Involute splines ISO 4156 (metric module, 30° side fit): pitch, major and minor diameter by module and tooth count + example shaft STEP/STL — dimension sheet Source: Xem Studio, https://xemstudio.com/objects/involute-splines-iso-4156-metric-module/ (sheet CC BY 4.0) Basis: ISO 4156:1981 Table 2 formulas (sample pages) and Roymech's transcription of the same table; basic dimensions, esv = 0, no tolerance; true involute shaft sections drawn from them Catalog version: 2026-10-20 Sizes: see table below - ISO 4156 (straight cylindrical involute splines, metric module, side fit) names a spline by module m and tooth count z. Pressure angles 30°, 37.5° and 45°; this page tabulates the 30° forms. Basic formulas (ISO 4156:1981 Table 2 sample pages, confirmed by Roymech's transcription): pitch Ø D = m z; circular pitch π m; basic tooth thickness π m / 2; external major Ø 30° m (z + 1); external minor Ø 30° flat root m (z − 1.5) and fillet root m (z − 1.8); internal major Ø minimum 30° flat root m (z + 1.5) and fillet root m (z + 1.8); 37.5° fillet root: external major m (z + 0.9), external minor m (z − 1.4), internal major m (z + 1.4); 45° fillet root: external major m (z + 0.8), external minor m (z − 1.2), internal major m (z + 1.2); form radius cF = 0.1 m. - The standard's major / minor diameters carry an effective-variation term (esv / tan αD, with esv the effective tooth thickness deviation, and the machining allowance (T + λ) / tan αD for the maximum internal major diameter); the table lists the basic values, esv = 0. The modules are 0.25 to 10 (ISO 4156 scope; Machinery's Handbook lists the preferred series 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 4, 5, 6, 8, 10). Tolerance classes H/h, H/f, H/e, H/d (side fit) apply tooth thickness deviations from ISO 286-type fundamental deviations; those are not in the table. - Compare ANSI B92.1 (inch pitch): the ANSI flat-root external minor is (N − 1.35) / P (or − 1.2 for 16/32 and finer) against ISO's m (z − 1.5); the two systems are not identical even at the same pitch diameter. Files: 10 external spline shaft sections, 25 mm long, one extruded solid with the basic 30° flat-root tooth: pitch, major and minor diameters from the table, true involute flanks, tooth thickness half the circular pitch. The 25 mm length is an example; the root fillet is not modelled (the flank is carried down to the root circle). Fillet-root and 37.5° / 45° shafts and internal splines are not drawn. - The standard (ISO 4156-1 to -3) is sold by ISO and linked, not reproduced; tooth counts are not limited by the sample pages read, so any z follows from the formulas. module m, mm teeth z pitch Ø D = m z, mm major Ø external (30°) m (z + 1) minor Ø external, flat root m (z − 1.5) minor Ø external, fillet root m (z − 1.8) major Ø internal min, flat root m (z + 1.5) major Ø internal min, fillet root m (z + 1.8) 0.5 10 5 5.5 4.25 4.1 5.75 5.9 0.5 12 6 6.5 5.25 5.1 6.75 6.9 0.5 16 8 8.5 7.25 7.1 8.75 8.9 0.5 20 10 10.5 9.25 9.1 10.75 10.9 0.5 24 12 12.5 11.25 11.1 12.75 12.9 0.5 30 15 15.5 14.25 14.1 15.75 15.9 0.5 36 18 18.5 17.25 17.1 18.75 18.9 0.5 48 24 24.5 23.25 23.1 24.75 24.9 0.75 10 7.5 8.25 6.375 6.15 8.625 8.85 0.75 12 9 9.75 7.875 7.65 10.125 10.35 0.75 16 12 12.75 10.875 10.65 13.125 13.35 0.75 20 15 15.75 13.875 13.65 16.125 16.35 0.75 24 18 18.75 16.875 16.65 19.125 19.35 0.75 30 22.5 23.25 21.375 21.15 23.625 23.85 0.75 36 27 27.75 25.875 25.65 28.125 28.35 0.75 48 36 36.75 34.875 34.65 37.125 37.35 1 10 10 11 8.5 8.2 11.5 11.8 1 12 12 13 10.5 10.2 13.5 13.8 1 16 16 17 14.5 14.2 17.5 17.8 1 20 20 21 18.5 18.2 21.5 21.8 1 24 24 25 22.5 22.2 25.5 25.8 1 30 30 31 28.5 28.2 31.5 31.8 1 36 36 37 34.5 34.2 37.5 37.8 1 48 48 49 46.5 46.2 49.5 49.8 1.25 10 12.5 13.75 10.625 10.25 14.375 14.75 1.25 12 15 16.25 13.125 12.75 16.875 17.25 1.25 16 20 21.25 18.125 17.75 21.875 22.25 1.25 20 25 26.25 23.125 22.75 26.875 27.25 1.25 24 30 31.25 28.125 27.75 31.875 32.25 1.25 30 37.5 38.75 35.625 35.25 39.375 39.75 1.25 36 45 46.25 43.125 42.75 46.875 47.25 1.25 48 60 61.25 58.125 57.75 61.875 62.25 1.5 10 15 16.5 12.75 12.3 17.25 17.7 1.5 12 18 19.5 15.75 15.3 20.25 20.7 1.5 16 24 25.5 21.75 21.3 26.25 26.7 1.5 20 30 31.5 27.75 27.3 32.25 32.7 1.5 24 36 37.5 33.75 33.3 38.25 38.7 1.5 30 45 46.5 42.75 42.3 47.25 47.7 1.5 36 54 55.5 51.75 51.3 56.25 56.7 1.5 48 72 73.5 69.75 69.3 74.25 74.7 1.75 10 17.5 19.25 14.875 14.35 20.125 20.65 1.75 12 21 22.75 18.375 17.85 23.625 24.15 1.75 16 28 29.75 25.375 24.85 30.625 31.15 1.75 20 35 36.75 32.375 31.85 37.625 38.15 1.75 24 42 43.75 39.375 38.85 44.625 45.15 1.75 30 52.5 54.25 49.875 49.35 55.125 55.65 1.75 36 63 64.75 60.375 59.85 65.625 66.15 1.75 48 84 85.75 81.375 80.85 86.625 87.15 2 10 20 22 17 16.4 23 23.6 2 12 24 26 21 20.4 27 27.6 2 16 32 34 29 28.4 35 35.6 2 20 40 42 37 36.4 43 43.6 2 24 48 50 45 44.4 51 51.6 2 30 60 62 57 56.4 63 63.6 2 36 72 74 69 68.4 75 75.6 2 48 96 98 93 92.4 99 99.6 2.5 10 25 27.5 21.25 20.5 28.75 29.5 2.5 12 30 32.5 26.25 25.5 33.75 34.5 2.5 16 40 42.5 36.25 35.5 43.75 44.5 2.5 20 50 52.5 46.25 45.5 53.75 54.5 2.5 24 60 62.5 56.25 55.5 63.75 64.5 2.5 30 75 77.5 71.25 70.5 78.75 79.5 2.5 36 90 92.5 86.25 85.5 93.75 94.5 2.5 48 120 122.5 116.25 115.5 123.75 124.5 3 10 30 33 25.5 24.6 34.5 35.4 3 12 36 39 31.5 30.6 40.5 41.4 3 16 48 51 43.5 42.6 52.5 53.4 3 20 60 63 55.5 54.6 64.5 65.4 3 24 72 75 67.5 66.6 76.5 77.4 3 30 90 93 85.5 84.6 94.5 95.4 3 36 108 111 103.5 102.6 112.5 113.4 3 48 144 147 139.5 138.6 148.5 149.4 4 10 40 44 34 32.8 46 47.2 4 12 48 52 42 40.8 54 55.2 4 16 64 68 58 56.8 70 71.2 4 20 80 84 74 72.8 86 87.2 4 24 96 100 90 88.8 102 103.2 4 30 120 124 114 112.8 126 127.2 4 36 144 148 138 136.8 150 151.2 4 48 192 196 186 184.8 198 199.2 5 10 50 55 42.5 41 57.5 59 5 12 60 65 52.5 51 67.5 69 5 16 80 85 72.5 71 87.5 89 5 20 100 105 92.5 91 107.5 109 5 24 120 125 112.5 111 127.5 129 5 30 150 155 142.5 141 157.5 159 5 36 180 185 172.5 171 187.5 189 5 48 240 245 232.5 231 247.5 249 6 10 60 66 51 49.2 69 70.8 6 12 72 78 63 61.2 81 82.8 6 16 96 102 87 85.2 105 106.8 6 20 120 126 111 109.2 129 130.8 6 24 144 150 135 133.2 153 154.8 6 30 180 186 171 169.2 189 190.8 6 36 216 222 207 205.2 225 226.8 6 48 288 294 279 277.2 297 298.8 8 10 80 88 68 65.6 92 94.4 8 12 96 104 84 81.6 108 110.4 8 16 128 136 116 113.6 140 142.4 8 20 160 168 148 145.6 172 174.4 8 24 192 200 180 177.6 204 206.4 8 30 240 248 228 225.6 252 254.4 8 36 288 296 276 273.6 300 302.4 8 48 384 392 372 369.6 396 398.4 10 10 100 110 85 82 115 118 10 12 120 130 105 102 135 138 10 16 160 170 145 142 175 178 10 20 200 210 185 182 215 218 10 24 240 250 225 222 255 258 10 30 300 310 285 282 315 318 10 36 360 370 345 342 375 378 10 48 480 490 465 462 495 498 Files elsewhere (not hosted by Xem Studio; license as stated by the publisher): - iTeh Standards: ISO 4156:1981 sample pages: Table 2 basic formulas (m z, m (z + 1), m (z - 1.5), m (z + 1.5)), modules 0.25 to 10 — web — Publisher's page; dimensions are facts — https://cdn.standards.iteh.ai/samples/9921/e5c84452a1134654b8dede51d1d84e10/ISO-4156-1981.pdf - Roymech: Involute splines (ISO 4156): module formulas for 30 degree flat and fillet root, 37.5 and 45 degrees — web — Publisher's page; dimensions are facts — https://roymech.org/Useful_Tables/Keyways/Splines_Inv.html - ISO: ISO 4156-1:2005 Straight cylindrical involute splines, metric module, side fit (standard; sold, not reproduced) — standard — ISO; dimensions are facts [verify license at link] — https://standards.iteh.ai/catalog/standards/iso/91545c02-7de1-4792-ba81-e79b17716af6/iso-4156-1-2005 - Machinery's Handbook, 31st ed. (online edition): Table 3: basic dimensions for involute splines ANSI B92.1-1996: pitch series 2.5/5 to 128/256, 6 to 60 teeth at 30 degrees — web — Publisher's page; dimensions are facts — https://online.flippingbook.com/view/954046886/1000 Free files (CC BY 4.0, Xem Studio; STEP + STL, 10 parts): https://xemstudio.com/files/hardware/involute-splines-iso-4156-metric-module/index.json API: https://xemstudio.com/api/geometry?object=involute-splines-iso-4156-metric-module