# Roundness measuring instruments

Selecting and using roundness instruments with controlled alignment, profile evaluation, filtering and realistic uncertainty limits.

Reviewed: 2026-11-01

Tags: inspection, dimensional-metrology, roundness

Report the cross-section, reference circle and filtering with a roundness result. These choices define the radial profile being evaluated.

**Illustrative calculation:** after the prescribed filtering and LSC fit, suppose the largest radial departure is **+1.8 µm** and the smallest is **−1.2 µm**. The peak-to-valley radial departure is `1.8 − (−1.2) = 3.0 µm`. It is not 6.0 µm: do not double a radial zone width as though converting a radius to a diameter. A different association requires recalculation from the profile, not relabelling this value.

Opposed diameter readings are also insufficient. The **EMRP IND62 TIM** guide explains that two-point diameter measurements can miss odd-lobed shapes such as triangular or five-lobed profiles. Its worked application concerns large rolls; the important distinction is geometric, not a transferable instrument accuracy. [Hemming and Widmaier, *Good Practice guide to measure roundness on roller machines and to estimate their uncertainty*, section 3.1, undated PDF hosted by PTB](https://www.ptb.de/emrp/fileadmin/documents/tim/GPG_roundness_measurement.pdf)

## What the instrument measures

Precision rotary instruments use a rotating workpiece or rotating measuring stylus to obtain a circumferential trace. NIST describes both arrangements and the use of equally spaced angular measurements to determine departures from a fitted circle. The spindle supplies a rotational reference, but its own motion contributes to the observed trace. [NIST/SEMATECH e-Handbook, Roundness measurements, undated page](https://www.itl.nist.gov/div898/handbook/mpc/section3/mpc344.htm)

Keep these quantities separate:

| Quantity | Boundary of the result |
| --- | --- |
| Roundness | Form of the evaluated circumferential section |
| Diameter | Size determined by the selected measurement and association method |
| Circular runout | Variation relative to the specified rotational datum arrangement |
| Cylindricity | Form of a cylindrical surface, requiring an appropriate three-dimensional sampling/evaluation strategy |

A good roundness result at one height does not establish the whole cylinder's form or its relationship to another feature. Record section positions and datum requirements rather than treating one convenient trace as complete coverage.

## Centering, leveling and contact

Center the feature relative to the rotational axis and level its axis before measuring. Mitutoyo explains that eccentricity causes polar distortion, often called limaçon error, while axis inclination introduces an elliptical error. Software correction has limits and is not a substitute for following the instrument's alignment procedure. [Mitutoyo, *Quick Guide—Roundness Testing*, alignment section, undated technical excerpt](https://www2.mitutoyo.co.jp/eng/products/menu/QuickGuide_Roundtest.pdf)

Clean the contact path and support surfaces; hold the part securely without introducing distortion. Define clamping and support when thin walls or compliant parts are involved. Check stylus access to the intended section, especially near shoulders, interrupted surfaces and small internal diameters. Choose tip geometry and contact force for that setup rather than copying a maximum machine specification into the inspection instruction.

A trace is a measurement through a finite contact, not an ideal mathematical point. Preserve tip identity, force and scan conditions when comparing results. A different tip or inaccessible recess can change what surface detail is captured even when the evaluation software is unchanged.

## Reference-circle selection

Mahr identifies four common circular association methods:

| Method | Association used |
| --- | --- |
| Least-squares circle, LSC | Minimizes the sum of squared profile departures |
| Minimum-zone circles, MZC | Two concentric enclosing circles with the least radial separation |
| Minimum circumscribed circle, MCC | Smallest circle enclosing the measured profile |
| Maximum inscribed circle, MIC | Largest circle fitting inside the measured profile |

These definitions concern the selected profile; they do not reconstruct missing surface information. Choose the association required by the specification and functional evaluation. Do not silently exchange LSC and MZC because the latter produces a more favourable number. [Mahr, MarForm Evaluation methods, undated](https://parameter.mahr.com/html/english/MarForm/formtester.html)

## Filters, angular sampling and interpretation

**Undulations per revolution (UPR)** describe circumferential frequency content. Record the filter type and passband/cutoff, not just a setting such as “50”. Mitutoyo shows that changing the cutoff changes the evaluated roundness and distinguishes low-pass from band-pass results. It also identifies 1 UPR with eccentricity and notes that a 2 UPR component can arise from leveling error or actual elliptical form. Harmonic content is therefore diagnostic evidence, not a unique diagnosis of a manufacturing fault. [Mitutoyo, filter and UPR guidance](https://www2.mitutoyo.co.jp/eng/products/menu/QuickGuide_Roundtest.pdf)

Record angular coverage, point count, speed and any excluded regions. Partial traces, notches, outlier deletion and smoothing need an explicit evaluation policy. A smooth polar plot may hide removed information; retain the underlying data and settings when investigating a process change.

## Bounded equipment example

Mitutoyo's **RA-120P Bulletin 1943, printed August 2008**, provides an example of why configuration details matter. It specifies radial rotational accuracy as **(0.04 + 6H/10000) µm**, with `H` the probing height in millimetres. At **H = 100 mm**, that expression is **0.10 µm**. This is the bulletin's spindle specification under its stated convention, not complete uncertainty for a 100 mm-tall part.

The same document lists a standard **1.6 mm carbide-ball stylus**, **70–100 mN measuring force (±30%)**, and a maximum probing depth of **100 mm with minimum internal diameter 30 mm**. That depth/diameter combination must not be generalized to another stylus or machine. This historical bulletin describes a named configuration; confirm the specification and calibration of the actual instrument being used. [Mitutoyo, RA-120P Bulletin 1943](https://www.mitutoyo.com/Images/002/282/1943_RA-120P.pdf)

## Verification, uncertainty and reporting

A single trace combines spindle and part errors. NIST explains that multiple traces with the standard rotated between measurements allow an error-separation analysis. Repeating the same setup alone does not separate a repeatable spindle contribution from part form. Use a validated multi-position or reversal procedure when the required uncertainty makes that separation significant. [NIST, roundness calibration designs](https://www.itl.nist.gov/div898/handbook/mpc/section3/mpc344.htm)

NPL recommends interim checks using a calibrated hemisphere for spindle performance and a sensitivity artefact such as a **flick standard** for sensor gain. These checks address different parts of the measurement chain. Evaluate uncertainty from the references, spindle, sensor response, alignment, contact, fixture, environment and profile processing. Display resolution, magnification and repeated agreement are not interchangeable with task uncertainty. [NPL, *Fundamental Good Practice in Dimensional Metrology*, GPG80, July 2005; corrected reprint October 2012, section on roundness verification](https://eprintspublications.npl.co.uk/3360/1/mgpg80.pdf)

Report the instrument and stylus, part support, section locations, reference-circle method, filter/passband, sampling and exclusions, result parameter and units, applicable checks and acceptance rule. Keep roundness, runout and cylindricity results separately identified so another operator can reproduce the intended measurement.

## Related reference

[Inspection and quality documents](../../sourcing/documents/index.md)