Ra to Rz Conversion
Drawings from U.S. customers usually call out Ra; European and Asian drawings often call out Rz. There is no formula that turns one into the other, but for a known process the ratio falls in a predictable band. Here is why, what the band is, and how to use it without getting a part rejected.
Why there is no exact conversion
Ra is an average: the mean distance of the profile from its center line over the whole trace. Rz is an extreme: the tallest peak-to-deepest-valley height in each sampling length, averaged over (normally) five of them. Two surfaces with the same Ra can have very different Rz. A regular turned surface keeps its peaks and valleys close to the average, so Rz is about four times Ra. A ground or lapped surface with an occasional deep scratch keeps nearly the same Ra, but every scratch lands in Rz.
The ratio is exact only for idealized shapes, which is where the familiar rules of thumb come from:
| Ideal profile | Rz / Ra | Why |
|---|---|---|
| Sine wave | 3.14 | Smooth periodic waviness. Rz / Ra = pi. |
| Turned feed marks (round-nose tool) | 3.90 | Rt = f² / 8r and Ra = f² / (18√3 r), so the ratio is fixed at about 3.9. |
| Triangle or sawtooth | 4.00 | Sharp-tool marks. Rz / Ra = 4 exactly. |
f = feed per revolution, r = tool nose radius. Example: 0.2 mm/rev with a 0.8 mm nose gives a theoretical Ra of 1.60 µm and Rt of 6.25 µm. Real surfaces come out rougher than theory.
Typical Rz / Ra ratio by process
| Process | Typical Rz / Ra | Why |
|---|---|---|
| Turning | 4 to 6 | Regular feed marks. Close to the ideal of about 3.9, pushed up by built-up edge, chatter and tearing. |
| Milling | 4 to 7 | Periodic cusps and tooth marks, with more variation across the cut than turning. |
| Grinding | 5 to 8 | Random scratches from many abrasive grains. A random profile has occasional deep valleys relative to its average. |
| Lapping, honing, polishing | 6 to 10 | Very low Ra, so a single stray scratch or a plateau-honed valley structure moves Rz a lot. |
Shop-floor rules of thumb with wide scatter, for estimating only. Tool wear, chatter, material and the measuring cutoff all move the ratio.
Ra with typical Rz range
| N grade | Ra (µm) | Ra (µin) | Typical Rz (µm) | Typical Rz (µin) |
|---|---|---|---|---|
| N1 | 0.025 | 1 | 0.1 to 0.25 | 3.94 to 9.84 |
| N2 | 0.05 | 2 | 0.2 to 0.5 | 7.87 to 19.7 |
| N3 | 0.1 | 4 | 0.4 to 1 | 15.7 to 39.4 |
| N4 | 0.2 | 8 | 0.8 to 2 | 31.5 to 78.7 |
| N5 | 0.4 | 16 | 1.6 to 4 | 63 to 157 |
| N6 | 0.8 | 32 | 3.2 to 8 | 126 to 315 |
| N7 | 1.6 | 63 | 6.4 to 16 | 252 to 630 |
| N8 | 3.2 | 125 | 12.8 to 32 | 504 to 1260 |
| N9 | 6.3 | 250 | 25.2 to 63 | 992 to 2480 |
| N10 | 12.5 | 500 | 50 to 125 | 1969 to 4921 |
| N11 | 25 | 1000 | 100 to 250 | 3937 to 9843 |
| N12 | 50 | 2000 | 200 to 500 | 7874 to 19685 |
Rz range = Ra x 4 to Ra x 10, the span of the process table. Turned and milled surfaces sit near the low end, ground and lapped surfaces near the high end. The Ra grades and microinch equivalents follow the surface finish chart.
Have a drawing with an Ra or Rz callout? , or browse CNC machining shops.
Measuring so the numbers compare
Ra and Rz only compare when they come from the same trace, filter and cutoff. For non-periodic profiles the default roughness cutoff follows the expected Ra:
| Ra over (µm) | Ra up to (µm) | Cutoff (mm) |
|---|---|---|
| 0.006 | 0.02 | 0.08 |
| 0.02 | 0.1 | 0.25 |
| 0.1 | 2 | 0.8 |
| 2 | 10 | 2.5 |
| 10 | 80 | 8 |
- Periodic profiles (turned, milled) take the cutoff from the spacing of the tool marks instead.
- Measure across the lay (perpendicular to the tool marks) unless the drawing says otherwise.
- If the drawing gives Rz, inspect Rz. Converting a callout to Ra for inspection is how parts get rejected at incoming inspection.
Related charts and processes
Frequently asked questions
- Is Rz 4 times Ra?
- Only for an ideal triangular profile. It is a fair first guess for a clean turned surface, where the theory gives about 3.9. Ground, honed and lapped surfaces have random profiles with occasional deep scratches, and Rz there often runs 6 to 8 times Ra or more.
- What is the difference between Rz, Rmax and Rt?
- Rz averages the biggest peak-to-valley height found in each sampling length, normally five of them. Rmax (called Rz1max in current ISO) is the largest of those five. Rt is the peak-to-valley over the whole evaluation length. On the same trace Rt is at least Rz1max, which is at least Rz.
- Is Rz the same in ISO, ASME and JIS?
- ISO 4287 (now ISO 21920-2), ASME B46.1 and the old DIN Rz all mean the average of the maximum heights per sampling length. The older ISO and JIS "ten-point height", now labeled RzJIS, averages the five highest peaks and five deepest valleys and reads differently. Check which one an older drawing means.
- What Rz should I expect from Ra 0.8 µm?
- Somewhere around 3.2 to 8 µm, depending on the process and on how clean the surface is. If the drawing calls out Rz, measure Rz; a profilometer reports both parameters from the same trace.
- Should I specify Ra or Rz?
- Ra is the U.S. default and fine for general machined surfaces. Rz (or Rmax) says more when peaks and scratches matter: sealing faces, press fits, bearing seats and surfaces under coatings. Where both matter, call out both.
