BA Thread Chart (BS 93): 0BA–16BA Dimensions & Tap Drills
Governed by BS 93:2008, British Association (BA) screw threads are metric instrument threads with a 47.5° flank angle, depth h = 0.600P, and crest/root radius r = 0.1809P. A 2BA screw has major diameter 4.70 mm, pitch 0.81 mm, pitch diameter 4.214 mm, and uses a Ø4.00 mm tap drill.
BS 93 British Association (BA) 47.5° Thread Dimensions, Tap Drill & 3-Wire Calculator (0BA–16BA)
Compute BS 93 metric-based British Association thread major diameter D, tabulated pitch P (rounded from 1.00 × 0.9^n mm), 47.5° thread depth h = 0.6P, crest/root radius r = 0.1809P, tap drill diameter, and 3-wire inspection reading Mw using best wire wbest = 0.54625P.
How the BS 93 Geometric Progression Sets Pitch and Diameter in the Series
Proposed by the British Association for the Advancement of Science and later standardized by British Standards Institution (BSI) in BS 93, the BA series is one of the most mathematically elegant thread systems ever devised. Starting at 0BA with major diameter D0 = 6.00 mm and pitch P0 = 1.00 mm (identical in nominal size and pitch to an ISO M6×1.0 screw, though incompatible in flank angle), each higher designation number n scales the pitch by a geometric factor of 0.9:
The pitch series is a rounded geometric progression, Pn ≈ 1.00 × 0.9n mm; use the tabulated pitches in Table 1. The major diameters are tabulated in BS 93 and are not generated by a closed formula.
Because the included flank angle is narrowed to 47.5° (23.75° half-angle), the fundamental sharp-triangle height rises to H = P / (2 · tan 23.75°) = 1.136336P. Truncating both crest and root by t = 0.26817P with circular arcs of radius r = t / (1/sin 23.75° − 1) = 0.1809P yields a working depth of h = 0.600P, basic pitch diameter d2 = D − 0.600P, and minor diameter d1 = D − 1.200P. For modern ISO 60° micro-threads below 1.4 mm, compare against the UNM / ISO 1501 miniature thread chart.
| BA Size | Major Diameter D | Pitch P (Equiv TPI, tabulated) | Pitch d2 / Minor d1 | Tap Drill (75% own method, rounded to metric drill) | Actual Engagement of Drill | Close Clearance Hole (own method: D + 0.15 × P) | Unrounded Geometric Pitch 1.00 × 0.9n (mm) |
|---|---|---|---|---|---|---|---|
| 0BA | Ø6.00 mm (0.2362") | 1.00 mm (25.4 TPI) | Ø5.400 / Ø4.800 mm | Ø5.10 mm (calc 5.10) | 75.0% | Ø6.15 mm | 1.0000 |
| 1BA | Ø5.30 mm (0.2087") | 0.90 mm (28.2 TPI) | Ø4.760 / Ø4.220 mm | Ø4.50 mm (calc 4.49) | 74.1% | Ø5.43 mm | 0.9000 |
| 2BA | Ø4.70 mm (0.1850") | 0.81 mm (31.4 TPI) | Ø4.214 / Ø3.728 mm | Ø4.00 mm (calc 3.97) | 72.0% | Ø4.82 mm | 0.8100 |
| 3BA | Ø4.10 mm (0.1614") | 0.73 mm (34.8 TPI) | Ø3.662 / Ø3.224 mm | Ø3.40 mm (calc 3.44) | 79.9% | Ø4.21 mm | 0.7290 |
| 4BA | Ø3.60 mm (0.1417") | 0.66 mm (38.5 TPI) | Ø3.204 / Ø2.808 mm | Ø3.00 mm (calc 3.01) | 75.8% | Ø3.70 mm | 0.6561 |
| 5BA | Ø3.20 mm (0.1260") | 0.59 mm (43.1 TPI) | Ø2.846 / Ø2.492 mm | Ø2.70 mm (calc 2.67) | 70.6% | Ø3.29 mm | 0.5905 |
| 6BA | Ø2.80 mm (0.1102") | 0.53 mm (47.9 TPI) | Ø2.482 / Ø2.164 mm | Ø2.30 mm (calc 2.32) | 78.6% | Ø2.88 mm | 0.5314 |
| 7BA | Ø2.50 mm (0.0984") | 0.48 mm (52.9 TPI) | Ø2.212 / Ø1.924 mm | Ø2.10 mm (calc 2.07) | 69.4% | Ø2.57 mm | 0.4783 |
| 8BA | Ø2.20 mm (0.0866") | 0.43 mm (59.1 TPI) | Ø1.942 / Ø1.684 mm | Ø1.80 mm (calc 1.81) | 77.5% | Ø2.26 mm | 0.4305 |
| 9BA | Ø1.90 mm (0.0748") | 0.39 mm (65.1 TPI) | Ø1.666 / Ø1.432 mm | Ø1.50 mm (calc 1.55) | 85.5% | Ø1.96 mm | 0.3874 |
| 10BA | Ø1.70 mm (0.0669") | 0.35 mm (72.6 TPI) | Ø1.490 / Ø1.280 mm | Ø1.40 mm (calc 1.39) | 71.4% | Ø1.75 mm | 0.3487 |
| 11BA | Ø1.50 mm (0.0591") | 0.31 mm (81.9 TPI) | Ø1.314 / Ø1.128 mm | Ø1.20 mm (calc 1.22) | 80.6% | Ø1.55 mm | 0.3138 |
| 12BA | Ø1.30 mm (0.0512") | 0.28 mm (90.7 TPI) | Ø1.132 / Ø0.964 mm | Ø1.00 mm (calc 1.05) | 89.3% | Ø1.34 mm | 0.2824 |
| 13BA | Ø1.20 mm (0.0472") | 0.25 mm (101.6 TPI) | Ø1.050 / Ø0.900 mm | Ø0.95 mm (calc 0.97) | 83.3% | Ø1.24 mm | 0.2542 |
| 14BA | Ø1.00 mm (0.0394") | 0.23 mm (110.4 TPI) | Ø0.862 / Ø0.724 mm | Ø0.80 mm (calc 0.79) | 72.5% | Ø1.03 mm | 0.2288 |
| 15BA | Ø0.90 mm (0.0354") | 0.21 mm (121.0 TPI) | Ø0.774 / Ø0.648 mm | Ø0.70 mm (calc 0.71) | 79.4% | Ø0.93 mm | 0.2059 |
| 16BA | Ø0.79 mm (0.0311") | 0.19 mm (133.7 TPI) | Ø0.676 / Ø0.562 mm | Ø0.60 mm (calc 0.62) | 83.3% | Ø0.82 mm | 0.1853 |
3-Wire Pitch Diameter Inspection for 47.5° BA Threads
The odd-numbered BA sizes (1BA, 3BA, 5BA, 7BA) follow the same exponential pitch and diameter equations as the even-numbered series, so one set of formulas covers every size in the table.
In the three-wire check, choose wires of diameter wbest from the table, since they touch both flanks at the pitch line. Measure the micrometer reading Mw over the three wires and compare it with the value listed for the same BA size. A reading that differs from the table by more than your gauge tolerance points to the pitch diameter, the wire size, or the wire set-up, so check those three items before reworking the part.
When turning custom brass or stainless BA instrument screws on a Swiss lathe or single-point threading in the Fanuc control G76 threading cycle, standard 60° thread wires will not contact at the pitch line. Using the general secant wire equation, derived here from the 47.5° flank geometry (own derivation), for half-angle α = 23.75°:
wbest = P / (2 · cos 23.75°) = 0.546252 · P
Mw = d2 − P · cot(23.75°) / 2 + w · (1 + 1 / sin 23.75°) = d2 − 1.136336P + 3.482907w
For general 60°, 55° Whitworth, and 29° Acme wires, see the three-wire thread measurement calculator.
G76 caution: 47.5° is not on the A-angle list that a third-party source gives for this control family. This page has not checked that list, so verify the accepted A-angles in your control manual before you program a BA thread with G76. If 47.5° is not accepted, use a special insert or a form tool ground to 47.5°. Q and R need a thread depth that this page does not give.
| BA Size | Thread Depth h = 0.6P | Crest/Root Radius r | Best Wire Size wbest | Measurement Over Wires Mw |
|---|---|---|---|---|
| 0BA | h = 0.600 mm (0.6P) | r = 0.1809 mm (0.1809P) | wbest = 0.5463 mm | Mw = 6.166 mm |
| 2BA | h = 0.486 mm (0.6P) | r = 0.1465 mm (0.1809P) | wbest = 0.4425 mm | Mw = 4.835 mm |
| 4BA | h = 0.396 mm (0.6P) | r = 0.1194 mm (0.1809P) | wbest = 0.3605 mm | Mw = 3.710 mm |
| 6BA | h = 0.318 mm (0.6P) | r = 0.0959 mm (0.1809P) | wbest = 0.2895 mm | Mw = 2.888 mm |
| 8BA | h = 0.258 mm (0.6P) | r = 0.0778 mm (0.1809P) | wbest = 0.2349 mm | Mw = 2.271 mm |
| 10BA | h = 0.210 mm (0.6P) | r = 0.0633 mm (0.1809P) | wbest = 0.1912 mm | Mw = 1.758 mm |
| 12BA | h = 0.168 mm (0.6P) | r = 0.0507 mm (0.1809P) | wbest = 0.1530 mm | Mw = 1.347 mm |
| 14BA | h = 0.138 mm (0.6P) | r = 0.0416 mm (0.1809P) | wbest = 0.1256 mm | Mw = 1.038 mm |
Worked Examples: Tapping 2BA, 4BA, and 8BA Instrument Threads
Worked Example 1 (2BA & 4BA Instrument Screws): For a 2BA screw (D = 4.70 mm, P = 0.81 mm), the engine returns pitch diameter d2 = 4.214 mm, minor diameter d1 = 3.728 mm, tap drill at 75%, rounded to the nearest metric drill, Ø4.00 mm, best wire diameter wbest = 0.4425 mm, and micrometer measurement over wires Mw = 4.835 mm. For 4BA (D = 3.60 mm, P = 0.66 mm), drill with Ø3.00 mm and inspect over 0.3605 mm wires to read Mw = 3.710 mm.
Worked Example 2 (8BA Horological & Live-Steam Model Fastener): For 8BA (D = 2.20 mm, P = 0.43 mm), the minor diameter is 1.684 mm, the tap drill at 75% is Ø1.80 mm, and the close clearance hole is Ø2.26 mm.
The metric-based BA pitch series is compared with the ISO 68-1 basis of metric threads (International Organization for Standardization (ISO)), unit conversions use NIST Special Publication 811, and the inch-series comparison points to ASME Codes & Standards. For a BA tap drill, check the engagement that the chosen drill actually gives (Table 1), not only the 75% target: in the 2BA example, the 75% bore is 3.971 mm, so the Ø4.00 mm drill gives 72.0%.
Cite this page
ToolSpecVault Engineering Data Team. (2026, November 2). BA Thread Chart (BS 93): 0BA–16BA Dimensions & Tap Drills. ToolSpecVault. https://toolspecvault.com/ba-british-association-thread-dimensions-tap-drill-chart/