Angularity

What angularity controls

Angularity relates a feature to a datum at a specified angle. The tolerance sets a linear zone. KEYENCE: orientation tolerances

In the ideal two-line example, 0.10° of error produces 0.08727 mm of normal spread over 50 mm and 0.17453 mm over 100 mm. Only the first fits a 0.10 mm zone. This assumes a straight segment, correctly established datum, no out-of-plane error and a zone free to contain the segment.

Use the requirement to communicate the functional orientation of such features as an inclined seating surface or an angled bore. Identify the controlled feature and its relationship to the datum before choosing a measurement. A reported angle between two fitted features is not, by itself, evidence that the entire required feature fits its tolerance zone.

Governing standard and drawing information

State the drawing's governing standard and edition. ASME lists Y14.5-2018 (R2024) for dimensioning and tolerancing; its official preview gives an issuance date of 11 February 2019 for the 2018 edition. ISO lists ISO 1101:2017, edition 4, published February 2017 and confirmed in 2022, for the geometrical-specification symbol language and interpretation rules. These are separate frameworks; similar symbols do not justify mixing their defaults or datum rules. ASME standard record, ASME preview, ISO 1101 record

Read the complete indication, not only the angularity symbol:

KEYENCE describes boxed theoretically exact dimensions separately from the feature-control frame that states permissible variation. Avoid applying a general plus/minus angular tolerance to a boxed angle without resolving the drawing's actual rules. KEYENCE: drawings and symbols

Surface zones and axial zones differ

For the simple surface case above, all of the required surface must fit the two-plane zone; checking only a convenient cross-section cannot establish that a wider surface fits. Bow, twist and local high points can matter even when the fitted plane's angle looks satisfactory. Keep a surface requirement separate from a requirement on a derived axis.

Hexagon's PC-DMIS 2021.1 angularity documentation illustrates both diametric and planar zones for axial features. It notes that planar zones on axial features need an adequately specified zone orientation. It also distinguishes the considered feature's sampled surface data from the toleranced feature derived for evaluation. These are important implementation details to check when programming that software, rather than assuming any cylinder fit evaluates any angularity indication. Hexagon: angularity

Do not silently replace a diametric zone with a two-plane calculation, or apply a surface-only interpretation to a bore axis. Similarly, keep material-condition and projected-zone requirements explicit where present. This page's unmodified surface example does not establish the interpretation of every feature-of-size indication or modifier combination.

Datums are part of the measurement

A physical datum feature may be uneven; the datum used for evaluation is an established ideal reference. KEYENCE's datum guide illustrates a surface plate establishing a datum plane from a part surface and distinguishes that reference from the imperfect surface itself. Its quoted definitions are explicitly from ISO 5459:2011 and ASME Y14.5-2009, so use it as an illustration rather than a replacement for the drawing's current governing edition. KEYENCE: datum features

Prepare the datum feature and fixture so dirt, burrs or unstable contact do not change the setup. Establish the required datum sequence and verify that the fixture or software alignment represents it. An arbitrary best-fit alignment of the whole part can obscure the relationship being inspected. Record how a datum was established when results need to be reproduced on another system.

Original geometric illustration

Assume a perfectly straight line segment of length L = 50 mm, lying in the plane of the angular error. Relative to the intended orientation, let its angular error be δ = 0.10°. The spread of its points normal to that intended direction is:

spread = L × |sin δ| = 50 × sin 0.10° ≈ 0.08727 mm.

For an illustrative 0.10 mm two-line zone in this section, that ideal segment can fit. At the same angular error, a 100 mm segment has spread 0.17453 mm and cannot fit that zone. This explains why the same angular error can have different linear consequences over different lengths.

The calculation assumes perfect straightness, a correctly established datum, no out-of-plane error and a zone free to contain the segment under the applicable constraints. It is not a universal conversion of angularity to a degree tolerance, and it does not prove acceptance of a real surface or bore. Surface form, zone shape, feature extent and the full drawing indication still govern.

Inspection methods and limitations

KEYENCE illustrates an angle-plate/mandrel setup that makes the nominally oriented mandrel parallel to a surface plate, followed by a dial-indicator sweep. It also describes a CMM method measuring the datum and controlled feature at multiple points. Those are possible methods, not universal substitutes for the indicated feature and datum construction. A mandrel's fit and alignment must be suitable for what it is meant to represent. KEYENCE: measuring angularity

Choose coverage that can reveal the expected error pattern. Include relevant edges and regions where bow, twist or machining transitions may occur, while accounting for the actual specified extent. Validate the measurement strategy against the part and acceptance requirement; increasing displayed decimal places does not improve sampling coverage.

PC-DMIS explicitly illustrates a measured angularity result smaller than the actual value because points were not measured densely enough. Its evaluation also depends on feature and datum mathematics. Preserve those settings with the program and review changes when migrating a routine. Hexagon: measured versus actual angularity

Report the requirement, evaluated feature/extent, datum setup, measured linear result, applicable measurement uncertainty and decision rule. Resolve an incomplete indication or uncertain datum interpretation before accepting a numerical pass/fail. These are proposed inspection-record fields, not a claim that one instrument or fitting algorithm certifies all angularity requirements.

Source scope

Standards dates above distinguish edition, issuance and confirmation. The Hexagon example is explicitly PC-DMIS 2021.1; KEYENCE's live tutorials have no verified technical revision date here. The trigonometric example and practical inspection-record guidance are original explanatory material.