Xem Studiomeasured geometry

Library › Hardware › Bearings, rails & motion ·

Spur gears, 24 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL

What is the pitch diameter, outside diameter and root diameter of a 24 DP spur gear, and how many teeth does it have? · Hardware · 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

Also called: 24 dp spur gear, 24 pitch spur gear, 24 diametral pitch gear dimensions, 24 dp gear pitch diameter, 24 dp 20 tooth gear, 24 dp gear stl, 24 dp gear step file, diametral pitch gear calculator, spur gear outside diameter formula dp, 14.5 degree pressure angle spur gear, 20 degree pressure angle spur gear, pitch diameter = teeth / dp, 24 pitch gear whole depth, inch pitch spur gear cad, 24p spur gear

Exact dimensions. Every file is drawn at true size with no tolerance added. The holes and pins that meet another part are listed below under Mating features, with the fit each joint needs; open those by your process's clearance before making the part. Mating features

sizes
13 in table

Notes

  • 24 diametral pitch (DP) means 24 teeth per inch of pitch diameter: pitch diameter = N / 24 in, outside diameter = (N + 2) / 24 in, circular pitch = π / 24 = 0.1309 in (3.325 mm), addendum 1 / 24 = 0.0417 in (1.058 mm), tooth thickness on the pitch circle π / (2 × 24) = 0.0654 in. Centre distance of two gears = (N1 + N2) / (2 × 24) in = 0.529 (N1 + N2) mm. Module equivalent: 1.0583. A 24 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.
  • 20 DP and finer is fine-pitch (ANSI B6.7): whole depth 2.2 / P + 0.002 in and dedendum 1.2 / P + 0.002 in for both 14.5° and 20° (minimum values), so both pressure angles share one root diameter here. 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 5/16 in (7.94 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.

Spur gears, 24 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20°… size chart

teeth Npitch 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, inexample bore, in
120.5 (12.70)0.5833 (14.82)0.396 (10.06)0.396 (10.06)0.4841 (12.30)0.4698 (11.93)5/161/8
140.5833 (14.82)0.6667 (16.93)0.4793 (12.18)0.4793 (12.18)0.5648 (14.34)0.5482 (13.92)5/161/8
160.6667 (16.93)0.75 (19.05)0.5627 (14.29)0.5627 (14.29)0.6454 (16.39)0.6265 (15.91)5/163/16
180.75 (19.05)0.8333 (21.17)0.646 (16.41)0.646 (16.41)0.7261 (18.44)0.7048 (17.90)5/163/16
200.8333 (21.17)0.9167 (23.28)0.7293 (18.53)0.7293 (18.53)0.8068 (20.49)0.7831 (19.89)5/161/4
241 (25.40)1.0833 (27.52)0.896 (22.76)0.896 (22.76)0.9681 (24.59)0.9397 (23.87)5/165/16
281.1667 (29.63)1.25 (31.75)1.0627 (26.99)1.0627 (26.99)1.1295 (28.69)1.0963 (27.85)5/165/16
301.25 (31.75)1.3333 (33.87)1.146 (29.11)1.146 (29.11)1.2102 (30.74)1.1746 (29.84)5/163/8
321.3333 (33.87)1.4167 (35.98)1.2293 (31.23)1.2293 (31.23)1.2909 (32.79)1.2529 (31.82)5/163/8
361.5 (38.10)1.5833 (40.22)1.396 (35.46)1.396 (35.46)1.4522 (36.89)1.4095 (35.80)5/163/8
401.6667 (42.33)1.75 (44.45)1.5627 (39.69)1.5627 (39.69)1.6136 (40.98)1.5662 (39.78)5/161/2
482 (50.80)2.0833 (52.92)1.896 (48.16)1.896 (48.16)1.9363 (49.18)1.8794 (47.74)5/165/8
602.5 (63.50)2.5833 (65.62)2.396 (60.86)2.396 (60.86)2.4204 (61.48)2.3492 (59.67)5/163/4

Mating features

Drawn at the exact size. Open press, slide, run and socket features by your process's clearance (tolerances by process); leave designed gaps and clamp fits as drawn.

featureexactmates withfitfiles
boreplain bore, example Ø per file (1/16 to 1 in, see the table)shaft of the same Øslidegear-*
centre distance(N1 + N2) / (2 × 24) in = 0.5292 (N1 + N2) mma second 24 DP gear of the same pressure angle (this family)designedgear-*
tooth form24 DP, 14.5° or 20° (the file name carries the angle); 14.5° and 20° gears do not mesh24 DP gear of the same pressure angledesignedgear-*

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

Martin Sprocket & GearG-85 spur gear data: PD = N / DP, OD = (N + 2) / DP, a = 1 / DP, ht = 2.157 / DP, t = 1.5708 / DPwebPublisher's page; dimensions are facts
Engineers EdgeGear design equations: 20 degree full-depth teeth (ANSI B6.1): PD, OD, a = 1/P, b = 1.25/P, ht = 2.25/P, centre distancewebPublisher's page; dimensions are facts
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)webPublisher's page; dimensions are facts
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 + 0.002webPublisher's page; dimensions are facts
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)webPublisher's page; dimensions are facts
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 inwebPublisher's page; dimensions are facts
SDP/SI48 DP inch spur gears (catalogue pages list the tooth counts and bores; CAD per part on each product page)webPublisher's page; dimensions are facts
SDP/SIInch pitch spur gear catalogue sheetwebPublisher's page; dimensions are facts

Free files

★ Free files 26 parts. Generated by Xem Studio from the standard; threads are plain cylinders at major diameter. CC BY 4.0. index.json

gear-dp24-14-5pa-12t24 DP spur gear, 12 teeth, 14.5° pressure angle: pitch Ø12.700 mm (0.5 in), outside Ø14.817 mm (0.5833 in), root Ø10.058 mm; face 7.94 mm (5/16 in) and bore Ø3.175 mm (1/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-12t24 DP spur gear, 12 teeth, 20° pressure angle: pitch Ø12.700 mm (0.5 in), outside Ø14.817 mm (0.5833 in), root Ø10.058 mm; face 7.94 mm (5/16 in) and bore Ø3.175 mm (1/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-14t24 DP spur gear, 14 teeth, 14.5° pressure angle: pitch Ø14.817 mm (0.5833 in), outside Ø16.933 mm (0.6667 in), root Ø12.175 mm; face 7.94 mm (5/16 in) and bore Ø3.175 mm (1/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-14t24 DP spur gear, 14 teeth, 20° pressure angle: pitch Ø14.817 mm (0.5833 in), outside Ø16.933 mm (0.6667 in), root Ø12.175 mm; face 7.94 mm (5/16 in) and bore Ø3.175 mm (1/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-16t24 DP spur gear, 16 teeth, 14.5° pressure angle: pitch Ø16.933 mm (0.6667 in), outside Ø19.050 mm (0.75 in), root Ø14.292 mm; face 7.94 mm (5/16 in) and bore Ø4.762 mm (3/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-16t24 DP spur gear, 16 teeth, 20° pressure angle: pitch Ø16.933 mm (0.6667 in), outside Ø19.050 mm (0.75 in), root Ø14.292 mm; face 7.94 mm (5/16 in) and bore Ø4.762 mm (3/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-18t24 DP spur gear, 18 teeth, 14.5° pressure angle: pitch Ø19.050 mm (0.75 in), outside Ø21.167 mm (0.8333 in), root Ø16.408 mm; face 7.94 mm (5/16 in) and bore Ø4.762 mm (3/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-18t24 DP spur gear, 18 teeth, 20° pressure angle: pitch Ø19.050 mm (0.75 in), outside Ø21.167 mm (0.8333 in), root Ø16.408 mm; face 7.94 mm (5/16 in) and bore Ø4.762 mm (3/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-20t24 DP spur gear, 20 teeth, 14.5° pressure angle: pitch Ø21.167 mm (0.8333 in), outside Ø23.283 mm (0.9167 in), root Ø18.525 mm; face 7.94 mm (5/16 in) and bore Ø6.350 mm (1/4 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-20t24 DP spur gear, 20 teeth, 20° pressure angle: pitch Ø21.167 mm (0.8333 in), outside Ø23.283 mm (0.9167 in), root Ø18.525 mm; face 7.94 mm (5/16 in) and bore Ø6.350 mm (1/4 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-24t24 DP spur gear, 24 teeth, 14.5° pressure angle: pitch Ø25.400 mm (1 in), outside Ø27.517 mm (1.0833 in), root Ø22.758 mm; face 7.94 mm (5/16 in) and bore Ø7.938 mm (5/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-24t24 DP spur gear, 24 teeth, 20° pressure angle: pitch Ø25.400 mm (1 in), outside Ø27.517 mm (1.0833 in), root Ø22.758 mm; face 7.94 mm (5/16 in) and bore Ø7.938 mm (5/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-28t24 DP spur gear, 28 teeth, 14.5° pressure angle: pitch Ø29.633 mm (1.1667 in), outside Ø31.750 mm (1.25 in), root Ø26.992 mm; face 7.94 mm (5/16 in) and bore Ø7.938 mm (5/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-28t24 DP spur gear, 28 teeth, 20° pressure angle: pitch Ø29.633 mm (1.1667 in), outside Ø31.750 mm (1.25 in), root Ø26.992 mm; face 7.94 mm (5/16 in) and bore Ø7.938 mm (5/16 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-30t24 DP spur gear, 30 teeth, 14.5° pressure angle: pitch Ø31.750 mm (1.25 in), outside Ø33.867 mm (1.3333 in), root Ø29.108 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-30t24 DP spur gear, 30 teeth, 20° pressure angle: pitch Ø31.750 mm (1.25 in), outside Ø33.867 mm (1.3333 in), root Ø29.108 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-32t24 DP spur gear, 32 teeth, 14.5° pressure angle: pitch Ø33.867 mm (1.3333 in), outside Ø35.983 mm (1.4167 in), root Ø31.225 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-32t24 DP spur gear, 32 teeth, 20° pressure angle: pitch Ø33.867 mm (1.3333 in), outside Ø35.983 mm (1.4167 in), root Ø31.225 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-36t24 DP spur gear, 36 teeth, 14.5° pressure angle: pitch Ø38.100 mm (1.5 in), outside Ø40.217 mm (1.5833 in), root Ø35.458 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-36t24 DP spur gear, 36 teeth, 20° pressure angle: pitch Ø38.100 mm (1.5 in), outside Ø40.217 mm (1.5833 in), root Ø35.458 mm; face 7.94 mm (5/16 in) and bore Ø9.525 mm (3/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-40t24 DP spur gear, 40 teeth, 14.5° pressure angle: pitch Ø42.333 mm (1.6667 in), outside Ø44.450 mm (1.75 in), root Ø39.692 mm; face 7.94 mm (5/16 in) and bore Ø12.700 mm (1/2 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-40t24 DP spur gear, 40 teeth, 20° pressure angle: pitch Ø42.333 mm (1.6667 in), outside Ø44.450 mm (1.75 in), root Ø39.692 mm; face 7.94 mm (5/16 in) and bore Ø12.700 mm (1/2 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-48t24 DP spur gear, 48 teeth, 14.5° pressure angle: pitch Ø50.800 mm (2 in), outside Ø52.917 mm (2.0833 in), root Ø48.158 mm; face 7.94 mm (5/16 in) and bore Ø15.875 mm (5/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-48t24 DP spur gear, 48 teeth, 20° pressure angle: pitch Ø50.800 mm (2 in), outside Ø52.917 mm (2.0833 in), root Ø48.158 mm; face 7.94 mm (5/16 in) and bore Ø15.875 mm (5/8 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-14-5pa-60t24 DP spur gear, 60 teeth, 14.5° pressure angle: pitch Ø63.500 mm (2.5 in), outside Ø65.617 mm (2.5833 in), root Ø60.858 mm; face 7.94 mm (5/16 in) and bore Ø19.050 mm (3/4 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
gear-dp24-20pa-60t24 DP spur gear, 60 teeth, 20° pressure angle: pitch Ø63.500 mm (2.5 in), outside Ø65.617 mm (2.5833 in), root Ø60.858 mm; face 7.94 mm (5/16 in) and bore Ø19.050 mm (3/4 in) are examples, the tooth form is the standard's; true involute flanks, no hub, keyway, chamfer or root filletSTEP · STL
Let your AI pull this. Add https://xemstudio.com/mcp to Claude, ChatGPT, Cursor or any MCP client (free, no account, one minute) and it can look up exact sizes, mating fits and free STEP/STL from every chat.
Set it up →

Plain text: sheet.txt · JSON: /api/geometry?object=spur-gears-dp-24

Spur gears, 24 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL, isometric render of a generated part
Render of gear-dp24-20pa-28t from the free STEP; not to scale.

Fits with

Spur gears, 12 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL, isometric render of a generated part
Spur gears, 12 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL13 sizes★ 26 files
Spur gears, 16 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL, isometric render of a generated part
Spur gears, 16 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL13 sizes★ 26 files
Spur gears, 20 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL, isometric render of a generated part
Spur gears, 20 diametral pitch (DP): 12 to 60 teeth, 14.5° and 20° involute, pitch / outside / root diameter and STEP/STL13 sizes★ 26 files
Spur gears, module 1: 10 to 80 teeth (20° involute), isometric render of a generated part
Spur gears, module 1: 10 to 80 teeth (20° involute)26 sizes★ 26 files
Spur gears, involute 20°: module 0.5, 1 and 2, 12–60 teeth, isometric render of a generated part
Spur gears, involute 20°: module 0.5, 1 and 2, 12–60 teeth21 sizes★ 21 files
Gear racks ISO 53 module 1 to 3: tooth profile, pitch, depth and root radius + module 1.5, 2.5, 3 rack STEP/STL, isometric render of a generated part
Gear racks ISO 53 module 1 to 3: tooth profile, pitch, depth and root radius + module 1.5, 2.5, 3 rack STEP/STL6 sizes★ 3 files

Questions

What is the pitch diameter of a 24 DP, 20 tooth gear?

0.8333 in (21.167 mm); outside diameter 0.9167 in (23.283 mm).

What is the tooth depth of a 24 DP gear?

Whole depth 2.2 / 24 + 0.002 = 0.0937 in (minimum, ANSI B6.7 fine pitch).

What is the centre distance of two 24 DP gears, 20 and 40 teeth?

(20 + 40) / (2 × 24) = 1.2500 in (31.750 mm).