Unified Screw Threads

§1The 1948 compromise

The Unified thread exists because two allies fighting the same war discovered, expensively, that their fasteners did not interchange — Britain on Whitworth’s 55°, America on Sellers’ 60°.

Through the Second World War, a British nut would not run properly on an American bolt of the same nominal size: the flank angles disagreed by five degrees and the forms by more, and every shared vehicle, aircraft and repair depot paid for it in seized threads and duplicated stock. The 1948 agreement between the United States, Britain and Canada resolved it by unifying on the American form — Sellers’ 60° flat-crested profile — with pitch series close to the old American National ones, creating UNC, UNF and their relatives as the single inch-thread system. Britain subsequently leapt past it to metric, which is why the british-fasteners page reads as history while this one does not: the Unified system remains the working standard of North American industry and of aerospace worldwide, where AN, MS and NAS hardware is Unified by definition. Geometrically it is the metric thread’s inch twin — the same 60° triangle, the same H = 0.866 p construction of the systems page — differing in how pitch is expressed (§3), in its pitch series, and in a class scheme (§5) with its own logic.

§2The basic profile

The Unified basic profile is the 60° sharp vee truncated by fixed fractions of its height: flat crests an eighth of a pitch wide, and roots relieved — rounded on the external thread — for fatigue.

Start from the fundamental triangle of height H = 0.866 p (the hero’s dashed construction). The crest is cut back H/8 from the sharp apex, leaving a flat exactly p/8 wide — Sellers’ signature, chosen in 1864 precisely because a flat crest could be measured with the instruments of the day and did not demand the perfect rounding Whitworth’s form required. The root is relieved more deeply, and on the external thread of any fastener that matters it is rounded: the root is where the whole tensile load funnels past a geometric notch, and the fatigue pages’ stress-concentration logic makes its radius the difference between a bolt that survives vibrating service (a UNJ-series rolled radius root, in aerospace) and one that cracks there. Between crest and root, the working dimensions fall out of the triangle exactly as the calculating-thread-dimensions page derives for metric — pitch diameter 0.6495 p below the major, basic minor 1.0825 p below — because the triangle neither knows nor cares which unit system measured its pitch. What changes is only §3: how that pitch is written down.

§3Reading a designation

The inch system counts threads rather than measuring pitch: a Unified thread is named by its diameter, its threads per inch, its series and its class — and p is simply the reciprocal of the count.

Take the hero’s 1/2-13 UNC-2A. The 1/2 is the nominal major diameter in inches (sizes below a quarter inch use the machine screws page’s gauge numbers, #0–#12). The 13 is threads per inch, so the pitch is p = 1/13 = 0.0769 in — 1.954 mm, sitting between metric’s M12×1.75 and M14×2 coarse pitches, which is no accident; comparable diameters want comparable pitches whatever the unit. UNC names the series — Unified National Coarse — where UNF is fine and UNEF extra-fine (§6). And 2A is the class and the side: A external, B internal, graded 1 to 3 (§5). The mental conversion every dual-system workshop runs daily is p = 25.4/TPI: 20 TPI is a 1.27 mm pitch, 13 TPI is 1.95 mm — and the reverse divide, 25.4/p, is how an unknown thread’s TPI is confirmed against a pitch gauge before anything is forced together, a habit the pipe-threads page will elevate into a survival skill.

§4Coarse against fine, worked

At any diameter the system offers a coarse and a fine pitch, and working both at half an inch shows exactly what fine buys — and what it costs.

§5Classes and the allowance

Fit in the Unified system is a class number and a side letter — and its distinctive idea is the allowance, a deliberate guaranteed gap built into the standard commercial class.

Externals are classed 1A, 2A, 3A and internals 1B, 2B, 3B, loosest to tightest. Class 1 is deliberately sloppy — quick-assembly hardware that must run together dirty, damaged or gloved. Class 2A/2B is the commercial default, the class of essentially every off-the-shelf bolt and nut, and it carries the system’s signature feature: 2A includes an allowance, a small guaranteed clearance below basic size, so that even a maximum-metal 2A bolt in a minimum-metal 2B nut assembles freely — and so that a plated bolt (the metric page’s 4-to-1 coating rule applies to any 60° thread) has somewhere for its coating to live. Class 3A/3B deletes the allowance entirely: basic size is the limit, the fit is snug, and it is specified where minimal play matters — set screws, precision adjustment, much aerospace hardware — at the price of clean threads and more care in assembly. The scheme is the fits-and-tolerances logic of the dimensioning pages transplanted onto a helix: class picks the tolerance width, the allowance sets the guaranteed clearance, and mixing classes across the joint (a 3A screw in a 2B nut) is legitimate and common when one side of the fit matters more than the other.

§6The other series

Beyond UNC and UNF the system fills its corners: an extra-fine series, constant-pitch series for large diameters, and a special designation for everything else.

UNEF — extra fine — pushes the §4 trade further still: maximum core and minimum helix for thin-wall parts, fine adjustments and short engagement lengths, at the cost of threads so shallow that damage tolerance nearly vanishes. The constant-pitch series (8UN, 12UN, 16UN) answer a scaling problem: coarse pitch grows with diameter, and by the time a stud is two or three inches across, its UNC pitch is enormous — deep threads, huge tapping torque, wrenching engagement lengths. Holding the pitch constant instead — eight threads per inch across the large sizes, the practice of boiler and pressure-vessel studding — keeps the thread proportions workable however big the diameter grows. UNS covers special combinations outside any standard series, written out in full because nothing may be assumed about them; and left-hand threads append LH exactly as the systems page described. The pattern to keep is that the series letters change only the pitch table, never the form: every one of them is the same 60° triangle of §2, generated by the same constants, measured by the same wires — one profile, dressed for different duties.

§7Quick reference

The working core of the page on one card rack.