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I am using ArcMap 10.8.1 for this project. I am attempting to bring a small town's CAD map of their streets and buildings into ArcMap and then will work on converting some of this data to shapefiles.

The CAD Drawing doesn't seem to have any sort of coordinate system, but I can use the measure tool within CAD and everything seems accurate there (the scale in the legend matches up with the measuring tool).

However, as soon as I bring it into ArcMap the drawing gets massive and is over 10x bigger than it should be. The scale bar should be 2000ft but when I measure it in ArcMap it is close to 30,000!

I am using the correct projected coordinate system from what I can tell (NAD1983 Illinois East) and the GCS is also NAD 1983, so I am unsure of what else I can do to match it up. I've tried playing with these a bit but with no luck.

I've never done something like this before, so I'm 100% sure I'm just missing a step here. I was able to move the drawing on top of a reference point I made using the BaseMap, but that's not much help if the scale is completely off.

Is there anything I am missing here?

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    The unit of your DWG drawing is probably set as millimetres while ArcMap expect (and interpret the coordinate as) meter (or same thing with inch and feet), try to set the DWG drawing unit to the same as the CRS you use in ArcMap – J.R Oct 29 '20 at 15:11
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Georeferenced CAD datasets themselves can only be scaled or shifted. Your ArcMap project uses a Transverse Mercator projection. Like all projections the distances, areas, shapes, and angels get preserved or distorted depending on the projection and the location of the data in that projection. These distortions will not be reflected in the georeferenced CAD dataset.

You can add your CAD data to a geodatabase and use the spatial adjustment tool to better fit the CAD to your projected data.

Here is some general information about georeferencing CAD data.

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Normally, city planners use a local projection in meters or feet for the CAD file (like Nad 83 UTM zone...). Most CAD don’t even handle basic unit like mm. or m. It’s up to the user to know. It can be specified in the CAD file file but it not always the case. Either this is the case and you have the wrong scale, or you have a file in meters or feet and are trying to open it in longitude and latitude.

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