Engineering CalculatorsSpline Sizing Calculator
Size a straight involute spline (ISO 4156 / ANSI B92.2M, metric module) from torque and diameter — get a drawing-ready dimension table including measurement over pins, an SAE/Dudley torque capacity with the governing failure mode, and a to-scale tooth profile you can export to DXF.
| Designation (z × m × α, root) | 18 × m2 × 30° fillet root |
| Number of teeth z | 18 |
| Module m | 2 mm |
| Pressure angle α | 30° |
| Pitch (reference) diameter D | 36 mm |
| Base diameter Db | 31.177 mm |
| Major (tip) diameter Dee | 38 mm |
| Minor (root) diameter Die | 32.4 mm |
| Form diameter DFe | 34.4 mm |
| Circular tooth thickness s | 3.142 mm |
| Circular space width E | 3.142 mm |
| Base pitch pb | 5.441 mm |
| Measurement over pins MRe (Ø3.84 mm) | 41.917 mm |
Nominal (basic / maximum-material) dimensions. The toleranced range for a chosen fit and tolerance class (4H/4h…7H/7h) is per ISO 4156-2.
New to ISO 4156? Read the guide: Involute Splines: Geometry, Measurement Over Pins & Torque Capacity — a plain-language explainer of the standard behind this calculator.
Geometry follows ISO 4156-1 / ANSI B92.2M (straight cylindrical involute splines, metric module, side fit): pitch diameter D = m·z, base diameter Db = m·z·cos α, external major diameter Dee = m·(z + a) and root diameter Die = m·(z − b) with the standard addendum/dedendum coefficients for the 30°, 37.5° and 45° pressure angles, basic circular tooth thickness s = 0.5·π·m, and the measurement over two pins from inv φ = s/D + inv α + DR/Db − π/z, MRe = Db/cos φ + DR (even tooth counts; the odd-count form multiplies by cos(90°/z)). The 30° profile is shared by ANSI B92.1 and DIN 5480. Torque capacity uses the SAE / ANSI B92.1 (Dudley) method: tooth shear τ = 2·T·Ks/(L·z·t·D), flank compressive (bearing) stress σc = 2·T·Ks/(L·z·h·D) with engagement height h = 0.9·m (flat root) or 1.0·m (fillet root), and a torsional-shear check on the shaft core at the minor diameter τ = 16·T·Ks/(π·Die³). The service factor rolls up the application factor Ka, load-distribution factor Km, fatigue-life factor Kf and wear-life factor Kw (Ks = Ka/Kf for a fixed spline, Ka·Km·Kd/Kw for a sliding one) and is compared against representative material design strengths. Nominal minor/form diameters and the measurement over pins are at the basic (maximum-material) tooth thickness; the toleranced range for a chosen fit/tolerance class is per ISO 4156-2. The DXF profile is a nominal involute outline (reference/CAM starting geometry), not a toleranced manufacturing drawing.
Validated: for a 30° flat-root spline with module m = 0.5 mm and z = 10 teeth, this tool returns D = 5.000 mm, Db = 4.330 mm and Dee = 5.500 mm, matching the ISO 4156-2:2021 dimension table exactly, and a measurement over Ø1.06 mm pins of 6.716 mm — reproducing the standard's tabulated MRe (4h class, 6.683–6.701 mm at the toleranced tooth thickness) once the basic maximum-material tooth thickness is used. The odd-tooth case (z = 11, Ø1.00 mm pins) returns 7.005 mm against the standard's 6.966–6.989 mm band, and the SAE torque-capacity formulae reproduce hand calculations for the flank-bearing and tooth-shear limits.