Controlled numerical screening
Profile-Ordinate Statistics Worksheet
Calculate transparent discrete statistics from equally spaced profile ordinates. This worksheet deliberately does ei infer Rz, Rq, Rt, a cutoff wavelength or ISO 21920 conformance from one Ra value.
No Ra-to-Rz conversionNo automatic cutoff tableNo ISO conformance claim
Decision boundary. The complete acquisition, stylus/instrument characteristics, levelling, filters, nesting indices, section lengths, end treatment, parameter operator and uncertainty evaluation must be performed by a controlled external metrology method. The outputs below use starred names (A*, Q*, H*) because this page does not reproduce the licensed ISO 21920-2/-3 operator.
4. Discrete screening result
Ordinate count
Removed arithmetic mean
A* mean absolute deviation
Q* RMS deviation
Q* / A*
Centered minimum
Centered maximum
H* maximum−minimum
Method and applicability
m = (1/N) Σ xᵢ
zᵢ = xᵢ − m
A* = (1/N) Σ |zᵢ|
Q* = √[(1/N) Σ zᵢ²]
H* = max(zᵢ) − min(zᵢ)
zᵢ = xᵢ − m
A* = (1/N) Σ |zᵢ|
Q* = √[(1/N) Σ zᵢ²]
H* = max(zᵢ) − min(zᵢ)
What is calculated
- Arithmetic-mean removal.
- Equal-weight discrete A*, Q* and range H*.
- Exact nm/µm/mm normalization.
What is not calculated
- Rz or Rt under a licensed operator.
- Filters, cutoff/nesting indices or section rules.
- Measurement uncertainty or conformity.
Input requirements
- One ordered, equally spaced dataset.
- One common ordinate unit.
- Controlled external acquisition and preprocessing.
Why one Ra value is insufficient. The centered profiles [−1, +1] and [−2, 0, 0, +2] both have mean absolute deviation 1. Their RMS deviations are 1 and √2, while their ranges are 2 and 4. Therefore Rq-like and height-extreme quantities cannot be recovered uniquely from Ra alone.
Sources and standards boundary
- ISO 21920-2:2021, edition 1, corrected English version 2022-06: published terms, definitions and parameters for profile-method surface texture. As of 2026-07-15 it is at stage 90.92 (to be revised); a committee draft is under development and is not the published edition.
- ISO 21920-3:2021, edition 1: published complete specification operator for profile-method surface texture. As of 2026-07-15 it is also at stage 90.92; a committee draft is under development.
- ISO 4287:1997 was withdrawn on 2021-12-20 and revised by ISO 21920-2:2021.
- ISO 3274:1996 was withdrawn on 2025-02-14 and revised by ISO 25178-601:2025. The former claim that ISO 21920 itself replaced and consolidated ISO 3274 was inaccurate.
- NBS Technical Note 1151, section 2.4.1, printed pages 8–9: gives the equal-spacing discrete mean-absolute and RMS expressions and states that RMS is at least the mean absolute deviation. These general numerical relations do not implement ISO 21920.
- PTB surface-metrology standards overview: identifies ISO 21920-2 as the terms/parameter part and ISO 21920-3 as the specification-operator part.
Luokitus: the arithmetic on this page is a general discrete screening calculation, not an “ISO formula calculator.” Exact ISO 21920-2 parameter definitions and ISO 21920-3 default/complete operator tables, limits and rules are NEEDS_LICENSED_SOURCE before any conforming implementation. No closed cutoff or evaluation-length table is reproduced or guessed.
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