Population Density Calculation using ArcMap 10.x and and Spatial Analyst

Download the "areagrid" of the world.

Open ArcMap

Verify that the spatial analyst extension is on [Go to "Customize" and then to "Extensions" and check the box for Spatial Analyst].

Load your population grid file and your area grid file into your table of contents.

Navigate to the Spatial Analyst Toolbox in ArcToolbox.  In the “Reclass” toolset, open the “Lookup” tool.  Use the "area" field in the area grid as the Lookup field to reclassify the area grid.

Use the resulting reclassified grid to perform the density calculation:  <popgrid> / <reclassified area grid>.  To do this, navigate to the “Map Algebra” toolset in ArcToolbox, and open the “Raster Calculator”.  Double click the population grid, click the "/" sign, then double click the reclassified area grid.

The "value" field in the resultant grid represents population density (people/sq kilometer) not population count (actual people per cell).

If you want to add the standard LandScan color scheme, right click the file, select "properties". Go to "symbology". Change the display to "classified" and click import. Find the LandScan Population layer file and double click. This will import the color scheme. Click "apply" to add the color scheme to your grid.