Understanding Surface Finish
RMS and Ra are based on different methods of calculating the roughness. Both are done with a profilometer, but the profilometer calculates the roughness differently for Ra and RMS.
Ra is the arithmetic average of surface heights measured across a surface. Simply average the height across the microscopic peaks and valleys. Ra and RMS are both representations of surface roughness, but each is calculated differently. Ra is calculated as the Roughness Average of a surfaces measured microscopic peaks and valleys. RMS is calculated as the Root Mean Square of a surfaces measured microscopic peaks and valleys. Each value uses the same individual height measurements of the surfaces peaks and valleys, but uses the measurements in a different formula. A single large peak or flaw within the microscopic surface texture will effect (raise) the RMS value more than the Ra value, which is why Ra is more commonly used today as a measurement.

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Ra roughness average is the main height as calculated over the entire measured length or area. It is quoted in micrometers or microinches. For 2 dimensional computation: Ra = 1/n * SUM(ABS[ZiZmean] from i = 1 to n
RMS is a Root Mean Squared calculation. That means you:
The Root Mean Square (RMS)average is precisely that: the square root of the average height deviations from the mean line/surface squared. RMS = SQRT[ 1/n* SUM(ZiZmean)^2 ] from i=1 to n 
Machining surface finish chart: Ra vs RMS
The following is the conversion chart for Ra (um), Ra (micro inch), Rz (um), RMS.
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