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To give context, I was using the Intersect Tool to find the number parcels that are located in multiple Sections of an STR. I tried both the Geoprocessing Tool, and calling the function in ArcPy. I noticed I got different results when my input was the same order for both methods, Parcel Layer first, then Section layer. However when I did Parcel Layer first, Section Layer second for the Geoprocessing Intersect Tool, then Section first, Parcel Second with the ArcPy Function, I obtained the same results.

Does order matter with the Intersect Tool?

I figure either it does, or I was just doing something wrong in my ArcPy script that was giving inconsistent results.

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    No, I don't think order matters. Either way the intersection is the area that is common to both feature classes. Either way the output is the lowest dimension geometry of the inputs... I think the only difference is the order of fields in the output, but it's not good practice to index fields arbitrarily so that shouldn't matter. – Michael Stimson Oct 5 '17 at 22:49
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As per the How Intersect works help:

When multiple feature classes or layers are specified in the list of input features, the order of the entries in the list does not affect the output feature type, but the spatial reference of the top entry on the tool dialog box (the first entry in scripting) in the list will be used during processing and set to the output.

I think the answer to your question will be that the order may matter if your inputs do not all share the same coordinate system.

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