Surface Finish Conversion Chart

Ra, the roughness average, is the mean of the absolute heights of the profile above and below its mean line. Rq is the root mean square of the same heights, which older US drawings call rms. Both are measured over the same length of the same trace, so the ratio between them depends only on the shape of the profile.

Exact. Micrometers to microinches: one microinch is 0.0254 µm, because the inch is 25.4 mm by definition. The ISO grades: N1 is 0.025 µm and each grade above is 10^0.3 times the one below, very nearly double, rounded to the R10 series of preferred numbers, so N7 is 1.6 µm and N12 is 50 µm. Counted from 1 µin, the same series gives the microinch values US charts print, which is why N7 reads 63 µin though 1.6 µm is 62.99. One value is not R10's: R10 has 3.15, and the published grade tables write it 3.2, so N8 is 3.2 µm and N6 is 32 µin, not 31.5 (Machinery's Handbook, p. 740). The reason is ISO 497, whose rounded series allows 3.2 for 3.15. This page follows the tables. Both columns are in the table under the converter. Switching the unit changes only how the value is shown; the grade and the results stay those of the number you typed.

Exact for a shape, not for a part. Rq over Ra is π/(2√2) = 1.111 for a sine wave, 2/√3 = 1.155 for a triangular profile with straight flanks, and √(π/2) = 1.253 for heights spread as a Gaussian. A real surface is none of these, so an Rq read from an Ra, or an Ra read from an old rms callout, is only as good as the shape you assume. Machinery's Handbook notes that an rms instrument reads about 11% higher than an Ra one, the sine's ratio, and that some manufacturers read rms on a drawing as Ra.

Not converted: Rz. Rz is a peak-to-valley height. Its ratio to Ra is π for a pure sine and 4 for a triangle, and for a real surface it changes with the shape and the sampling length. No current standard gives a factor. DIN 4768-1 Supplement 1 (1978, since withdrawn) printed a chart of how far Ra and Rz scatter against each other, a band rather than a factor, so this page does not print one. Agree on an Rz limit with the shop, or measure both. Typical finish by machining process is left out for the same reason: it is experience, not a formula.

Worked example. Ra 1.6 µm is 62.99 µin, grade N7. As a sine it has Rq 1.777 µm. An old 125 rms callout, read as a sine, is Ra 112.5 µin (2.859 µm), between N7 and N8. Load the first with the button under the inputs.

Sources: Machinery's Handbook, 27th ed., p. 728 (Ra, rms and the microinch), p. 689 (the R10 preferred numbers, ANSI Z17.1) and p. 740 (the grades as ISO 1302:1992 gave them, checked against this page). The N grades were dropped from ISO 1302 in 2002 but are still on drawings. ISO 497 and DIN 4768-1 are named from secondary sources.