid to approximate the curvature of Earth's surface in calculations. A geoid is an irregularly shaped ellipsoid that approximates geographic formations that make up the Earth's surface. Compared to Earth’s actual physical surface, the geoid is still considerably smoother but accounting for the Earth’s curvature through such an approximation is more accurate than a 2D representation of it.
Comparison of the conceptual difference between planar and geodesic distance.
The difference between distance results from planar and geodesic calculations varies with study area size and map projection. Geodesic calculations are always more accurate, no matter the situation. Since planar distance only preserves certain elements when approximating a surface’s curvature to a 2D plane, it is always distorted. In general, as the size of the study area increases, the impact of Earth's curvature is larger, meaning planar calculations will become increasingly less accurate. To reduce this distortion while using a planar calculation, you could project the surface’s curvature using map projections suited to preserving distance in your study area and ensure your study area is located at the center of the projection. It is important to choose the appropriate projection for your situation when using planar distance. To learn more about picking the right projection for your data and analysis, see ArcGIS: The Importance of Coordinate Systems for Spatial Analysis. To learn more about coordinate system concepts, see Coordinate Systems: What’s the Difference?
Example 1
To highlight the difference between geodesic and planar distance, we can calculate and compare the distance between Lisbon, Portugal, and Naples, Italy, using a Web Mercator projection. We can see that the planar distance is significantly overestimating this distance. The geodesic result is just over 600 kilometers shorter than the planar distance, which equates to a 30 percent difference. If we choose locations even farther apart, such as Lisbon and Budapest, Hungary, that difference increases to about 950 kilometers which is about a 40 percent difference.
Optimal paths between Lisbon, Portugal, and Naples, Italy, as well as Lisbon, Portugal, and Budapest, Hungary. The projection is Web Mercator.
The map projection used above is Web Mercator, which preserves angles and is the default projection for a new map in ArcGIS Pro. Using a projection such as this, without choosing it for your specific purposes, causes the distortion to be particularly large. If we were to choose a more suitable projection for our situation, the distortion we’d see from the planar calculations would decrease. However, this improvement has a limit, since planar calculations simplify the analysis to a 2D system. No matter what projection is used, planar will be less accurate than geodesic.
Example 2
As another example, we can compare the Euclidean distance between Port of Spain, Venezuela, and Freetown, Sierra Leone, using a map projection more suitable for distance calculations in this area, the WGS 1984 Equidistant Cylindrical (standard parallel=0) projection. This projection preserves distance near the equator and is a choice suitable for this use case. While the total distance between the two cities is much larger than in the previous example, the planar calculation is only distorted by 1.5 percent.
Optimal path between Port of Spain, Venezuela in South America, and Freetown, Sierra Leone in Africa. The projection is WGS 1984 Equidistant Cylindrical (standard parallel=0).
While selectively choosing a more suitable projection can give us a better answer, we still see there is a noticeable difference of 80 kilometers between the two calculation methods. Depending on your application, this error can have downstream consequences if the limitations of the planar calculations are not understood.
Which one?
Since geodesic accounts for Earth’s curvature while calculating distance, it is always more accurate than planar. This is especially true when you have a large study area located in a region more susceptible to projection distortion. However, planar distance can save processing time during analyses at the expense of accuracy. If your study area is the size of a city or a small county but your data has a high resolution, planar calculations would be faster, and the impact of distortion could be minimized with a suitable projection. When accuracy is more important than speed, geodesic is the recommended method.
Learn more
Our distortion-free distance tools take advantage of geodesic distance calculations to provide accurate distance analyses. If you haven’t used them yet, now is the time to try them out. The tools in the Distance toolset that have a geodesic option are Distance Accumulation, Distance Allocation, Optimal Corridor Connections, and Optimal Region Connections.
The remaining tools in the Distance toolset support inputs created with the geodesic setting: Least Cost Corridor, Optimal Path As Line, and Optimal Path As Raster.
Whether you choose to use planar or geodesic distance, the tools in the Distance toolset have you covered.
To learn more about the distance computations in Spatial Analyst, see the following blog series and conceptual documentation:
- Distance Analysis Simplified
- Distance analysis
- Doing More with the New and Improved Distance Tools in Spatial Analyst
The original blog was first published in the ArcGIS Blog, and can be found here: