Gear Profile Shift CalculatorPROFILE SHIFT

1. 1Enter module m, both tooth counts z1 and z2 and the pressure angle (normally 20°).
2. 2Enter the centre distance a' you need, e.g. the existing bearing bore spacing or motor mount position.
3. 3Choose how to split Σx: balanced sliding for general use, or all on the pinion when it has very few teeth.
4. 4Check that undercut, tip thickness and contact ratio show ✓ for both gears; otherwise adjust teeth or centre distance.
5. 5Click “Open in 3D generator” to build the spur gear pair with the computed x1 and x2 and download STEP / STL.

Profile shift moves the cutting tool (the basic rack) outward or inward by x·m when the gear is generated. Positive shift thickens the root, sharpens the tip and increases the centre distance of the pair. For a target centre distance a', first solve the working pressure angle from cos α' = a·cos α / a', then use the involute function inv α = tan α − α to get Σx = (z1+z2)(inv α' − inv α)/(2 tan α) — the only total shift that lets the gears mesh without backlash at a'.

Undercut: a gear with z teeth avoids undercut when x ≥ xmin = 1 − z·sin²α/2 (about +0.30 for z12 at 20°). Pointed tips: more positive shift thins the tip; keep tip thickness sa ≥ 0.25 m, or ≥ 0.4 m for case-hardened gears. Contact ratio: shift and tip shortening both reduce it — aim for εα ≥ 1.2. Pass all three before drawing or printing.

Printed pinions often use 10–14 teeth to save space; without shift they undercut badly and the roots are weak. Once the tool gives x1 and x2, one click opens the spur gear pair generator with the same shifts and centre distance so you can download STEP / STL directly. For FDM, add 0.05–0.1 mm backlash or a slightly larger centre distance.

inv α = tan α − α
a = m(z1 + z2) / 2 ;  cos α' = a·cos α / a'
Σx = x1 + x2 = (z1 + z2)(inv α' − inv α) / (2 tan α)
y = (a' − a) / m ;  k = Σx − y  (tip shortening)
da = m(z + 2 + 2x − 2k) ;  df = m(z − 2.5 + 2x)
zmin = 2(1 − x) / sin²α  →  xmin = 1 − z·sin²α / 2
balanced: x_small = Σx/2 + (0.5 − Σx/2)·lg(u) / lg(z1·z2 / 100),  u = z_large / z_small

Results are for design reference only; confirm against supplier catalogues and the applicable standards before manufacturing.