Reduction ratio
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Output RPM
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Output torque
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Safety factor
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Spur Gear Design & Strength Calculator
3D mesh data is generated on demand from the current geometric parameters. These precision STL files can be used for 3D printing or imported directly into 3D CAD software (SolidWorks, Fusion 360, Onshape, etc.) for assembly.
When assembling the gears or designing/machining a bracket, the exact **center distance** is — mm. Use this shaft spacing as the machining reference for proper gear backlash and meshing.
Teeth: 15T | Diameter: 45mm
Teeth: 30T | Diameter: 90mm
This calculator examines dimensions, speed and torque conversion, and simplified bending strength for a pair of external spur gears. With driving tooth count z1 and driven tooth count z2, the gear ratio is i = z2/z1. These correspond to N1 and N2 on screen. Output speed is n2 = n1/i, and the two gears rotate in opposite directions.
Module m and tooth count give pitch diameter d = mz. For standard gears without profile shift, center distance is a = m(z1+z2)/2. Pitch-line velocity is v = πd1n1/60000: d1 in mm and n1 in rpm give v in m/s. This differs from tooth-tip speed and sliding speed at the tooth contact. Output torque uses a fixed efficiency η = 0.97, giving T2 = ηiT1.
The Lewis bending model treats a tooth as a cantilever to assess bending at its root. Tangential force is Ft = 2000T1/d1 and bending stress is σ ≈ Ft/(bmY), with b and m in mm and stress in MPa. Y is a dimensionless tooth form factor depending on tooth count. The screen shows allowable tangential force and allowable input torque instead of stress itself; its safety factor is allowable input torque divided by input torque.
Module m sets tooth size in mm; its input minimum is 0.5 mm. Both meshing gears need the same module and pressure angle. Overall size depends on the application, so the default 3 mm module is a useful learning starting point. Tooth counts N1 and N2 are integers with input minima of 6. Acceptance by the form does not establish manufacturability: the tool warns about undercutting when the driver has fewer than 17 teeth.
Thickness b is axial face width in mm, with an input minimum of 1 mm. A preliminary reference is b = 8m–12m, but suitable width depends on load distribution and support. Pressure-angle choices are 20° and 14.5°. The strength calculation currently uses a 20° Y table that does not change with this selection.
Each shaft-hole diameter specifies the central bore in mm, with an input minimum of 2 mm. It must be smaller than the root diameter, with adequate surrounding material. Choose steel, aluminum or POM to compare the stored allowable stress values. Input speed starts at 1 rpm and the torque field starts at 0.1 N·m. Actual operating ranges must follow the ratings of the real components.
① Choose driving and driven tooth counts for the desired reduction, then enter module and face width.
② Select pressure angle, both bore diameters and material, then enter input speed and torque.
③ Review the automatically updated center distance, output speed and torque, allowable torque, safety factor and warnings together.
④ Inspect the arrangement in 2D and 3D and download STL files if needed. Before machining, check tolerances, backlash, shaft connections and the actual tooth profile as well as shaft spacing.
Enter m = 3 mm, N1 = 20, N2 = 40, b = 30 mm, pressure angle 20°, bore diameters 8 mm and 12 mm, steel, n1 = 1000 rpm and T1 = 10 N·m. The ratio is 2.00:1, pitch diameters are 60.0 mm and 120.0 mm, and center distance is 90.0 mm. Output speed is 500 rpm and output torque with 97% efficiency is 19.40 N·m.
For the same case, direct calculation gives pitch-line velocity 3.142 m/s and input-based tangential force 333.33 N. The tool uses the smaller of Y1 = 0.320 and Y2 = 0.3882 with its stored steel allowable stress of 140 MPa. Allowable force is 4032 N, allowable input torque is 120.96 N·m and displayed safety factor is 12.10. Pitch-line velocity and tangential force illustrate the equations; they are not separate result fields.
The model assumes standard external involute spur gears without profile shift and a rigid shaft arrangement. Geometry omits deformation, backlash and assembly errors. Losses are represented by a fixed 97% efficiency rather than individual friction calculations; real efficiency changes with speed or material are not modeled.
Lewis values provide a simplified bending comparison. They do not replace checks for contact fatigue, wear, impact, dynamic loads, misalignment, heat, lubrication or service life. Stored material stresses are not guaranteed values for every heat treatment or manufacturing condition. In particular, selecting 14.5° still uses the 20° form-factor table, limiting the strength result. STL files are starting points for reviewing shape; manufacturing and assembly tolerances and process requirements need separate decisions.
Does a higher gear ratio increase power? It can reduce speed and increase torque, but creates no power. This tool assumes losses through its efficiency value.
Is a safety factor of at least 1 permission to manufacture? It means the simplified bending criterion on screen is met. It does not validate other failure modes or operating conditions.
Is matching module enough for meshing? Pressure angle and tooth-profile conditions must also match. Check center distance, undercutting, interference and backlash together.