{
 "version": "2026-10-20",
 "license": "Dimension sheets are written by Xem Studio from the cited sources and are free to use (CC BY 4.0, attribute 'Xem Studio'). Linked files belong to their publishers under the license shown; Xem Studio does not host them. 'license_verified: false' means the license shown is from memory or the publisher's page as last read and should be confirmed at the link before commercial use.",
 "slug": "spur-gears-involute",
 "name": "Spur gears, involute 20°: module 0.5, 1 and 2, 12–60 teeth",
 "kind": "hardware",
 "category": "Hardware",
 "group": "Stirling & thermoacoustic",
 "year": null,
 "question": "What is the outer diameter and centre distance for module 1 spur gears?",
 "tags": [
  "gear",
  "spur gear",
  "involute",
  "motion",
  "mechanism",
  "stirling",
  "long earth society"
 ],
 "aliases": [
  "module 1 gear",
  "spur gear stl",
  "involute gear 20 teeth",
  "gear outer diameter formula",
  "gear centre distance",
  "3d printed gears",
  "module 0.5 gear"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": true,
 "free_files": 21,
 "url": "https://xemstudio.com/objects/spur-gears-involute/",
 "sheet_txt": "https://xemstudio.com/objects/spur-gears-involute/sheet.txt",
 "sheet": {
  "basis": "ISO 53 / DIN 867 basic rack, 20° pressure angle, standard addendum (1 m) and dedendum (1.25 m); true involute flanks generated point by point",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Pitch diameter = module × teeth; outer diameter = module × (teeth + 2); centre distance between two gears = module × (N1 + N2) / 2. Module 1, 20T + 40T → 30 mm centres.",
   "Printed gears: module 1 is the practical floor on an FDM printer with a 0.4 mm nozzle; module 0.5 needs resin. Add 0.1–0.15 mm to the centre distance for backlash on printed pairs.",
   "Bores are plain; hubs carry an M3 set-screw hole. Pair with the 623/625 bearings and 3/5 mm dowels in the library for a crank train.",
   "Long Earth Society: gear trains for Stirling displacer drives and the 2:1 reduction on the flywheel-driven generator builds."
  ],
  "table": {
   "columns": [
    "module",
    "teeth",
    "pitch_dia_mm",
    "outer_dia_mm",
    "root_dia_mm",
    "face_mm",
    "bore_mm"
   ],
   "rows": [
    [
     "1",
     12,
     12,
     14,
     9.5,
     6,
     3
    ],
    [
     "1",
     15,
     15,
     17,
     12.5,
     6,
     3
    ],
    [
     "1",
     16,
     16,
     18,
     13.5,
     6,
     4
    ],
    [
     "1",
     20,
     20,
     22,
     17.5,
     6,
     5
    ],
    [
     "1",
     24,
     24,
     26,
     21.5,
     6,
     5
    ],
    [
     "1",
     30,
     30,
     32,
     27.5,
     6,
     5
    ],
    [
     "1",
     36,
     36,
     38,
     33.5,
     6,
     6
    ],
    [
     "1",
     40,
     40,
     42,
     37.5,
     6,
     6
    ],
    [
     "1",
     48,
     48,
     50,
     45.5,
     6,
     8
    ],
    [
     "1",
     60,
     60,
     62,
     57.5,
     6,
     8
    ],
    [
     "0.5",
     16,
     8,
     9,
     6.75,
     4,
     2
    ],
    [
     "0.5",
     20,
     10,
     11,
     8.75,
     4,
     2
    ],
    [
     "0.5",
     24,
     12,
     13,
     10.75,
     4,
     3
    ],
    [
     "0.5",
     30,
     15,
     16,
     13.75,
     4,
     3
    ],
    [
     "0.5",
     40,
     20,
     21,
     18.75,
     4,
     3
    ],
    [
     "0.5",
     60,
     30,
     31,
     28.75,
     4,
     4
    ],
    [
     "2",
     12,
     24,
     28,
     19,
     10,
     5
    ],
    [
     "2",
     15,
     30,
     34,
     25,
     10,
     6
    ],
    [
     "2",
     20,
     40,
     44,
     35,
     10,
     8
    ],
    [
     "2",
     30,
     60,
     64,
     55,
     10,
     8
    ],
    [
     "2",
     40,
     80,
     84,
     75,
     10,
     10
    ]
   ]
  }
 },
 "sheet_text": "Spur gears, involute 20°: module 0.5, 1 and 2, 12–60 teeth — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/spur-gears-involute/  (CC BY 4.0)\nBasis: ISO 53 / DIN 867 basic rack, 20° pressure angle, standard addendum (1 m) and dedendum (1.25 m); true involute flanks generated point by point\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Pitch diameter = module × teeth; outer diameter = module × (teeth + 2); centre distance between two gears = module × (N1 + N2) / 2. Module 1, 20T + 40T → 30 mm centres.\n- Printed gears: module 1 is the practical floor on an FDM printer with a 0.4 mm nozzle; module 0.5 needs resin. Add 0.1–0.15 mm to the centre distance for backlash on printed pairs.\n- Bores are plain; hubs carry an M3 set-screw hole. Pair with the 623/625 bearings and 3/5 mm dowels in the library for a crank train.\n- Long Earth Society: gear trains for Stirling displacer drives and the 2:1 reduction on the flywheel-driven generator builds.\n\nmodule  teeth  pitch_dia_mm  outer_dia_mm  root_dia_mm  face_mm  bore_mm\n1  12  12.0  14.0  9.5  6  3\n1  15  15.0  17.0  12.5  6  3\n1  16  16.0  18.0  13.5  6  4\n1  20  20.0  22.0  17.5  6  5\n1  24  24.0  26.0  21.5  6  5\n1  30  30.0  32.0  27.5  6  5\n1  36  36.0  38.0  33.5  6  6\n1  40  40.0  42.0  37.5  6  6\n1  48  48.0  50.0  45.5  6  8\n1  60  60.0  62.0  57.5  6  8\n0.5  16  8.0  9.0  6.75  4  2\n0.5  20  10.0  11.0  8.75  4  2\n0.5  24  12.0  13.0  10.75  4  3\n0.5  30  15.0  16.0  13.75  4  3\n0.5  40  20.0  21.0  18.75  4  3\n0.5  60  30.0  31.0  28.75  4  4\n2  12  24.0  28.0  19.0  10  5\n2  15  30.0  34.0  25.0  10  6\n2  20  40.0  44.0  35.0  10  8\n2  30  60.0  64.0  55.0  10  8\n2  40  80.0  84.0  75.0  10  10\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\n- Wikipedia: Involute gear — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Involute_gear\n- Wikipedia: Gear — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Gear\n- KHK Gears: Gear technical reference (module, pressure angle, formulas) — web, PDF — KHK site terms [verify license at link] — https://khkgears.net/new/gear_knowledge/\n- Long Earth Society: Engine builds that use these parts (videos and write-ups) — web, video — LES site — https://longearthsociety.com/engineering/\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 21 parts): https://xemstudio.com/files/hardware/spur-gears-involute/index.json\nAPI: https://xemstudio.com/api/geometry?object=spur-gears-involute\n",
 "sources": [
  {
   "publisher": "Wikipedia",
   "title": "Involute gear",
   "url": "https://en.wikipedia.org/wiki/Involute_gear",
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   "title": "Gear",
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   "formats": [
    "web"
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   "license": "CC BY-SA 4.0 (text)",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "KHK Gears",
   "title": "Gear technical reference (module, pressure angle, formulas)",
   "url": "https://khkgears.net/new/gear_knowledge/",
   "formats": [
    "web",
    "PDF"
   ],
   "license": "KHK site terms",
   "license_verified": false,
   "hosted": false
  },
  {
   "publisher": "Long Earth Society",
   "title": "Engine builds that use these parts (videos and write-ups)",
   "url": "https://longearthsociety.com/engineering/",
   "formats": [
    "web",
    "video"
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   "license": "LES site",
   "license_verified": true,
   "hosted": false
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 ],
 "xem": {
  "status": "free-files",
  "sheet_free": true,
  "mesh_price_usd": null,
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  "tolerance_mm": null
 },
 "related": [
  "crank-conrod-flywheel-kit",
  "ratchet-and-pawl",
  "ball-bearings-metric",
  "dowel-pins-metric",
  "set-screws-metric",
  "nema-17-stepper"
 ],
 "faq": [
  {
   "q": "What is the outer diameter of a module 1 20 tooth gear?",
   "a": "22 mm (module × (teeth + 2)); pitch diameter 20 mm; root diameter 17.5 mm."
  },
  {
   "q": "How do I calculate gear centre distance?",
   "a": "Module × (N1 + N2) / 2. Two module-1 gears with 20 and 40 teeth sit 30 mm apart; add 0.1–0.15 mm for printed backlash."
  },
  {
   "q": "What is the smallest gear module that 3D prints well?",
   "a": "Module 1 with a 0.4 mm nozzle (tooth thickness 1.57 mm at the pitch line); module 0.8 is marginal; module 0.5 needs resin or a 0.2 mm nozzle."
  },
  {
   "q": "What pressure angle are these gears?",
   "a": "20°, the modern standard; they mesh with any 20° involute gear of the same module, including brass stock gears."
  }
 ],
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   "note": "module 2, 12 teeth, 20° PA, 10 mm face, Ø5 bore"
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   "note": "module 2, 20 teeth, 20° PA, 10 mm face, Ø8 bore, hub with M3 set screw"
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   "note": "module 2, 30 teeth, 20° PA, 10 mm face, Ø8 bore, hub with M3 set screw"
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   "note": "module 2, 40 teeth, 20° PA, 10 mm face, Ø10 bore, hub with M3 set screw"
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}