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I have the same problem as Curlew in Get Raster Values from a Polygon Overlay in Opensource GIS Solutions and thecrashlandingdodo in Step-by-step: How do I extract Raster values from Polygon overlay with Q-GIS or R?. Curlew says it's rather easily done in ArcGIS, but I just don't know how and R is on my to-learn list.

I have many polygons in a shapefile and a raster with different values. I would like to know for each polygon how many percent each raster value has in that polygon. Any of the zonal stats does not seem to do this (or did I miss something?).

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In ArcGIS, you can use tabulate area for this. It will give you a table as output with the number of pixels of each class within each polygon. Then you need to divide each column by a the total count and you have the percent. Note that ArcGIS selects a default raster size for internal analysis. So it is better to specify the pixel size in the environment of the tool (otherwise, you could have resampling errors).

From QGIS, this answer indicates that SAGA GIS has the tool

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