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I'm trying to count the total number of points contained within a polygon layer.

I have a series of buffer layers, each getting progressively larger and encompassing more points.

I have used the "summarize within" / "spatial join" tool as suggested by Esri: https://support.esri.com/en/technical-article/000023531

However, these tools provide the count of points for each polygon, rather than the count of unique points for the entire layer.

I could add up the point count for each polygon but, as some points sit within two or more overlapping polygons, this would result in some points being counted more than once.

How can I ensure I am counting each individual point within a polygon LAYER only once?

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You could join your polygon layer into a single polygon feature. Or more straightforward, when you create your polygon Buffer, you can set the dissolve type to "Dissolve all output features into a single feature", which you can then follow up by using the summarize within tool.

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