Profile Shift Coefficient Calculator

Inputs

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Specify gear size by metric module (mm) or imperial diametral pitch (teeth per inch).
Module in mm (metric) or diametral pitch in 1/in (imperial).
mm
Standard (reference) pressure angle. z_min and all involute functions follow from it.
°
Pinion or single-gear tooth count.
teeth
Addendum modification coefficient for gear 1 (rack shifted outward = positive).
Screen one gear, or a meshing external pair including center distance.
Mating gear tooth count (external mesh).
teeth
Addendum modification coefficient for gear 2.

Results

Default result
Edit inputs
Min shift, gear 1(x₁,min)
0.298
Pass

Gear 1: shift meets the theoretical no-undercut minimum.

Theoretical minimum to avoid undercut at ha* = 1.

Also computed

Tip thickness, gear 1(s_a1)Pass0.871mm

Tip thickness is above the customary 0.4·m minimum.

Tooth thickness, gear 1(s₁)3.578mm

Working pressure angle(αw)21.787°

Center distance(a')48.575mm

Reference center distance(a₀)48.000mm

Center distance mod. coeff.(y)0.2875

Method notes 6 notes
  • Standard full-depth basic rack (ha* = 1.0) assumed for z_min, tip diameter and tip thickness. Stub or special racks change these values.
  • Gear 1: shift meets the theoretical no-undercut minimum.
  • Gear 2: shift meets the theoretical no-undercut minimum.
  • Center distance follows from the shift sum only; how x is split between the gears is a design choice (balance pinion strength vs tip thinning).
  • Tip shortening k* keeps the standard bottom clearance at the modified center distance; small values are often left unshortened, accepting reduced clearance.
  • This is a geometry screen: contact ratio, root bending and flank pressure still need their own checks.

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