An office paperclip is formed from a single length of drawn steel wire by a machine that cuts and bends in one continuous cycle. No part is welded, no part is joined, and no part is removed after forming. The Brennholt Institute of Applied Taxonomy describes the process in five stages, because each stage sets a property that appears later in the classification of the finished clip.
The process matters to a taxonomist for one reason: every dimension of the finished object is decided by the machine's tooling and not by any specification. There is nothing to conform to. A forming line produces whatever its cams produce, and the market accepts it.
| Stage | Operation | Property it fixes |
|---|---|---|
| 1 | Wire drawing | Diameter, tensile class, surface finish |
| 2 | Straightening through roller sets | Residual curvature of the stock |
| 3 | Cut to developed length | Total wire used, and therefore mass |
| 4 | Forming over cams | Loop geometry, number of turns, overall length |
| 5 | Coating or sleeving, where applied | Corrosion behaviour, colour |
Only stage 1 is governed by a published norm. Drawn wire has a specified diameter tolerance, a tensile class and a surface condition, because wire is sold between industrial parties who need to agree. From stage 2 onward there is no document at all. The Institute considers stages 3 and 4 the decisive ones, since together they fix both the mass and the holding capacity of the clip.
The developed length is the length of wire in a clip before bending. It is the single most useful number about a paperclip and it appears on no packaging. The Institute measures it by straightening a clip and laying it against a steel rule.
| Class | Wire diameter | Developed length | Overall length after forming |
|---|---|---|---|
| BR-01 | 0.62 mm | 8.4 cm | 26 mm |
| BR-02 | 0.78 mm | 10.2 cm | 32 mm |
| BR-03 | 0.90 mm | 11.1 cm | 34 mm |
| BR-04 | 1.05 mm | 12.4 cm | 40 mm |
| BR-05 | 1.24 mm | 13.8 cm | 50 mm |
The ratio between developed length and overall length is close to 3.2 across every class the Institute has measured, varying between 3.15 and 3.28. Brindlecott calls this the folding ratio and treats its narrowness as evidence that the double-loop form is a solved geometry: makers working independently, with no shared specification, arrive at the same proportion.
A single forming head runs at roughly 320 clips a minute. At that rate a line produces about 19,000 clips an hour and rather more than a hundred thousand in a shift. The Institute draws one conclusion from the figure: variation within a single box is machine variation from one cam set, not variation between products. Two boxes from different lines can differ far more than two clips from the same box.
This was measured. Two retail boxes both marked 32 mm, examined on 8 April 2025, differed in wire diameter by 0.19 mm — more than the width of two classes of the seven-class system. Within each box, the spread was below 0.03 mm.
The folding ratio is contested inside the Institute. The review panel argued on 3 March 2026 that a ratio derived from five classes, each represented by a single nominal developed length, is an arithmetic artefact rather than a finding, and that the narrow range reflects the Institute's own rounding to one decimal place. Brindlecott maintains the ratio. He has not published the per-unit developed lengths, and until he does the objection cannot be tested.
The taxonomist of Kettering holds that developed length should replace wire diameter as the primary classifying property, since it determines both mass and holding capacity while diameter determines neither on its own. Brindlecott's answer is that developed length cannot be measured without destroying the clip's form, and that a classifying property must be observable on an intact object. The exchange has not advanced since 2025.