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I have grid data representing different values(1-4) and a polygon shapefile with different zones.

How do I calculate percentage distribution for all the values in each polygon in ArcGIS Desktop?

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    Welcome to GIS SE. Thank you for taking the Tour. Please remember to include all software in use in the body of the question. You also may need to explain if/how you want to prorate the portions of pixels not contained within vectors.
    – Vince
    Jan 6 '17 at 12:59
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You can use the tabulate area tool in ArcGIS spatial analyst. It will give your the frequency of each raster value inside each polygon, which you can convert to percentage afterwards. Just make sure to set the pixel size of the analysis equal to the pixel size of your raster, because the default value is often too large.

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