Surface roughness Ra
Arithmetic mean profile roughness, measurement scale and units, standards generations, and comparisons with Rq, Rz and Sa.
Tags: parts-and-design, surface-texture, metrology
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Identity and meaning
Ra is the mean absolute height of a roughness profile relative to its reference line. Keep the filter and evaluation settings with the result. KEYENCE, arithmetical mean height
A calculated example is 32 µin × 0.0254 = 0.8128 µm. This unit conversion does not establish equivalence between two measurement procedures or acceptance limits. A bare number such as 32 does not distinguish micrometres from microinches.
AA, for arithmetic average, and CLA, for center line average, are related names listed by ZEISS. The ZEISS ISO 21920 poster defines Ra over the evaluation length, le. These names do not identify the filtering, measurement direction or standards edition. ZEISS, Surface parameters, ISO 21920, August 2023
Mathematical meaning and units
An explanatory expression for the arithmetic mean is:
Ra = (1 / L) × integral from 0 to L of |z(x)| dx
For N equally spaced, equally weighted profile heights:
Ra ≈ (|z1| + |z2| + ... + |zN|) / N
Here z is height relative to the reference line of the assessed roughness profile. L is the applicable assessment length, whose basis depends on the standards generation discussed below. These expressions are explanatory synthesis of the cited arithmetic-mean definition, not an instrument filtering algorithm. The absolute values prevent peaks and valleys from cancelling. KEYENCE, Ra definition
Ra has units of length. Micrometres, µm, and microinches, µin, describe height, while an evaluation length or filter scale can be expressed in millimetres. They are different quantities. The exact inch definition is 1 in = 25.4 mm. Therefore 1 µin = 0.0254 µm, and 1 µm ≈ 39.3701 µin. NIST, SI units, length
Standards generations
ISO lists ISO 21920-2:2021 as the published first edition for profile terms and parameters, with a corrected version dated June 2022. Its lifecycle identifies ISO 4287:1997 and associated amendments and corrigenda as withdrawn predecessors. At this article's review date, ISO also lists a replacement committee draft under development. A draft is not the published replacement edition. ISO, ISO 21920-2:2021 catalogue
| Context | Length basis and applicability |
|---|---|
| ISO 4287:1997 explanation | KEYENCE defines Ra and Rq on a sampling length. Its older educational pages describe this generation and do not establish the current ISO 21920 rules. KEYENCE, profile parameters |
| ISO 21920 explanation | Ra and Rq use the evaluation length. Section-based treatment remains for parameters such as Rz, Rp and Rv. Mahr describes the removal of the old sampling-length terminology and the introduction of nesting indices. Mahr, standards transition |
Mahr reports that MarWin retains older ISO 4287 and ISO 13565 evaluation modes because existing drawings still use them. This is evidence of separate software modes, not evidence that every instrument supports both generations. A historical requirement and a result evaluated under a newer standard are not automatically interchangeable. That last statement is synthesis from the documented changes. Mahr, MarWin and ISO 21920
Measurement scale and evaluation length
A roughness profile is a processed profile. In the older cutoff terminology, removal of long-wavelength components separates roughness from the primary profile. Filter choice is part of the result's definition. KEYENCE, cutoff
For ISO 21920, ZEISS describes the S-filter as suppressing short-wave components, the L-filter as suppressing long-wave components, and the F-operator as removing nominal form. The evaluation length is the evaluated part of the acquired trace. Traverse length also includes pre-travel and post-travel. ZEISS, ISO 21920 terminology
Measurement length, direction relative to grooves and data evaluation affect the reported value. ZEISS also identifies temperature, humidity and surface condition as influences, and warns that different nesting indices can produce different results. Consequently, two Ra numbers alone do not establish a like-for-like comparison. This comparison limit is synthesis of those measurement dependencies. ZEISS, roughness measurement factors
A numerical value without its instrument method, filters, length, direction and measurement location leaves the assessed texture incompletely described. Those missing conditions do not have universal values supplied by this article.
Ra compared with other height parameters
| Parameter | Meaning and distinction |
|---|---|
| Rq | Root mean square profile height. Squaring gives large height deviations more weight than the absolute-value average in Ra. KEYENCE's cited explanation uses ISO 4287 sampling lengths. KEYENCE, Rq |
| Rz | KEYENCE's ISO 4287 explanation describes the maximum peak-to-valley distance on a sampling length. ZEISS's ISO 21920 poster describes Rz as the mean of the peak-to-valley distances of individual sections. The first description is a within-length definition, not a complete statement of older reporting rules. These sources do not establish that averaging first appeared with ISO 21920. Rz is not Ra multiplied by a universal constant. KEYENCE, Rz, ZEISS, ISO 21920 parameters |
| Sa | Areal arithmetic mean height extends the absolute-height average to a surface relative to its mean plane. It belongs to areal surface texture, not a single profile trace. A line Ra and an area Sa have different spatial coverage even when their numbers match. KEYENCE, Sa |
The following mathematical example is synthesis, not measured production data. Assume four equally weighted heights in micrometres, already referenced to a zero mean and processed over the same assessment domain:
| Synthetic heights, µm | Ra, µm | Rq, µm | Peak-to-valley span, µm |
|---|---|---|---|
-1, -1, 1, 1 |
1 | 1 | 2 |
-2, 0, 0, 2 |
1 | about 1.414 | 4 |
The same Ra can coexist with different extremes and Rq values. The span column is not a certified Rz result. An Rz result also depends on the applicable section and aggregation definition. For an identical set of heights and weights, the root mean square inequality gives Rq ≥ Ra. It supplies a bound, not a fixed conversion factor.
Applicability and limits
A contact instrument records stylus motion along the surface. Tip geometry limits access to narrow grooves, and stylus wear can change the measured profile. Contact force can mark the surface. These are measurement-method limitations, not properties represented by Ra itself. KEYENCE, contact instruments
The arithmetic average loses the positions, signs and spacing of individual deviations. This is a mathematical limitation of the Ra definition. Equal Ra therefore does not establish equal scratch depth, lay, waviness, dimensional tolerance or complete topography. A smaller Ra means a smaller absolute-height average only within the stated measurement basis.
Surface texture can affect friction, sealing, adhesion and optical behavior, but those relationships do not make Ra alone a functional qualification. ZEISS describes ISO 21920 as a measurement and specification framework rather than a source of application-specific tolerances. This reference therefore supplies no machining recipe, finishing-process selection, acceptance limit or prediction of service performance from Ra alone. ZEISS, standard scope and surface function
Source coverage and uncertainty
This draft uses publicly accessible manufacturer explanations, the ZEISS August 2023 poster and ISO's catalogue metadata. It does not reproduce or claim access to the complete paid standards. KEYENCE's profile definitions explicitly describe ISO 4287:1997, while the Mahr and ZEISS material explains the ISO 21920 transition. The manufacturer pages without stated revision dates were accessed on 2026-10-29 PDT.
The article does not cover every historical Rz convention, national adoption, drawing default or acceptance rule. No numerical uncertainty budget, calibration certificate, representative sampling study or customer surface data was examined. Accordingly, the worked arithmetic is not a measurement uncertainty estimate or proof of conformance.
Related reference
Dimensions, tolerances and specifications describes the surrounding specification context. Roughness height and dimensional tolerance answer different questions.