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I have a shapefile of U.S. counties in USA Contiguous Albers Equal Area Conic. I want to do distance calculations. For example, distances from one county to another.

I do not know how to interpret the coordinates. In another thread, I understand that the distance is in meters. Is that correct?

The ultimate goal is to use the distance as a part of a statistical procedure. Specifically, I am using it in a regression discontinuity design, in which I restrict the sample to counties that are a given distance from a particular line in the U.S. (e.g., the Central Time Zone). So, I'd like the distance to be fairly accurate because I am restricting the sample to be say 20 miles on either side of this line, and the distance should be accurate from a symmetrical perspective.

How may I recover a latitude and longitude? I wanted to recover them so that I can apply the distance formula for coordinates by hand to get the distances in miles in a way that I can interpret. I've come across projections and UTM when searching, but I do not know what that means.

I use ArcMap in ArcGIS 10.1. Thank you very much for any help!

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2 Answers 2

I would not recommend trying to recover a latitude and longitude in order to "apply the distance formula for coordinates by hand to get the distances in miles" because the length of a degree of longitude varies depending on its latitude i.e. 0 m at poles, and about 110 km (= 70 miles) at around 30 degrees N or S.

I think you will be far better to get your distances in meters direct from using Near with your Albers coordinate system and then multiply them by 39.37 to get inches, and divide that by 63,360 to get miles.

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So, are you saying that Albers is reliable for distance? I thought it is only reliable for area. –  user1690130 Oct 15 '12 at 10:20
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@PolyGeo Albers is a conic projection, and does not give accurate distances along any line. –  Devdatta Tengshe Oct 15 '12 at 10:36
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@Devdatta Accuracy is always relative. For many purposes, Euclidean distance calculations in a good projected coordinate system will be fine, as shown by PolyGeo here. What we are missing in this thread is any indication of what the county-county distances will be used for: some clarification of that would indicate whether it would be worthwhile resorting to geodetic formulas (like the Haversine approximation for a perfectly spherical earth). BTW, Albers does give perfectly accurate distances among some pairs of points. –  whuber Oct 15 '12 at 15:17
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@whuber Thanks for pointing that out. I just added clarification: "The ultimate goal is to use the distance as a part of a statistical procedure. Specifically, I am using it in a regression discontinuity design, in which I restrict the sample to counties that are a given distance from a particular line in the U.S. (e.g., the Central Time Zone). So, I'd like the distance to be fairly accurate because I am restricting the sample to be say 20 miles on either side of this line, and the distance should be accurate from a symmetrical perspective." Please let me know if I should clarify further. –  user1690130 Oct 15 '12 at 15:48
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That's great, J.G. Just one more item: how exactly are you measuring distances between counties (polygons) and a line? If you are using some crude approximation like the distance from a centroid to the line, then high accuracy in the distance calculations is surely overkill. Of greater import will be getting relative distances correct--that is, to properly sort counties by distance within the error suggested by a centroidal approximation--and of using a reproducible method so peer reviewers will know what you did. –  whuber Oct 15 '12 at 15:51

While there are equidistant projections, they preserve distance only from some standard point or line.

To get accurate distances, over a large area such at the United States, your best option is to repoject the data to a geographic coordinate system, and then use the Haversine formula to derive the distance.

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Is there a straightforward way to apply Haversine in ArcGIS? –  PolyGeo Oct 15 '12 at 11:08
    
easiest option, is to have your data in geographic coordinate system, and then use the measure tool. Make sure that you are display units is miles. That way you will get the geodesic distance by default. –  Devdatta Tengshe Oct 15 '12 at 11:38
    
@DevdattaTengshe Thank you for posting this! I may be having some difficulty with projection. I believe I have a Feature, though I'm not sure. I took the shapefile of the U.S. counties and converted it from a feature to points (or are points now something else?), where each point is a county centroid. Under Data Management, I see Projections and Transformations. I tried the Project command under Feature. I inputed that I want the NAD83 Geographic Coordinates. I don't think much changed, but I may be mistaken--What was supposed to change? And, where is the Measure tool located? –  user1690130 Oct 15 '12 at 15:56
    
@DevdattaTengshe Perhaps I am not inputting the correct things into the Projection tool? What exactly is the input? What should the output look like? –  user1690130 Oct 15 '12 at 17:06
    
@JG The Measure Tool is on the Tools toolbar but I am assuming that you have hundreds of measurements to make which would probably make use of that impractical. In any event the words of whuber are more along the lines of my thinking. –  PolyGeo Oct 15 '12 at 21:33

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