# Straightness

Distinguishing surface-line and derived-median-line straightness, with explicit extent, sampling and evaluation choices.

Reviewed: 2026-11-01

Tags: parts-and-design, specifications, gdt, straightness

## Meaning and governing framework

Straightness controls form without a datum. Identify the surface line or derived feature before choosing the measurement. [KEYENCE form tolerances](https://www.keyence.com/ss/products/measure-sys/gd-and-t/type/form-tolerance.jsp)

An exact 100 mm line with slope 0.001 has a height range of **0.100 mm** relative to horizontal and **zero straightness error**. In the separate bow example, both endpoints are at zero but the center departs by 0.020 mm. Orientation and sampling can change what a simple height comparison reveals.

Read the drawing's governing standard and edition. ASME lists **Y14.5-2018 (R2024)**; ISO lists **ISO 1101:2017**, edition 4, February 2017, confirmed in 2022. These separate systems supply interpretation rules; a similar symbol does not establish identical defaults. Reaffirmation and confirmation do not create newly numbered technical editions. [ASME record](https://www.asme.org/codes-standards/find-codes-standards/y14-5-dimensioning-tolerancing/2018), [ISO 1101 record](https://www.iso.org/standard/66777.html)

ISO's straightness-specific references are **ISO 12780-1:2011**, vocabulary and parameters, and **ISO 12780-2:2011**, specification operators. Both records identify edition 1, April 2011, confirmation in 2021, and systematic review underway. Their stated scope concerns complete straightness profiles of integral features. Do not silently transfer that surface-profile scope to every derived-axis indication. [ISO Part 1](https://www.iso.org/standard/53622.html), [ISO Part 2](https://www.iso.org/standard/53623.html)

## Surface line or derived median line

**PC-DMIS 2023.2** distinguishes surface straightness, evaluated between parallel lines in the relevant workplane, from axial straightness, evaluated using a derived median line inside a cylindrical zone. Its cylindrical-feature implementation constructs section centers from surface data; a single fitted ideal cylinder axis is not the same dataset. [Hexagon straightness, surface and axis sections](https://docs.hexagonmi.com/pcdmis/2023.2/en/helpcenter/mergedProjects/core/geometric_tolerances/Straightness.htm)

| Requirement information | Question to resolve |
| --- | --- |
| Attachment | Is a surface element or a derived feature controlled? |
| Direction/workplane | Which line elements and section orientation apply? |
| Zone | Is the value a two-line separation or a cylinder diameter? |
| Extent | What length, area or local/per-unit requirement applies? |
| Modifiers | What additional conditions are explicitly specified? |

Do not replace a diameter zone with a plus/minus radius allowance of the same number. Likewise, an isolated trace on a wide face does not establish every required line element. Whole-face flatness and individual-line straightness answer different questions, even when the same instrument can acquire both datasets.

## Original examples: tilt and missed bow

First consider the exact straight segment `y = 0.001x`, over **0 ≤ x ≤ 100 mm**. Its height range relative to the horizontal reference is **0.100 mm**, but its ideal straightness is **zero**: coincident straight lines can contain it. A reference-oriented height span includes tilt and cannot automatically be relabeled as a straightness error.

Now consider the deliberately bowed profile:

`y(x) = 4h × x(L − x) / L²`, with `L = 100 mm` and `h = 0.020 mm`.

At **x = 0** and **100 mm**, `y = 0`. At **x = 50 mm**, `y = h = 0.020 mm`. Thus endpoint-only readings miss a **20 µm** center departure. Horizontal lines at y = 0 and y = 0.020 mm form one candidate enclosing strip for the entire ideal profile.

This constructs an envelope about a selected orientation; it does not perform arbitrary measured-data optimization or specify a production tolerance. The example assumes the exact equation, complete profile knowledge and no measurement error. Real traces require a suitable association method and cannot establish unmeasured regions merely because their endpoints agree.

## Acquisition and evaluation

KEYENCE illustrates leveling a long target with small jacks for a height-gauge traverse, and describes a CMM alternative. It also notes sensitivity to contact force and difficulty with parts that cannot be leveled. Those examples show measurement arrangements, not a universal support pattern or sufficient point count. [KEYENCE measuring straightness](https://www.keyence.com/ss/products/measure-sys/gd-and-t/form-tolerance/straightness.jsp)

Choose trace locations and spacing to reveal expected bow, local tooling effects and transitions. Document what length was actually measured. Preserve support and restraint: a flexible object can change form under its own weight, clamping or probe contact. A result acquired in an agreed restraint state should not silently represent the unrestrained part.

For axial evaluation, plan the cross-sectional acquisition and center construction explicitly. PC-DMIS 2023.2 requires the appropriate sectional data for its cylindrical/conical implementation. It documents DEFAULT minimum-zone and LSQ fits, which can produce different results, and material-condition options for cylindrical axial straightness. These are named software capabilities, not authority to extend modifiers to an ordinary surface trace. [Hexagon feature types, mathematics and modifiers](https://docs.hexagonmi.com/pcdmis/2023.2/en/helpcenter/mergedProjects/core/geometric_tolerances/Straightness.htm)

Record the selected algorithm rather than changing it to obtain a favorable result. Check the software's actual construction against the governing requirement, including relevant size evaluation when a material condition applies. A least-squares size or fitted axis used elsewhere in the program is not automatically the appropriate input for this control.

## Interpretation and acceptance

Keep straightness separate from size, location and orientation requirements. Straightness alone does not establish whether a shaft fits its mating feature or whether a guide surface points in the intended direction. Apply the complete product definition and resolve incomplete attachment, direction or extent before accepting a numerical result.

For a useful human or agent handoff, retain the part/revision, governing edition, controlled feature, trace/section orientation, extent, modifiers, support condition, acquisition coverage, filtering, association and program version. Report the linear result in its specified units with applicable uncertainty and decision rule. Preserve the profile or section data where needed to explain disagreement between methods.

These are proposed inspection-record fields rather than a normative report template. Sparse sampling, different workplanes, changed restraint and different fitting methods can produce different numbers for the same part; investigate those inputs before treating a disagreement as a manufacturing change.

## Source scope

The ISO 12780 records describe integral-feature profile scopes; they are not a replacement for the full drawing interpretation. Hexagon's example is explicitly PC-DMIS 2023.2. KEYENCE's live tutorials have no verified technical revision date here. The line and parabolic-profile calculations and proposed record fields are original explanatory guidance.

[Dimensions, tolerances and specifications](index.md)