Spur Gear Calculator

One number sets the size of a tooth: the module in millimetres, or its reciprocal, the diametral pitch in teeth per inch. From there the pitch diameter is m·z and everything else follows from standard full-depth proportions — addendum one module, dedendum 1.25, clearance 0.25 — giving the tip at m(z + 2), the root at m(z − 2.5) and the base circle at d·cos α. Circular pitch is πm along the pitch circle, and the nominal tooth thickness is exactly half of it, with no backlash taken out.

Two gears mesh only if they share a module and a pressure angle; then the ratio is the tooth counts and the theoretical centre distance is half the sum of the pitch diameters. Contact ratio — the path of contact divided by the base pitch — is how many tooth pairs are engaged on average. Above about 1.2 the drive overlaps smoothly; below 1.0 it is not continuous at all. Below 2 ÷ sin²α teeth, which is 17 or 18 at 20°, the cutter undercuts the root and weakens the tooth.

Nominal reference geometry only: no profile shift or correction, no backlash allowance, no tip relief, no root fillet radius, no tolerance class and no material. Real gears are cut thinner than the theoretical half-pitch, and the centre distance given here is the theoretical one before that allowance. Load capacity belongs to a rating standard — AGMA or ISO 6336, both licensed — and is cited here only as a label. Use this to set out and check a design, not as a manufacturing drawing. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.