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So I have two map documents with two different Coordinate Systems set for the layers but using copies of the same shapefile.

Map 1: Coordinate System: NAD_1983_StatePlane_Massachusetts_Mainland_FIPS_2001_Feet Linear Unit: Foot_US The shapefile in this map has same coordinate system but is in Meters.

Map 2: Coordinate System: WGS_1984_Web_Mercator_Auxiliary_Sphere Linear Unit: Meters The shapefile's coordinate system in this map document is in the NAD_1983_StatePlane_Massachusetts_Mainland_FIPS_2001_Feet and its linear unit is Foot_US.

GIS Software is ArcGIS 10.2.2

I am measuring a distance of a building with the measure tool. In map 1 it is telling me the wall is 100 ft long. In Map 2 it is telling me that it is 135 ft long.

Which one (if either) is correct and, how do I know?

  • What is the native coordinate system for the shapefile? – Kevin Sep 16 '14 at 20:13
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    Can you edit your question to include the GIS software and version that you are using, please? – PolyGeo Sep 16 '14 at 20:16
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    @PolyGeo Why does that information matter for this question? Any correctly working GIS will produce the same results reported here. – whuber Sep 17 '14 at 17:24
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    @Poly But this is not a question about the software--as the lack of software-specific tags makes clear. The problem can be reproduced in any GIS, using any data (or no data at all!). The best GIS to use, therefore, is your favorite one rather than whatever one the OP might have used. Software documentation would not be relevant here, either, except insofar as it might explain about projected coordinate systems--but such material is scarcely authoritative (and might not be accessible to some people) and other references should be preferred. – whuber Sep 17 '14 at 20:22
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    @Poly And that's perfectly fine: we are a stronger site for having people who approach questions differently. But I maintain--and would like to emphasize--that it is not only unnecessary but invalid to require that every question on this site reference some kind of software. We are about GIS in general, not just GIS programming or applications. An incomplete discussion of this issue took place early in our history; perhaps you would like to contribute some thoughts to that meta thread. – whuber Sep 17 '14 at 21:59
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The projection that you use will distort the properties of your objects. You can select your projection to preserve the shape, the area OR the distances but not all at the same time. If you want a specific feature to be preserved, you need to select a projected coordinate system with this property (conformal for shape, equal-area for area or equidistant for distance). However, you must be aware that equidistant projection are only valid for a set of direction.

On the other hand, local projection system (such as for your map 1) are meant to minimize all the distortions in their range of validity. So if you are in Mainland Massachusset you can trust the distance on map 1. (Your error will be less than 1/20 inch per 100 feet as mentioned by @whuber in his comment).

So, to answer your question, the best measure is on Map 1, but it will not be the exact value.

Finally, note that some software have tools to compute the "true" distance (geodesic distance) on maps whatever the projection is used to display the data.

As a remark, the CRS of your shapefile should not affect your result if your projection is well managed.

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    (+1) Your estimate of the error is actually a little conservative: the maximum distance distortion within the entire state is 102 parts per million, which amounts to an error of no more than 1/8 inch over 100 feet. (On the mainland the error is limited to 40 ppm, which is about 1/20 inch over 100 feet.) These errors are likely much smaller than the inherent accuracy of the map, unless it was obtained at an enormous scale such as a high-precision survey map of a small building. – whuber Sep 17 '14 at 19:45
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From ESRI:

"WGS 1984 Web Mercator and WGS 1984 Web Mercator (Auxiliary Sphere) use a conformal projection that preserves direction and the shape of data but distorts distance and area. Published in 1569 by Gerardus Mercator, the Mercator projection was created for use in navigation. A straight line drawn on a map in this projection provides a bearing by which one could fly a plane or sail a ship between two points."

http://support.esri.com/cn/knowledgebase/techarticles/detail/39404

NAD_1983_StatePlane_Massachusetts_Mainland_FIPS_2001_Feet Linear Unit: Foot_US would be more accurate for the measurement of linear distance as there would be less distortion than with the Web Mercator Projection

  • What, then, is the answer to the question? – whuber Sep 17 '14 at 17:23
  • I thought it would be evident from the first sentence in the quotation, but have updated my answer for clarification's sake. – cl3 Sep 17 '14 at 19:00
  • Because all projections "distort distance and area," what matters is how much distortion occurs. Even the SP 83 projection distorts distances. Your edit makes that point much plainer, thank you. – whuber Sep 17 '14 at 19:38

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