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I have a world map in the WGS 1984 Geographical Coordinate System. I want to measure the lengths of borders between countries in kilometers. To get the units in meters, I have first used the Define Projection tool and then the Project tool to change to the Robinson Projected Coordinate System. After that, I am using the Intersection tool and setting the output type to "line" to get a Shape_length column where I will have all the borders and their lengths. But, the value in the Shape_length column appears to be wrong as it measures the borders to be only a few meters. The Measure tool does the same thing.

I can't get my head around what I am doing wrong. I've attached a print screen of the data frame. What could the problem be?

enter image description here

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    I suspect that the units are in degrees. By the looks of the image the data frame is unprojected and you calculated the values in the units of the data frame – user681 Aug 8 '14 at 13:40
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    Agree with Dan, but even when you get the data projected, distances in projected units will not perfectly match geodetic distances. The difference will vary based on the type of projection but for areas as large as countries they will all have errors. Some will preserve relative distance better than others. – Russell at ISC Aug 8 '14 at 14:02
  • possible duplicate of Layers with same coordinate system should align/overlap but do not? – Erica Aug 9 '14 at 12:10
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The Define Projection tool only changes the associated projection, it does not modify the geometry of the feature or shapefile. (Useful if you get data with no associated projection. Not useful if you're trying to transform to a different coordinate system.)

Since you ran this before running Project (which mathematically transforms the data into a different coordinate system), your data is still retaining the decimal degree numbers, but with different units. So the geometry calculations still use the same raw numbers that were associated with decimal degrees, but erroneously assume different units (meters).

Try running just Project, and see if the measurements are more what you expect. (If the original world border data has no existing projection, then use Define Projection to assign it WGS84, and then Project to the new coordinate system.)

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Quoted from About coordinate systems and map projections

Other projections minimize overall distortion but don't preserve any of the four spatial properties of area, shape, distance, and direction. The Robinson projection, for example, is neither equal area nor conformal but is aesthetically pleasing and useful for general mapping.

You may want to check out this resource:

Useful Map Properties: Distances and Scale

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