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I am wondering if there is a tool for calculating variance in a custom size moving window in ArcMap ?

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The standard deviation is the square root of the variance.

You can use the Focal Statistics tool to calculate the standard deviation of your window, then square the result (multiply by itself) using the Times tool or the Raster Calculator to get the variance.

Your moving window can be a square, rectangle, circle, annulus (donut), wedge or a custom window defined by a kernel file.

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