Ra, Rz and the fit: why the rule Rz equals four times Ra misleads
Two parameters answering different questions
Ra is the arithmetic mean roughness. The instrument takes the distances of the profile from the mean line, takes their magnitudes and averages them over the measured length. A single deep scratch practically disappears in that average.
Rz is an extreme value. The measured length is divided into five sections, in each section the distance between the highest peak and the deepest valley is taken, and those five values are averaged. A deep groove shows up here in full.
Both describe the same surface and still answer different questions. Ra says something about the general condition of a face, Rz about its extremes. For a sealing face or a press fit, the extremes are what count.
Why the ratio depends on the profile shape
The conversion factor between Ra and Rz is not a constant; it follows from the shape of the profile.
Turning and milling produce an almost regular sawtooth profile from the feed marks of the cutting edge. For an ideal triangular profile of amplitude A, Ra = A/2 and Rz = 2A, so the ratio is 4. That is why the rule of thumb works on turned surfaces.
Grinding, EDM and lapping look different. There the peaks and valleys are randomly distributed, roughly normally. For such a distribution with standard deviation σ, Ra ≈ 0.8 · σ and Rz ≈ 5 · σ. That puts the ratio between 6 and 7.
| Profile shape | Produced by | Rz / Ra |
|---|---|---|
| periodic | turning, milling, reaming, broaching | about 4 |
| stochastic | grinding, honing, EDM, lapping, casting | about 6 to 7 |
The roughness converter distinguishes both cases and also gives a range, because there is scatter within one profile shape as well.
In practice: a ground surface with Ra 0.4 µm has a peak-to-valley height of roughly 2.4 to 2.8 µm, not 1.6 µm. Use the wrong factor and you underestimate the roughness by 50 percent. On a press fit that is exactly the order of magnitude you cannot afford to get wrong on the interference.
What a process can actually deliver
A roughness requirement only makes sense if a process reaches it without an extra operation. The overview below gives the range between what is still achievable with care and the usual production value.
| Process | Ra in µm |
|---|---|
| Sand casting, flame cutting | 12.5 … 50 |
| Rough turning, sawing | 6.3 … 25 |
| Drilling | 1.6 … 12.5 |
| Finish turning, finish milling | 0.8 … 6.3 |
| Reaming, broaching | 0.4 … 3.2 |
| Wire EDM | 0.4 … 3.2 |
| Grinding | 0.1 … 1.6 |
| Honing, fine grinding | 0.05 … 0.4 |
| Lapping | 0.012 … 0.2 |
Experience values from production engineering, not a standard. Material, tool condition and coolant shift the limits in both directions.
The steps between the rows are steps in cost. From Ra 1.6 to Ra 0.8 you can often still get there in turning with a smaller feed and a sharper edge. From Ra 0.8 to Ra 0.4 normally takes a different machine. Writing Ra 0.8 on every face because it looks thorough makes parts more expensive with no functional return.
Roughness and fits belong together
In measurement
A two-point measurement touches the highest points. If the peak-to-valley height is large compared with the size tolerance, you are essentially measuring the roughness. As a rough limit, Rz should be at most a quarter of the size tolerance. For IT7 at Ø 30 mm with 21 µm of tolerance that means Rz below about 5 µm, so roughly Ra 1.25 µm on a turned surface. A reamed bore meets that, a rough-turned one does not.
In assembly
Pressing parts together deforms the roughness peaks plastically. The share of interference lost in the process is called smoothing and is estimated to DIN 7190:
smoothing ≈ 0.8 · (Rz_bore + Rz_shaft)
Example: Rz 10 µm in the bore, Rz 6.3 µm on the shaft
→ 0.8 · 16.3 = 13 µm come off the interference
For an H7/p6 pairing at Ø 30 mm the interference lies between 1 and 35 µm. After subtracting the smoothing, nothing is left in the unfavourable case and the joint is loose. That is why every calculated press fit needs a roughness specification, and one that is actually held.
On sealing faces
Radial shaft seals come with their own requirements: Rz between 1 and 4 µm is customary, and the surface has to be lead-free. Lead-free means plunge ground in practice, because a surface ground or turned with axial feed carries a fine helix that acts like a conveyor screw. Such a seat pumps oil outwards even though the roughness is correct and the seal is sound.
In fatigue strength
Every groove is a notch. On cyclically loaded parts a rough surface measurably lowers the fatigue strength, and the stronger the material, the more it matters. A high-strength quenched and tempered steel reacts far more sensitively to grooves than a soft structural steel. On shaft shoulders with a transition radius it is therefore worth a finer surface exactly where the stress is highest.
What belongs on the drawing
The roughness specification to ISO 21920, which since 2021 replaces the former ISO 4287 and ISO 4288, asks for more than a number: the parameter, the limit rule and, where it matters, the cut-off wavelength of the filter. In practice a clear combination is usually enough.
- Ra on its own is enough for uncritical faces and is the most common specification.
- Rz in addition wherever individual deep grooves are a problem: sealing faces, press fits, dynamically loaded parts.
- Rmr or the material ratio curve wherever a load-bearing surface is required, for example on honed cylinder bores. A plateau profile with deep oil grooves has a high Rz and still a high bearing area, which Ra alone cannot express.
- The lay direction where it has a function, that is on sealing seats.
The old roughness classes N1 to N12 still turn up on legacy drawings. Only the Ra value in them is standardised; the Rz column in such tables has always been a conversion with an assumed factor. So when moving an old drawing to Rz, take the profile shape of the process into account rather than copying the table column.
Frequently asked questions
Can I simply convert Rz into Ra?
Only if you know the profile shape, and even then only as an estimate. On turned surfaces the factor is around 4, on ground ones between 6 and 7. A conversion does not replace a measurement: two surfaces with identical Ra can differ by a factor of two in Rz.
What do the US values 32 and 63 µin mean?
Those are microinch values for Ra. 32 µin corresponds to 0.8 µm, 63 µin to 1.6 µm and 125 µin to 3.2 µm. One micrometre is 39.37 microinches. Those three values correspond to the old classes N6, N7 and N8.
Why does my instrument give a different value every time?
Because roughness is a local property. Two traces on the same face give different values, especially for Rz. On top of that comes the influence of the filter cut-off: the same face measured with a different filter gives a different parameter. That is why the measuring conditions belong in the report whenever a case is disputed.
Is a smoother surface always better?
No. Sliding pairs need valleys to hold lubricant. A cylinder bore polished to a mirror finish would have no oil supply and would seize. That is why honed bores are deliberately made as plateau profiles: smooth load-bearing areas with deep oil grooves in between.