Surface Roughness Converter (Ra, µin, CLA, RMS, Rz, N Grade)
Surface Roughness Converter (Ra, µin, CLA, RMS, Rz, N Grade)
Ra in micrometres and microinches, CLA, AA, RMS and the ISO N grades — with a plain account of which of those conversions are exact and which are guesses. Ra to CLA is an identity. Ra to Rq depends on the profile shape. Ra to Rz has no valid conversion at all, and every chart on the web prints one anyway.
Ra, CLA, RMS, Rz and N grades
Ra 63 µin, the figure on most older imperial drawings
One identity, one ratio that depends on shape, and one that does not exist
- Ra
- the arithmetic mean of the absolute deviations of the profile from its mean line, over the evaluation length. Definition unchanged from ISO 4287 to ISO 21920-2
- 0.0254
- micrometres per microinch, exactly, because the inch is exactly 25.4 mm. This is the only exact conversion on the page
- kq
- π/(2√2) = 1.1107 for a sine profile, 2/√3 = 1.1547 for a triangular one, √(π/2) = 1.2533 for Gaussian random heights. All three are derived; the “1.11” in every chart is the sine value with its assumption dropped
- kz
- π for a sine, exactly 4 for a triangle, 7.5 for a Gaussian profile taking Rz as 6σ, and 2 for a square wave. That is the whole published 4-to-7 spread and more, produced by nothing but changing the profile shape at constant Ra. No standard gives a value
Worked example
Ra 63 µin, the figure on most older imperial drawings
A microinch is 0.0254 µm exactly, so 63 µin is 1.6002 µm — and that is the whole of the exact part
The same surface written as CLA or AA is also 63: they are three names for one parameter, not three parameters
The nearest N grade is N7, whose Ra is 1.6 µm — which converts exactly to 62.99 µin, not the 63 the charts print. The microinch ladder is its own rounded series
Rq at the chart's 1.11 is 1.7762 µm; at the Gaussian 1.2533 it is 2.0056 — a 13% spread from the model alone
Rz at the chosen 5× is 8.001 µm, and the published range 4× to 7× puts it anywhere from 6.40 to 11.20. That is why this page will not print one figure and call it a conversion
The N grades, and what the ladder actually is
| Grade | Ra (µm) | Exact (µin) | Charts print (µin) | Chart against exact | Exact doubling from N1 | Against doubling | Mantissa |
|---|---|---|---|---|---|---|---|
| N1 | 0.025 | 0.98 | 1 | -1.57 | 0.0250 | 0.00 | 2.500 |
| N2 | 0.05 | 1.97 | 2 | -1.57 | 0.0500 | 0.00 | 5.000 |
| N3 | 0.1 | 3.94 | 4 | -1.57 | 0.1000 | 0.00 | 1.000 |
| N4 | 0.2 | 7.87 | 8 | -1.57 | 0.2000 | 0.00 | 2.000 |
| N5 | 0.4 | 15.75 | 16 | -1.57 | 0.4000 | 0.00 | 4.000 |
| N6 | 0.8 | 31.50 | 32 | -1.57 | 0.8000 | 0.00 | 8.000 |
| N7 | 1.6 | 62.99 | 63 | -0.01 | 1.6000 | 0.00 | 1.600 |
| N8 | 3.2 | 125.98 | 125 | 0.79 | 3.2000 | 0.00 | 3.200 |
| N9 | 6.3 | 248.03 | 250 | -0.79 | 6.4000 | -1.56 | 6.300 |
| N10 | 12.5 | 492.13 | 500 | -1.57 | 12.8000 | -2.34 | 1.250 |
| N11 | 25 | 984.25 | 1000 | -1.57 | 25.6000 | -2.34 | 2.500 |
| N12 | 50 | 1,968.50 | 2000 | -1.57 | 51.2000 | -2.34 | 5.000 |
Rq ÷ Ra, derived for profiles whose shape is known
| Profile | Rq ÷ Ra | Per cent above Ra | What it is |
|---|---|---|---|
| Sine wave | 1.11072 | 11.07 | a single-frequency profile; the figure every conversion chart quotes |
| Triangular (ideal single-point turning) | 1.15470 | 15.47 | the sawtooth a perfectly sharp tool at constant feed would leave |
| Gaussian random heights | 1.25331 | 25.33 | grinding, lapping, shot blasting — many overlapping cutting events |
| Square wave | 1.00000 | 0.00 | a two-level profile; the theoretical floor of the ratio |
Rz ÷ Ra for the same four profiles, at identical Ra
| Profile | Rz ÷ Ra | Why |
|---|---|---|
| Sine wave | 3.1416 (π) | Peak-to-valley is 2A and Ra is 2A/π, so the ratio is exactly π. Derived, not measured |
| Triangular (ideal turning) | 4.0000 | Peak-to-valley is 2A and Ra is A/2. Exactly four, which is where the bottom of the published range comes from |
| Gaussian random heights | 7.5199 | Taking Rz as the 6σ span of a normal distribution and Ra as σ√(2/π). That is the top of the published range, and it is a grinding or blasting surface |
| Square wave | 2.0000 | Ra equals the amplitude and peak-to-valley is twice it. Below the whole published range — a reminder that 4 is not a floor either |
Typical Ra by process, and the Rz band it implies
| Process | Typical Ra (µm) | Typical Ra (µin) | N grade | Best achievable (µm) | Rz at 4× to 7× (µm) |
|---|---|---|---|---|---|
| Lapping | 0.013 – 0.1 | 1 – 4 | N1 – N3 | 0.006 | 0.05 – 0.7 |
| Polishing, mechanical | 0.025 – 0.4 | 1 – 16 | N1 – N5 | 0.012 | 0.10 – 2.8 |
| Honing | 0.05 – 0.4 | 2 – 16 | N2 – N5 | 0.013 | 0.20 – 2.8 |
| Grinding, fine | 0.1 – 0.4 | 4 – 16 | N3 – N5 | 0.05 | 0.40 – 2.8 |
| Turning, finish | 0.4 – 1.6 | 16 – 63 | N5 – N7 | 0.1 | 1.60 – 11.2 |
| Reaming | 0.4 – 1.6 | 16 – 63 | N5 – N7 | 0.2 | 1.60 – 11.2 |
| EDM, finish | 0.4 – 1.6 | 16 – 63 | N5 – N7 | 0.1 | 1.60 – 11.2 |
| Milling, face | 0.8 – 3.2 | 31 – 126 | N6 – N8 | 0.4 | 3.20 – 22.4 |
| Drilling | 1.6 – 6.3 | 63 – 248 | N7 – N9 | 0.8 | 6.40 – 44.1 |
| Sand casting, as-cast | 12.5 – 25 | 492 – 984 | N10 – N11 | 6.3 | 50.00 – 175.0 |
Three conversions: one exact, one shape-dependent, one fiction
Start with the one that is exact. Ra is the arithmetic mean of the absolute deviations of the surface profile from its mean line. CLA — centre line average — is the same parameter under the older British and ISO name, and AA, arithmetic average, is the same parameter again under the American one. Engineers Edge states it flatly: Ra is “also known as arithmetic average (AA)”, ISO used CLA, and “both are interpreted identical”. So a drawing calling for 63 CLA is calling for Ra 63 µin, and the only arithmetic involved is that a microinch is 0.0254 µm exactly. 63 µin is 1.6002 µm. There is nothing else in that leg, and any chart with separate Ra and CLA columns showing different numbers is wrong.
Now the one that depends on the shape of the surface. Rq, the root-mean-square roughness, still called RMS on older drawings, weights large deviations more heavily than Ra does, so it is always the larger of the two. Every conversion chart on the web prints Rq = 1.11 × Ra. That figure is the exact value for a sine wave: for a sinusoid, Ra is 2A/π and Rq is A/√2, so the ratio is π/(2√2) = 1.1107. Machined surfaces are not sinusoids. A triangular profile — the sawtooth an ideally sharp tool at constant feed would leave — gives 2/√3 = 1.1547. A surface whose heights are Gaussian, which is what grinding, honing, lapping and shot blasting produce because many independent cutting events overlap, gives √(π/2) = 1.2533. Those three numbers are derived and then confirmed here by numerical integration and Monte Carlo, and they span 1.11 to 1.25 — thirteen per cent, from the profile shape alone. That is the whole of the “typically 1.11 to 1.3” the literature reports. So the ratio is an input on this page, with the three derived values printed beside it.
And the one that does not exist. Rz is a peak-to-valley measure: the profile is divided into sections and the largest peak-to-valley height in each is averaged. Ra averages the whole profile. There is no mathematical relationship between them, and there cannot be, because two surfaces can have identical Ra and completely different extremes — a gently waved surface and the same surface with one deep scratch. The demonstration is in the third table above: at identical Ra, a square profile gives Rz/Ra = 2, a sine gives π, a triangle gives exactly 4 and a Gaussian profile with Rz taken as its 6σ span gives 7.5. Those four numbers are not measurements with scatter; they are exact consequences of four shapes. The published rule of thumb, Rz ≈ 4 to 7 × Ra, is a description of which shapes real machining processes produce — turning nearer the bottom, grinding and EDM nearer the top — and no standard sanctions a fixed factor. This page therefore makes it an input, prints the 4× and 7× bounds either side of whatever you choose, and says in the row label that no standard backs it.
The N grades, and which standard is current. N1 to N12 are a ladder of Ra values: 0.025, 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.3, 12.5, 25, 50 µm. They double exactly as far as N8 and then follow the R10 preferred-number series of ISO 3 — 6.3 rather than 6.4, 12.5 rather than 12.8, 25 rather than 25.6 — each about two per cent below the doubling value. The grade numbers come from the annex of ISO 1302:1978, and here is the part worth knowing: ISO 21920, published in December 2021, replaced ISO 1302, ISO 4287, ISO 4288 and ISO 13565-2 and -3, all of which were withdrawn at the end of 2021. The N-number approach is now explicitly discouraged. Ra, Rq and Rt keep their definitions in ISO 21920-2; Rp, Rv and Rz are now computed over section lengths rather than sampling lengths, so a figure measured to the old standard and one measured to the new can differ on the same surface. Put the Ra value on new drawings, and read the N grade on old ones.
One more thing every chart omits. The microinch column in the N-grade tables is not a conversion of the micrometre column. N9 is 6.3 µm, which converts to 248.0 µin, and every published chart prints 250. N8 is 3.2 µm, which is 126.0 µin, and the charts print 125. The microinch figures are a separate conventional ladder — 1, 2, 4, 8, 16, 32, 63, 125, 250, 500, 1000, 2000 — that grew up alongside the metric one, and the two disagree by up to 1.6 per cent. It rarely matters, and it matters absolutely if you are arguing about whether a surface conforms. For the trade gauges these finishes are specified alongside, see the sheet metal gauge converter and the wood screw size converter; for the fractions the drawings are dimensioned in, the inch fraction converter. This page does the arithmetic. Where the answer carries a consequence — a dose, a structural load, a legal area, a medical measure — confirm it against the authority that governs it before relying on it.
Frequently asked questions
Is CLA the same as Ra?
Yes, exactly. CLA (centre line average) and AA (arithmetic average) are older names for the parameter now called Ra. A drawing calling for 32 CLA is calling for Ra 32 µin, which is Ra 0.8128 µm. If a conversion chart shows Ra and CLA as separate columns with different numbers, the chart is wrong.
What is RMS in surface finish, and is it 1.11 times Ra?
RMS is Rq, the root-mean-square roughness. The 1.11 factor is the exact ratio for a sine profile — π/(2√2) = 1.1107 — and nothing else. A triangular profile gives 1.1547 and a Gaussian random surface, which is what grinding and lapping produce, gives 1.2533. Real surfaces run between about 1.0 and 1.3, and the spread is the profile shape rather than measurement error.
How do I convert Ra to Rz?
You do not, and no standard says you can. Published rules of thumb give Rz between four and seven times Ra, and the true figure depends on the process: four is the exact value for an ideal triangular profile, 7.5 comes out of a Gaussian one. Two surfaces with the same Ra can have very different Rz, which is the whole reason both parameters exist. If a drawing specifies Rz, measure Rz.
What is N7 in Ra?
1.6 µm, which is 62.99 µin exactly — although every chart prints 63, because the microinch ladder is its own rounded series. N7 is the commonest general machining callout: a normal milled or turned finish with no special effort.
Is ISO 4287 still current?
No. ISO 21920, published in December 2021, replaced ISO 1302, ISO 4287, ISO 4288 and ISO 13565-2 and -3, and all of those were withdrawn at the end of 2021. Ra, Rq and Rt keep their definitions in ISO 21920-2. Rp, Rv and Rz are now evaluated over section lengths rather than sampling lengths, so the same surface can read differently under the two standards.
Are the N grades still used?
On drawings, constantly; in standards, no. They came from ISO 1302:1978, which is withdrawn, and their use is now explicitly discouraged. They survive because a whole generation of drawings carries them and because a single letter-and-number is easier to put in a title block than a parameter, a value and a sampling length. Specify Ra on anything new.
Why does the microinch column not match the micrometre column?
Because it is a separate ladder. The metric grades are 0.025, 0.05 … 25, 50 µm and the inch ones are 1, 2 … 1000, 2000 µin, and they were rounded independently. 6.3 µm is really 248.0 µin and the charts say 250; 3.2 µm is 126.0 and the charts say 125. The disagreement runs up to 1.6 per cent.
Does a smoother surface mean a better part?
Not necessarily, and specifying one costs money. A cylinder bore is honed to a deliberately cross-hatched finish because it has to hold oil; a sealing face needs a particular Ra band rather than the lowest achievable; a surface that is too smooth can cold-weld or fail to bond an adhesive. Every step down the N ladder roughly doubles the machining time.
Related calculators
References
- ISO 21920-1, -2 and -3:2021, Geometrical product specifications (GPS) — Surface texture: Profile, published December 2021. Copyrighted; cited by number and part. Digital Surf’s technical note What are the differences between ISO 4287 and ISO 21920? (digitalsurf.com, read 26 September 2026) records what it replaced: “ISO 21920 standard officially replaces ISO 1302, ISO 4287, ISO 4288, ISO 13565-2 and -3 which were withdrawn at the end of 2021”, that Ra, Rq and Rt keep their definitions, and that Rp, Rv and Rz are now computed over section lengths rather than sampling lengths.
- finishing.com, Surface finishes N1 thru N12 (finishing.com/75/60.shtml, read 26 September 2026), for the grade ladder and its provenance: the N numbers come from ISO 1302:1978, and “ISO 21920 obsoleted ISO 1302 and its whole N-number approach, and N numbers are now strongly discouraged”. The ladder itself is not a table this page has to copy: it is the R10 preferred-number series of ISO 3, written with 3.2 in place of R10’s 3.15.
- Engineers Edge, Surface Roughness (Finish) Review and Equations (engineersedge.com/surface_finish.htm, read 26 September 2026): Ra is “also known as arithmetic average (AA)” and “ISO standards use the term CLA (Center Line Average)”, with “both are interpreted identical”. That is the whole of the Ra ↔ CLA ↔ AA conversion: there is not one.
- Kemet, Surface Roughness Explained: Ra vs Rz vs Rq (kemet.co.uk/blog/lapping/surface-roughness-explained, read 26 September 2026): Rq is “typically” 1.11 to 1.3 times Ra but “there’s no fixed universal conversion factor between them”, and “two surfaces can have identical Ra values but very different Rz values”.
- MetricMech, Surface Finish Chart: Ra by Process (metricmech.com/reference/surface-finish-chart, read 26 September 2026), citing ISO 4287 and ASME B46.1, for the typical and best-achievable Ra bands by process reproduced in the table below, for “Rz ≈ 4 × Ra to 7 × Ra” and for “Rq ≈ 1.11 × Ra for typical machined surfaces” — which this page shows is the sine-wave value and not a machined-surface one.
- ISO 3:1973, Preferred numbers — Series of preferred numbers, which defines the R5, R10, R20 and R40 series. Copyrighted; cited by number. The R10 series used here — 1, 1.25, 1.6, 2, 2.5, 3.15, 4, 5, 6.3, 8 — is the rounded decimal geometric series with ten steps per decade and is recomputed on this page from 10^(n/10) rather than copied.
- National Institute of Standards and Technology, Refinement of Values for the Yard and the Pound, Federal Register notice of 1 July 1959, which fixed the international inch at exactly 25.4 mm and the avoirdupois pound at exactly 0.45359237 kg. Both exact values are used throughout this batch; every inch-to-millimetre figure here is therefore exact, not approximate.