A callout like 1/4-20 UNC-2A packs five facts: the nominal size (1/4 in), the pitch (20 threads per inch), the series (UNC, coarse), the class (2, the standard commercial fit) and whether it is external (A) or internal (B). An added R, as in UNRC, means the external thread must have a rounded root of at least 0.108 P radius; it changes only the minor diameter. Everything else on this page follows from those five facts and the ASME B1.1 formulas.[1]
| Class | Where it is used | What changes |
|---|---|---|
| 1A / 1B | Quick assembly in dirty conditions; rare on machined parts | Widest pitch diameter tolerance (1.5 × class 2); external has an allowance |
| 2A / 2B | The default for bolts, nuts and tapped holes, commercial and aerospace | Standard tolerance; external carries an allowance for plating and easy assembly |
| 3A / 3B | Close fits: set screws, precision assemblies, socket head cap screws | Tightest pitch diameter tolerance (0.75 × class 2); external has no allowance |
B1.1 defines every limit from three things: the basic thread form, one pitch diameter tolerance formula, and a set of multipliers. The calculator follows the standard's own order of operations, including the rule that the class 2A pitch diameter tolerance is kept to six decimal places and only the final limits are rounded to four.[1]
| Quantity | Formula (P = pitch, D = basic major, LE = D) | B1.1 reference |
|---|---|---|
| Fundamental triangle height H | 0.866025 P | Table 5 |
| Basic pitch diameter D2 | D − 0.649519 P | Table 5 |
| Basic minor diameter D1 | D − 1.082532 P | Table 5 |
| UNR design minor diameter d3 | D1 − H/8 = D1 − 0.108253 P | Table 5, 8.3.1(e) |
| Class 2A pitch diameter tolerance | 0.0015 ∛D + 0.0015 √LE + 0.015 ∛P², six decimal places | 5.8.1(c) |
| Pitch diameter tolerance, other classes | 1A = 1.5 × 2A · 3A = 0.75 × 2A · 1B = 1.95 × 2A · 2B = 1.30 × 2A · 3B = 0.975 × 2A | 5.8.1(c), 5.8.2(b) |
| Allowance (external only) | 1A and 2A: 0.300 × class 2A pitch diameter tolerance · 3A: none | 5.8.1(a) |
| Major diameter tolerance, external | 1A: 0.090 ∛P² · 2A and 3A: 0.060 ∛P² | 5.8.1(b) |
| Major and pitch diameter limits, external | max = basic − allowance · min = max − tolerance | 8.3.1(a) to (d) |
| Minor diameter, external (reference) | max = D1 − allowance (UNR: also − H/8) · min = pitch diameter min − 0.649519 P | 8.3.1(e), (f) |
| Pitch diameter limits, internal | min = D2 · max = D2 + tolerance | 8.3.2 |
| Minor diameter limits, internal | min = D1 rounded to 0.001 in at 0.138 in and up (3B keeps four places) · max = min + tolerance per 5.8.2(c) | 5.8.2(c), 8.3.2(e), (f) |
| Major diameter, internal | min = basic D · tolerance (reference) = 0.144338 P + pitch diameter tolerance | 5.8.2(a) |
The minor diameter of an external thread and the major diameter of an internal thread are not dimensioned limits in B1.1; the standard GO thread gage covers them. The calculator prints them anyway, labeled reference, because a machinist setting a thread mill or a thread-turning tool needs a number to aim at.
| Step | External, class 2A | Internal, class 2B |
|---|---|---|
| Pitch P, height H | 0.0500 in, H = 0.043301 in | |
| Basic pitch diameter D2 | 0.2500 − 0.649519 × 0.05 = 0.217525 → 0.2175 in | |
| Basic minor diameter D1 | 0.2500 − 1.082532 × 0.05 = 0.195873 → 0.1959 in | |
| Class 2A pitch diameter tolerance | 0.0015 × 0.62996 + 0.0015 × 0.5 + 0.015 × 0.13572 = 0.003731 in | |
| Allowance | 0.300 × 0.003731 = 0.0011 in | none |
| Major diameter | max 0.2500 − 0.0011 = 0.2489 · min 0.2489 − 0.0081 = 0.2408 | min 0.2500 (basic) |
| Pitch diameter | max 0.2175 − 0.0011 = 0.2164 · min 0.2164 − 0.003731 = 0.2127 | min 0.2175 · max 0.2175 + 1.30 × 0.003731 = 0.2224 |
| Minor diameter | UNR max 0.1959 − 0.0011 − 0.0054 = 0.1894 (ref) · min 0.2127 − 0.0325 = 0.1802 (ref) | min 0.196 · tolerance 0.25 P − 0.4 P² = 0.0115 · max 0.207 |
| Tensile stress area | 0.7854 × (0.2500 − 0.0487)² = 0.0318 in² | |
Those are the numbers B1.1 Table 2 prints for 1/4-20 UNC, and the calculator reproduces the table for #4-40, #10-24, #10-32, 1/4-28, 3/8-16, 1/2-13, 3/4-10, 1-8 and 1-1/2-6 as well, in every class. For a custom UNS size the same formulas apply; B1.1 uses them for any diameter and pitch combination, which is why a 0.3125-32 or a 1.000-14 can be toleranced without a table.
Basic major diameters and pitches per ASME B1.1 Table 1 for the coarse (UNC) and fine (UNF) series. The calculator reads this table when the page loads.[1]
| Series | Size | TPI | Major diameter (in) |
|---|---|---|---|
| UNC | #1-64 | 64 | 0.0730 |
| UNC | #2-56 | 56 | 0.0860 |
| UNC | #3-48 | 48 | 0.0990 |
| UNC | #4-40 | 40 | 0.1120 |
| UNC | #5-40 | 40 | 0.1250 |
| UNC | #6-32 | 32 | 0.1380 |
| UNC | #8-32 | 32 | 0.1640 |
| UNC | #10-24 | 24 | 0.1900 |
| UNC | #12-24 | 24 | 0.2160 |
| UNC | 1/4-20 | 20 | 0.2500 |
| UNC | 5/16-18 | 18 | 0.3125 |
| UNC | 3/8-16 | 16 | 0.3750 |
| UNC | 7/16-14 | 14 | 0.4375 |
| UNC | 1/2-13 | 13 | 0.5000 |
| UNC | 9/16-12 | 12 | 0.5625 |
| UNC | 5/8-11 | 11 | 0.6250 |
| UNC | 3/4-10 | 10 | 0.7500 |
| UNC | 7/8-9 | 9 | 0.8750 |
| UNC | 1-8 | 8 | 1.0000 |
| UNC | 1-1/8-7 | 7 | 1.1250 |
| UNC | 1-1/4-7 | 7 | 1.2500 |
| UNC | 1-1/2-6 | 6 | 1.5000 |
| UNF | #0-80 | 80 | 0.0600 |
| UNF | #2-64 | 64 | 0.0860 |
| UNF | #4-48 | 48 | 0.1120 |
| UNF | #6-40 | 40 | 0.1380 |
| UNF | #8-36 | 36 | 0.1640 |
| UNF | #10-32 | 32 | 0.1900 |
| UNF | #12-28 | 28 | 0.2160 |
| UNF | 1/4-28 | 28 | 0.2500 |
| UNF | 5/16-24 | 24 | 0.3125 |
| UNF | 3/8-24 | 24 | 0.3750 |
| UNF | 7/16-20 | 20 | 0.4375 |
| UNF | 1/2-20 | 20 | 0.5000 |
| UNF | 9/16-18 | 18 | 0.5625 |
| UNF | 5/8-18 | 18 | 0.6250 |
| UNF | 3/4-16 | 16 | 0.7500 |
| UNF | 7/8-14 | 14 | 0.8750 |
| UNF | 1-12 | 12 | 1.0000 |
Not covered here: UNEF and constant-pitch UN series (the same formulas apply; use the custom entry with the size and pitch), UNJ threads (a different thread form; see the UNJ page), threads with a non-standard length of engagement, and the coating allowance rules of B1.1 para. 7. Metric ISO threads use ISO 965 and are not modelled.
C&W turns, mills and taps Unified threads to the class on the drawing and checks them with GO and NO GO gages matched to that class, with AS9100D traceability on every lot.