# Ra & RMS: Calculating Surface Roughness

## WHAT DOES RA MEAN?

As described in ASME B46.1, Ra is the arithmetic average of the absolute values of the profile height deviations from the mean line, recorded within the evaluation length. Simply put, Ra is the average of a set of individual measurements of a surfaces peaks and valleys.

Calculating Ra

L = evaluation length
Z(x) = the profile height function

The digital approximation is:

## WHAT DOES RMS MEAN?

As described in ASME B46.1, RMS is the root mean square average of the profile height deviations from the mean line, recorded within the evaluation length.

Calculating RMS

L = evaluation length
Z(x) = the profile height function

The digital approximation is:

## What is the difference between Ra and RMS?

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. The formulas are shown below. One can infer from examination of the formulas, that a single large peak or flaw within the microscopic surface texture will effect (raise) the RMS value more than the Ra value.

The electropolishing process may improve a surface finish by up to 50%. The electropolishing reaction removes material while it improves surface roughness. Because of the material removal, process run times are often limited to maintain dimensional tolerances. Limited run times result in real world surface roughness improvements from 10 to 35%. Remember, electropolishing improves a surface on the microscopic level. If a material has a texture or surface scratch, electropolishing will only result in a lustrous texture or lustrous scratch. Mechanical polishing is utilized to remove macroscopic texture or blemishes.

Request A Quote »