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In some instances, the Kernel Density tool generates a blank output with a very small extent. In other cases, wrong density values are generated.
To check the extent of the layer, right-click the layer, click Properties, and click the Source tab.
The issue occurs because the projection of the data is in a geographic coordinate system (GCS). To use the tool, the data must be in a projected coordinate system (PCS) that has a linear unit of measurement because the tool calculates the number of features per unit area.
Examples of linear units of measurement are feet, meters, kilometers, and so forth.
A GCS uses decimal degrees based on a spheroid as its units of measure, and is therefore, subject to spatial distortion that affects the accuracy of distance.
Re-project the data into a suitable PCS using the Project (Data Management) tool. For more information about this tool, refer to the following ArcGIS Help document, Project (Data Management).