# Spur gears, involute 20°: module 0.5, 1 and 2, 12–60 teeth > What is the outer diameter and centre distance for module 1 spur gears? - Category: Hardware › Stirling & thermoacoustic - Kind: Hardware - 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 - Page: https://xemstudio.com/objects/spur-gears-involute/ · JSON: https://xemstudio.com/api/geometry?object=spur-gears-involute · Plain text: https://xemstudio.com/objects/spur-gears-involute/sheet.txt - License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses ## 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. ## Sizes | module | teeth | pitch_dia_mm | outer_dia_mm | root_dia_mm | face_mm | bore_mm | |---|---|---|---|---|---|---| | 1 | 12 | 12.0 | 14.0 | 9.5 | 6 | 3 | | 1 | 15 | 15.0 | 17.0 | 12.5 | 6 | 3 | | 1 | 16 | 16.0 | 18.0 | 13.5 | 6 | 4 | | 1 | 20 | 20.0 | 22.0 | 17.5 | 6 | 5 | | 1 | 24 | 24.0 | 26.0 | 21.5 | 6 | 5 | | 1 | 30 | 30.0 | 32.0 | 27.5 | 6 | 5 | | 1 | 36 | 36.0 | 38.0 | 33.5 | 6 | 6 | | 1 | 40 | 40.0 | 42.0 | 37.5 | 6 | 6 | | 1 | 48 | 48.0 | 50.0 | 45.5 | 6 | 8 | | 1 | 60 | 60.0 | 62.0 | 57.5 | 6 | 8 | | 0.5 | 16 | 8.0 | 9.0 | 6.75 | 4 | 2 | | 0.5 | 20 | 10.0 | 11.0 | 8.75 | 4 | 2 | | 0.5 | 24 | 12.0 | 13.0 | 10.75 | 4 | 3 | | 0.5 | 30 | 15.0 | 16.0 | 13.75 | 4 | 3 | | 0.5 | 40 | 20.0 | 21.0 | 18.75 | 4 | 3 | | 0.5 | 60 | 30.0 | 31.0 | 28.75 | 4 | 4 | | 2 | 12 | 24.0 | 28.0 | 19.0 | 10 | 5 | | 2 | 15 | 30.0 | 34.0 | 25.0 | 10 | 6 | | 2 | 20 | 40.0 | 44.0 | 35.0 | 10 | 8 | | 2 | 30 | 60.0 | 64.0 | 55.0 | 10 | 8 | | 2 | 40 | 80.0 | 84.0 | 75.0 | 10 | 10 | ## Where the files are - Wikipedia: [Involute gear](https://en.wikipedia.org/wiki/Involute_gear) — web — CC BY-SA 4.0 (text) - Wikipedia: [Gear](https://en.wikipedia.org/wiki/Gear) — web — CC BY-SA 4.0 (text) - KHK Gears: [Gear technical reference (module, pressure angle, formulas)](https://khkgears.net/new/gear_knowledge/) — web, PDF — KHK site terms (verify at link) - Long Earth Society: [Engine builds that use these parts (videos and write-ups)](https://longearthsociety.com/engineering/) — web, video — LES site ## Free STEP/STL (21 parts, CC BY 4.0, Xem Studio) Index: https://xemstudio.com/files/hardware/spur-gears-involute/index.json - gear-m1-12t-b3: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-12t-b3.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-12t-b3.stl) — module 1, 12 teeth, 20° PA, 6 mm face, Ø3 bore - gear-m1-15t-b3: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-15t-b3.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-15t-b3.stl) — module 1, 15 teeth, 20° PA, 6 mm face, Ø3 bore, hub with M3 set screw - gear-m1-16t-b4: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-16t-b4.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-16t-b4.stl) — module 1, 16 teeth, 20° PA, 6 mm face, Ø4 bore, hub with M3 set screw - gear-m1-20t-b5: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-20t-b5.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-20t-b5.stl) — module 1, 20 teeth, 20° PA, 6 mm face, Ø5 bore, hub with M3 set screw - gear-m1-24t-b5: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-24t-b5.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-24t-b5.stl) — module 1, 24 teeth, 20° PA, 6 mm face, Ø5 bore, hub with M3 set screw - gear-m1-30t-b5: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-30t-b5.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-30t-b5.stl) — module 1, 30 teeth, 20° PA, 6 mm face, Ø5 bore, hub with M3 set screw - gear-m1-36t-b6: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-36t-b6.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-36t-b6.stl) — module 1, 36 teeth, 20° PA, 6 mm face, Ø6 bore, hub with M3 set screw - gear-m1-40t-b6: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-40t-b6.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-40t-b6.stl) — module 1, 40 teeth, 20° PA, 6 mm face, Ø6 bore, hub with M3 set screw - gear-m1-48t-b8: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-48t-b8.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-48t-b8.stl) — module 1, 48 teeth, 20° PA, 6 mm face, Ø8 bore, hub with M3 set screw - gear-m1-60t-b8: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-60t-b8.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m1-60t-b8.stl) — module 1, 60 teeth, 20° PA, 6 mm face, Ø8 bore, hub with M3 set screw - gear-m0.5-16t-b2: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-16t-b2.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-16t-b2.stl) — module 0.5, 16 teeth, 20° PA, 4 mm face, Ø2 bore, hub with M3 set screw - gear-m0.5-20t-b2: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-20t-b2.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-20t-b2.stl) — module 0.5, 20 teeth, 20° PA, 4 mm face, Ø2 bore, hub with M3 set screw - gear-m0.5-24t-b3: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-24t-b3.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-24t-b3.stl) — module 0.5, 24 teeth, 20° PA, 4 mm face, Ø3 bore, hub with M3 set screw - gear-m0.5-30t-b3: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-30t-b3.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-30t-b3.stl) — module 0.5, 30 teeth, 20° PA, 4 mm face, Ø3 bore, hub with M3 set screw - gear-m0.5-40t-b3: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-40t-b3.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-40t-b3.stl) — module 0.5, 40 teeth, 20° PA, 4 mm face, Ø3 bore, hub with M3 set screw - gear-m0.5-60t-b4: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-60t-b4.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m0.5-60t-b4.stl) — module 0.5, 60 teeth, 20° PA, 4 mm face, Ø4 bore, hub with M3 set screw - gear-m2-12t-b5: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-12t-b5.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-12t-b5.stl) — module 2, 12 teeth, 20° PA, 10 mm face, Ø5 bore - gear-m2-15t-b6: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-15t-b6.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-15t-b6.stl) — module 2, 15 teeth, 20° PA, 10 mm face, Ø6 bore, hub with M3 set screw - gear-m2-20t-b8: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-20t-b8.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-20t-b8.stl) — module 2, 20 teeth, 20° PA, 10 mm face, Ø8 bore, hub with M3 set screw - gear-m2-30t-b8: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-30t-b8.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-30t-b8.stl) — module 2, 30 teeth, 20° PA, 10 mm face, Ø8 bore, hub with M3 set screw - gear-m2-40t-b10: [STEP](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-40t-b10.step) · [STL](https://xemstudio.com/files/hardware/spur-gears-involute/gear-m2-40t-b10.stl) — module 2, 40 teeth, 20° PA, 10 mm face, Ø10 bore, hub with M3 set screw ## Questions **What is the outer diameter of a module 1 20 tooth gear?** 22 mm (module × (teeth + 2)); pitch diameter 20 mm; root diameter 17.5 mm. **How do I calculate gear centre distance?** 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. **What is the smallest gear module that 3D prints well?** 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. **What pressure angle are these gears?** 20°, the modern standard; they mesh with any 20° involute gear of the same module, including brass stock gears. ## Fits with - [Crank discs, connecting rods and flywheels for model engines](https://xemstudio.com/objects/crank-conrod-flywheel-kit/) - [Ratchet wheels and pawl (anti-reverse / one-way drive)](https://xemstudio.com/objects/ratchet-and-pawl/) - [Ball bearings, 683 to 6210 and flanged F6xx (ISO 15)](https://xemstudio.com/objects/ball-bearings-metric/) - [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/) - [Set screws (grub screws), M3–M8 (ISO 4026)](https://xemstudio.com/objects/set-screws-metric/) - [NEMA 17 stepper motor](https://xemstudio.com/objects/nema-17-stepper/)