Ra, Rz and Rt are all calculated from the same measured profile, but they answer different questions. Ra is an average and hides single scratches, Rz averages five peak-to-valley heights, and Rt is the total height of the roughness profile within the evaluation length. This guide shows how each is defined, how they relate, which mistakes cause rejected parts, and how to estimate the finish of a turned surface before cutting.
TorqueMath · checked against the standards listed below and the calculator’s test cases · Updated
One profile, three values
A stylus instrument traces the surface along a line and records the height z of the profile. The waviness is filtered out with a cut-off wavelength λc, and what is left is the roughness profile. Under ISO 4287:1997 and ISO 4288:1996 the usual evaluation length is five sampling lengths lr (each one cut-off long) unless something else is specified. The ISO 21920 series partly uses different evaluation and specification rules; the definitions and tables below refer explicitly to the older system, which most drawings and instruments in use still follow.
Which standard? ISO 21920 (2021) has replaced ISO 4287, ISO 4288 and ISO 1302 and changes some defaults and drawing symbols. Check which standard your drawing and your instrument refer to.
Ra (arithmetic mean deviation): the average distance of the profile from its mean line, ignoring the sign.
Rz (maximum height of profile, averaged): in each sampling length take highest peak + deepest valley, then average the five values.
Rt (total height of profile): the highest peak plus the deepest valley within the specified evaluation length, so Rt ≥ Rz always. It is not a maximum over the whole workpiece.
How the three values react
Because Ra is an average, a surface with one deep scratch and a surface without it can have similar Ra values, depending on the width and depth of the scratch. Rz picks the scratch up in one of its five sampling lengths, and Rt reports it in full. That is why sealing faces and running surfaces are often specified with Rz or Rt (or both), and general machined surfaces with Ra.
| Value | What it is | Sensitive to single scratches? | Typical use on drawings |
|---|---|---|---|
| Ra | average deviation from the mean line | hardly | general machined surfaces, US drawings (µin) |
| Rz | mean of 5 single peak-to-valley heights | partly (1 of 5) | European drawings, fits, sealing surfaces |
| Rt | largest peak-to-valley over ln | fully | sealing faces, critical running surfaces |
There is no exact conversion from Ra to Rz. The ratio depends on the shape of the profile. For turned surfaces Rz is typically about 4 to 7 × Ra; for ground or honed surfaces the ratio is different. Use a conversion only as a rough guide, and measure the parameter that the drawing asks for.
Cut-off and evaluation length
The same surface gives different values with a different cut-off λc, so the cut-off is part of the result. For non-periodic profiles (ground, lapped, eroded) ISO 4288 chooses λc from the expected Ra; for periodic profiles such as turned surfaces it is chosen from the feed-mark spacing (RSm). Unless the drawing says otherwise, the evaluation length is 5 × λc.
| Expected Ra (µm) | Cut-off λc (mm) | Evaluation length ln (mm) |
|---|---|---|
| 0.006 < Ra ≤ 0.02 | 0.08 | 0.40 |
| 0.02 < Ra ≤ 0.10 | 0.25 | 1.25 |
| 0.10 < Ra ≤ 2.00 | 0.80 | 4.00 |
| 2.00 < Ra ≤ 10.0 | 2.50 | 12.50 |
| 10.0 < Ra ≤ 80.0 | 8.00 | 40.00 |
Periodic profiles use other selection rules; ISO 21920-3 uses a changed specification system.
Old names: Rz DIN, Rz ISO, Rmax and “Rautiefe”
Older drawings and catalogues use names that look the same but are not:
- Rz (DIN 4768, ISO 4287:1997): the mean of five single peak-to-valley heights, as above. This definition is found on many older and still used European drawings; on newer drawings the standard stated on the drawing applies.
- Rz ISO / ten-point height (ISO 4287:1984, JIS RzJIS): the mean of the five highest peaks plus the five deepest valleys inside one sampling length. It is a different value from today's Rz, so the two cannot be compared directly.
- Rmax (DIN 4768): the largest of the five single peak-to-valley heights (today Rz1max). It is not the same as Rt, whose peak and valley may lie in different sampling lengths.
- Rautiefe: in older editions of DIN 4762 (for example DIN 4762-1:1960) the “Rauhtiefe” was denoted Rt, and “gemittelte Rautiefe” meant Rz. In the workshop the word is now often used for Rz, so read the symbol, not the word.
Predicting the finish in turning
In turning, the nose radius r of the insert leaves a row of arcs, one per revolution, spaced by the feed f. For an idealised round nose this gives a geometric cusp height that grows with the square of the feed and falls with the nose radius:
f in mm/rev, r in mm; multiply by 1000 for µm. These are geometric values for an ideal circular cutting edge, not roughness values measured to ISO: filtering, the real edge shape, vibration and material deformation are not included, so measured values can differ considerably.
| Ra (µm) | Ra (µin) | N grade | Typical process |
|---|---|---|---|
| 0.2 | 8 | N4 | fine grinding, honing, lapping |
| 0.4 | 16 | N5 | grinding, fine turning with wiper inserts |
| 0.8 | 32 | N6 | finish turning, grinding: bearing seats |
| 1.6 | 63 | N7 | finish turning, finish milling |
| 3.2 | 125 | N8 | normal turning and milling |
| 6.3 | 250 | N9 | rough turning, sawing |
| 12.5 | 500 | N10 | roughing, flame cutting |
Process ranges are typical, not limits; a good machine and sharp tool can do better, a worn tool worse.
Worked example: turning a shaft seat to Ra 0.8 µm with a CNMG 120408 insert
- The insert code ends in 08, so the nose radius is r = 0.8 mm. Start with a typical finishing feed f = 0.20 mm/rev.
- Geometric cusp height: hth = 0.20² / (8 × 0.8) = 0.00625 mm = 6.25 µm.
- Geometric Ra: 0.20² / (31.2 × 0.8) = 0.0016 mm = 1.60 µm (63 µin). That misses the Ra 0.8 callout.
- Feed for the target in the simplified geometric model: f = √(31.2 · r · Ra) = √(31.2 × 0.8 × 0.0008) = 0.141 mm/rev, which gives Ra,geo ≈ 0.8 µm.
- The measured Ra can differ considerably depending on material, tool geometry, wear, vibration and measuring conditions, so this feed is only a starting value. A wiper insert can allow higher feeds with a good finish; the insert maker's data and a measurement on a test part decide.
Start at about 0.14 mm/rev with an R0.8 insert (geometric model), cut a test part and measure it with the cut-off the drawing asks for. Adjust the feed, or use a wiper insert per the maker's data, from that measurement.
Common mistakes
- Converting a drawing's Rz into Ra with a fixed factor and then machining to the Ra value. Measure the parameter the drawing asks for.
- Measuring with the wrong cut-off. A shorter λc filters out more and gives a smaller value; a longer one gives a larger value.
- Treating Rz and Rt as the same. Rt is never smaller than Rz and reacts to a single defect.
- Using the old ten-point Rz ISO from a Japanese or old catalogue as if it were today's Rz.
- Measuring across the wrong direction. On turned parts measure along the axis, across the feed marks, unless the drawing says otherwise.
- Treating the geometric turning value as a measured value. Measured Ra can differ considerably; measure a test part.
Sources and standards
- ISO 21920-2:2021 Geometrical product specifications – Surface texture: Profile – Terms, definitions and surface texture parameters. Current standard for Ra, Rz and Rt; it replaced ISO 4287:1997, which many drawings still cite.
- ISO 21920-3:2021 – Specification operators (replaced ISO 4288:1996, the source of the cut-off table above).
- ISO 21920-1:2021 – Indication of surface texture (replaced ISO 1302:2002). The N grades come from older ISO 1302 editions (ISO/R 1302:1971) and are no longer part of the 2002 edition.
- ISO 4287:1997 and ISO 4288:1996 (withdrawn) – definitions and cut-off rules used on many existing drawings and instruments.
- DIN 4768:1990 (withdrawn) – Rz and Rmax; DIN 4762 (withdrawn) – terms, including Rautiefe.
- Mitutoyo, “Quick Guide to Surface Roughness Measurement” – practical notes on old and new Rz definitions.
- Turning formulas: geometric cusp height of a round nose, as used in the insert makers' handbooks and in our surface roughness calculator, how it was checked.