Spur Gear Design Formulas

Basic spur gear dimensions can be calculated from the module, tooth count, and pressure angle. This table covers common dimensions for a standard, unshifted external spur gear in the metric module system. It is a geometry reference; it does not size a gear for torque, speed, life, noise, or manufacturing accuracy.

Standard spur gear geometry table

Using module and tooth count

Module m is the reference diameter divided by tooth count, so the reference diameter is d = z m. For example, a 40-tooth gear with module 2 mm has a reference diameter of 80 mm. The circular pitch is the reference-circle circumference divided by the number of teeth: πd/z = πm, or about 6.283 mm in this example.

For a standard involute gear with a 20° reference pressure angle, the base diameter is d_b = d cos α. Using 80 mm and 20° gives approximately 75.175 mm. The base circle is the geometric reference from which an involute tooth flank is generated; it is not the root diameter.

Standard versus profile-shifted gears

The table uses zero profile shift. In this standard system, addendum is one module, the tip diameter is d + 2m, and the root diameter follows the conventional 2.5m deduction shown by the manufacturer reference. Profile shift changes tooth dimensions and can change working pitch geometry, center distance, and clearance. If a gear drawing specifies a shift coefficient, do not use the unshifted dimensions without recalculating the pair.

The module system is metric. In an inch diametral-pitch system, tooth count and pitch diameter use a different relationship; do not enter diametral pitch as though it were module. A mating pair must share a compatible tooth system, module, pressure angle, and geometry.

Dimensions do not prove gear capacity

Two gears with matching basic dimensions may still be unsuitable for a load. Tooth bending strength, contact stress, material, heat treatment, face width, lubrication, alignment, quality grade, operating temperature, and duty cycle all affect capacity and life. The basic dimensions also do not determine backlash or manufacturing tolerances.

Check the manufacturer drawing and the applicable gear rating method before releasing a design. Confirm that the selected cutter or manufacturing process can produce the required tooth form and that the complete gear pair satisfies center-distance and interference constraints.

Source

The standard spur gear dimensions and equations follow KHK Gears’ calculation reference, specifically its standard spur gear section. Circular pitch is shown as the reference circumference divided by tooth count, which reduces to πm using d=zm. KHK distinguishes this standard case from profile-shifted gears. Use the selected manufacturer’s current drawing and engineering guidance for a real gear set.