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Surface roughness (Ra)

No surface is perfectly smooth – it has microscopic peaks and valleys. $R_a$ is the arithmetic mean deviation of the surface profile from a mean line, given in micrometers. A lower $R_a$ means a finer, smoother surface, which usually requires more machining.

R_a = \dfrac{1}{L}\int_0^L |y(x)|\,dx

arithmetic mean deviation

Symbols

$R_a$	surface roughness	µm
$y(x)$	profile height from the mean line	µm
$L$	sampling length	mm

Example

A ground surface typically has $R_a \approx 0.4$ µm,

while a turned surface may be around $R_a \approx 3.2$ µm.

Do not specify a lower

R_a

than the function actually needs – fine finishing is costly.

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← Hole-basis system (IT tolerances) · Gear ratio →

Part of Machine Design: Tolerances and fits.