Spur gears, 16 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL — dimension sheet Source: Xem Studio, https://xemstudio.com/objects/spur-gears-dp-16/ (sheet CC BY 4.0) Basis: AGMA / ANSI diametral-pitch relations: pitch Ø = N / DP, outside Ø = (N + 2) / DP, minimum dedendum per ANSI B6.1 (20° coarse), Machinery's Handbook (14.5°) and ANSI B6.7 (20 DP and finer); true involute flanks generated point by point Catalog version: 2026-10-20 Sizes: see table below - 16 diametral pitch (DP) means 16 teeth per inch of pitch diameter: pitch diameter = N / 16 in, outside diameter = (N + 2) / 16 in, circular pitch = π / 16 = 0.1963 in (4.987 mm), addendum 1 / 16 = 0.0625 in (1.587 mm), tooth thickness on the pitch circle π / (2 × 16) = 0.0982 in. Centre distance of two gears = (N1 + N2) / (2 × 16) in = 0.794 (N1 + N2) mm. Module equivalent: 1.5875. A 16 DP gear does not mesh with a metric module gear unless the two are within rounding of each other; use the module pages for metric gears. - Below 20 DP the coarse-pitch proportions apply: 20° (ANSI B6.1) dedendum 1.25 / P, whole depth 2.25 / P; 14.5° dedendum 1.157 / P, whole depth 2.157 / P (all minimum values), so the 14.5° root circle is a little larger. The table lists root and base diameters for both pressure angles so a hob or a CAD mate can be checked. 14.5° and 20° gears do not mesh: the pair must have the same DP and the same pressure angle. 14.5° is the older Brown & Sharpe / Boston Gear stock form (undercut below 32 teeth), 20° the current standard (undercut below 18 teeth). - Files: 26 gears, a 14.5° and a 20° gear for each of the 13 tooth counts, as one extruded solid with a plain bore. Flanks are the true involute of the base circle, tooth thickness on the pitch circle half the circular pitch (no backlash), outside and root diameters as in the table, the root circle held at the root diameter for every tooth count (the flank is carried down to it; the real root fillet and trochoid are not modelled). Example choices (not published values): face width 1/2 in (12.70 mm), which is 8 / DP rounded to 1/16 in, and a bore of about a third of the root diameter picked from 1/16, 1/8, 3/16, 1/4, 5/16, 3/8, 1/2, 5/8, 3/4, 1 in. Hubs, keyways and set-screw holes are not drawn. Teeth below 32 (14.5°) and 18 (20°) are drawn without profile shift, so they are undercut-prone as real unshifted gears are. - Stock tooth counts: the 12 to 60 range covers common stock gears (Boston Gear lists 16 DP 14.5° 14-tooth with 0.875 in pitch diameter, 1 in outside diameter, 0.5 in face, 0.375 in bore, which the formulas above reproduce; SDP/SI lists 48 DP gears from 14 to 108 teeth). Face widths and bores of stock gears vary by maker and series; those are not a standard. - Left out: the 25° pressure angle, stub and profile-shifted teeth, tolerances (AGMA quality numbers), backlash allowances, helical and bevel forms, and hub dimensions. Maker CAD: SDP/SI publishes inch-pitch spur gears with per-part CAD; linked, not copied. teeth N pitch Ø = N / DP, in (mm) outside Ø = (N + 2) / DP, in (mm) root Ø 14.5°, in (mm) root Ø 20°, in (mm) base Ø 14.5°, in (mm) base Ø 20°, in (mm) example face, in example bore, in 12 0.75 (19.05) 0.875 (22.22) 0.6054 (15.38) 0.5938 (15.08) 0.7261 (18.44) 0.7048 (17.90) 1/2 3/16 14 0.875 (22.22) 1 (25.40) 0.7304 (18.55) 0.7188 (18.26) 0.8471 (21.52) 0.8222 (20.88) 1/2 1/4 16 1 (25.40) 1.125 (28.57) 0.8554 (21.73) 0.8438 (21.43) 0.9681 (24.59) 0.9397 (23.87) 1/2 1/4 18 1.125 (28.57) 1.25 (31.75) 0.9804 (24.90) 0.9688 (24.61) 1.0892 (27.66) 1.0572 (26.85) 1/2 5/16 20 1.25 (31.75) 1.375 (34.92) 1.1054 (28.08) 1.0938 (27.78) 1.2102 (30.74) 1.1746 (29.84) 1/2 3/8 24 1.5 (38.10) 1.625 (41.27) 1.3554 (34.43) 1.3438 (34.13) 1.4522 (36.89) 1.4095 (35.80) 1/2 3/8 28 1.75 (44.45) 1.875 (47.62) 1.6054 (40.78) 1.5938 (40.48) 1.6943 (43.03) 1.6445 (41.77) 1/2 1/2 30 1.875 (47.62) 2 (50.80) 1.7304 (43.95) 1.7188 (43.66) 1.8153 (46.11) 1.7619 (44.75) 1/2 1/2 32 2 (50.80) 2.125 (53.97) 1.8554 (47.13) 1.8438 (46.83) 1.9363 (49.18) 1.8794 (47.74) 1/2 5/8 36 2.25 (57.15) 2.375 (60.32) 2.1054 (53.48) 2.0938 (53.18) 2.1783 (55.33) 2.1143 (53.70) 1/2 5/8 40 2.5 (63.50) 2.625 (66.67) 2.3554 (59.83) 2.3438 (59.53) 2.4204 (61.48) 2.3492 (59.67) 1/2 3/4 48 3 (76.20) 3.125 (79.38) 2.8554 (72.53) 2.8438 (72.23) 2.9044 (73.77) 2.8191 (71.60) 1/2 3/4 60 3.75 (95.25) 3.875 (98.42) 3.6054 (91.58) 3.5938 (91.28) 3.6306 (92.22) 3.5238 (89.51) 1/2 1 Files elsewhere (not hosted by Xem Studio; license as stated by the publisher): - Martin Sprocket & Gear: G-85 spur gear data: PD = N / DP, OD = (N + 2) / DP, a = 1 / DP, ht = 2.157 / DP, t = 1.5708 / DP — web — Publisher's page; dimensions are facts — https://martinsprocket.com/docs//partinterchange/g-85.pdf - Engineers Edge: Gear design equations: 20 degree full-depth teeth (ANSI B6.1): PD, OD, a = 1/P, b = 1.25/P, ht = 2.25/P, centre distance — web — Publisher's page; dimensions are facts — https://engineersedge.com/gear_formula.htm - Machinery's Handbook, 31st ed. (online edition): Spur gearing: 14.5 degree full-depth tooth proportions (a = 1/P, b = 1.157/P, ht = 2.157/P) — web — Publisher's page; dimensions are facts — https://online.flippingbook.com/view/954046886/872 - Machinery's Handbook, 31st ed. (online edition): Table 4: tooth proportions for fine-pitch involute spur and helical gears of 14.5, 20 and 25 degrees (ANSI B6.7): b = 1.2/P + 0.002, ht = 2.2/P + 0.002 — web — Publisher's page; dimensions are facts — https://online.flippingbook.com/view/954046886/870 - Machinery's Handbook, 31st ed. (online edition): Spur gearing: outside and root diameter formulas, 20 degree fine-pitch full-depth teeth (20 P and finer) — web — Publisher's page; dimensions are facts — https://online.flippingbook.com/view/954046886/873 - Applied Industrial (Boston Gear): Boston Gear 16 DP 14.5 degree 14-tooth steel spur gear: PD 0.875 in, OD 1 in, face 0.5 in, bore 0.375 in — web — Publisher's page; dimensions are facts — https://www.applied.com/c-brands/c-regal-rexnord/c-boston-gear/nb14b-3-8/16-DP-14-5-PA-14-Teeths-Steel-Spur-Gear/p/101752354 - SDP/SI: 48 DP inch spur gears (catalogue pages list the tooth counts and bores; CAD per part on each product page) — web — Publisher's page; dimensions are facts — https://shop.sdp-si.com/s1084z-048a040.html - SDP/SI: Inch pitch spur gear catalogue sheet — web — Publisher's page; dimensions are facts — https://shop.sdp-si.com/media/pdf/81001085.pdf Free files (CC BY 4.0, Xem Studio; STEP + STL, 26 parts): https://xemstudio.com/files/hardware/spur-gears-dp-16/index.json API: https://xemstudio.com/api/geometry?object=spur-gears-dp-16