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I have 16-day Enhanced Vegetation Index (EVI) images for an area across roughly 10 years. 244 images in all. I would like to average these over the time period to get an average EVI value.

Is there a limit to the number of rasters ArcGIS Desktop can perform analysis on in Raster Calculator?

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You can use Cell Statistics instead of raster calculator to get the average. I do not expect there is a limit to the number of raster to be used, but adding 244 is also too much in raster calculator. Cell statistics can do the same job and it can handle many raster, but not tested with hundreds of images. when using Cell Statistics tool, use the statistics_type of Mean to get the average.

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