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I'm using ArcMap 10.5.

I have two individual days of precip data rasters from NOAA/NWS.

I want to combine the two days with the cumulative total storm precip displayed in a new raster.

Many of the cells contain no data, and display as a value of -10000.

I've tried the raster calculator but the missing data cells cause a strange display.

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Your NoData cells actually contain the value -10'000 and therefore produce said "strange values". So you need to tell the Raster Calculator to ignore these values. You can do this using SetNull (see this link), as the expression below shows:

SetNull("raster1" == -10000, "raster1") + SetNull("raster2" == -10000, "raster2")

This will change the -10'000 to actual NoData values in your raster before processing.

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