Ra is the arithmetic mean of the absolute heights of a roughness profile relative to its mean line. It measures an average, not the deepest scratch or highest peak.
Last updated 2026-10-15
Ra = average of |profile height|. Take the absolute values after referencing the roughness profile to its mean line, then average them. Report a length unit, usually µm or µin, and the measurement conditions. A lower Ra means a smaller average deviation under those conditions.
For a continuous roughness profile:
Ra = (1/L) ∫₀ᴸ |z(x)| dx
Here z(x) is the profile height relative to the mean line, x is distance along the trace, and L is the averaging length required by the chosen measurement method. For equally spaced discrete samples:
Ra ≈ (|z₁| + |z₂| + … + |zₙ|) / n
Signed heights can cancel, so averaging z directly does not calculate Ra. Raw unfiltered surface heights also need form removal, filtering and the appropriate reference line before they represent a roughness profile. Mitutoyo’s parameter guide illustrates the Ra and Rq definitions.
Suppose five illustrative roughness-profile heights are −2, +1, 0, +2, −1 µm, already referenced to a mean line of zero.
| Sample | z (µm) | |z| (µm) |
|---|---|---|
| 1 | -2 | 2 |
| 2 | +1 | 1 |
| 3 | +0 | 0 |
| 4 | +2 | 2 |
| 5 | -1 | 1 |
Ra = (2 + 1 + 0 + 2 + 1) / 5 = 1.2 µm. The signed average is zero, which shows why the absolute values matter. For these same points, Rq = √((4 + 1 + 0 + 4 + 1) / 5) ≈ 1.414 µm.
1 µin = 0.0254 µm exactly, so µin = µm / 0.0254. The example above is 1.2 µm ≈ 47.2 µin.
| Ra (µm) | Ra (µin), rounded |
|---|---|
| 0.8 | 31.5 |
| 1.6 | 63.0 |
| 3.2 | 126.0 |
A callout such as “Ra 1.6 µm max” specifies an upper roughness limit under the stated measurement conditions. An unlabelled “Ra 32” is ambiguous: confirm the drawing units. See the surface finish chart for other reference values.
| Parameter | What it describes | Practical distinction |
|---|---|---|
| Ra | Arithmetic mean of absolute profile heights. | A useful average that does not preserve the shape or location of defects. |
| Rq / RMS | Root mean square of profile heights. | Squaring the heights gives larger deviations more weight. Rq is at least Ra for the same data and weighting. |
| Rz | A peak-to-valley height parameter; its definition and aggregation depend on the specified standard. | Check the standard and edition when comparing modern and legacy results. |
There is no universal Ra-to-Rq or Ra-to-Rz conversion factor. A ratio estimated for one process or profile is not a measured value for another. The Ra-to-Rz estimator can support preliminary comparisons, but does not replace measuring the required parameter.
Two surfaces can share an Ra yet have different isolated valleys or peaks. Select additional parameters from the functional requirement rather than assuming Ra alone describes sealing, wear or fatigue behaviour.
ISO 4287:1997 is withdrawn; ISO lists ISO 21920-2:2021 as its replacement for profile terminology and parameters. ISO 21920-3:2021 covers specification operators and associated settings.
Legacy drawings may still explicitly require ISO 4287 and the associated legacy measurement rules. Do not silently apply a different edition: agree the applicable method before comparing results. The five-point example above explains an arithmetic average; it does not reproduce all requirements of either standard.
Public references checked on 15 October 2026. Diagrams and the five-point example are original teaching material. Unit conversions use 25.4 mm per inch. Full standards are not reproduced; use the specified edition for inspection.
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