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I want to find the minimum distance of each point to its enclosed boundary, I have been trying to use the near tool, but the field is giving 0 as values.

This is a picture of the attribute table.

enter image description here

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According to the Special Considerations section of How proximity tools calculate distance in ArcGIS reference, "When one feature contains or is within another feature, the distance between them is zero. This means that when a feature is inside a polygon, the distance between the feature and the surrounding polygon is zero." So that appears to be operating as designed.

Would you be able to turn the polygons into polylines and try the Near tool again?

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