For a standard metric spur gear, module and tooth count determine several basic diameters and tooth proportions. This table gives calculated examples for unshifted external spur gears with a 20-degree reference pressure angle. It is a geometry reference only: it does not specify gear strength, accuracy grade, backlash or fit tolerance.

Metric Gear Module Tooth Dimensions

How module sets the scale

Module m is the reference diameter per tooth. For tooth count z, the reference diameter is d = mz. A module of 2 mm with 20 teeth therefore has a 40 mm reference diameter. KHK’s standard spur-gear equations also give addendum ha = m, dedendum hf = 1.25m, tip diameter da = d + 2m and root diameter df = d − 2.5m for the basic unshifted profile shown here. Circular pitch is πm, and the basic circular tooth thickness is half that pitch before backlash or manufacturing allowances are applied.

The base diameter depends on pressure angle: db = d cos α. The examples use α = 20 degrees, so a change in pressure angle changes the base diameter and involute shape even when module and tooth count remain the same. The listed dimensions are calculated from the formulas rather than transcribed from a catalog table; rounded values are for reference and may differ slightly from a drawing or supplier data after rounding.

Use matching gear specifications

Two gears normally need compatible module, pressure angle and tooth form to mesh as intended. Their tooth counts set the speed ratio, while their reference diameters and center distance determine the nominal layout. A basic pair’s center distance is half the sum of the reference diameters when there is no profile shift. For a 12-tooth and 24-tooth pair at module 3 mm, that basic center distance is 54 mm. This geometric relation does not check undercut, contact ratio, strength, noise or lubrication.

Profile shift changes working geometry and may alter tip diameter, root clearance, contact ratio and center distance. Helical gears use normal and transverse modules and a helix angle; internal gears, bevel gears and worm pairs use different relationships. Do not apply the external spur-gear examples to those cases. Also check whether the selected tooth count and module combination is commercially available and consistent with the design standard on the drawing.

Why the table omits tolerance limits

Nominal dimensions are not manufacturing tolerances. Gear quality class, tooth thickness allowance, backlash, runout, lead error, mounting distance, material, heat treatment and load rating all influence the finished component. The dimensions in this table cannot be used alone to order a replacement gear or approve a drive. For production, specify the governing gear standard and quality grade and obtain a controlled drawing or manufacturer calculation for the exact duty.

For a quick check, calculate d = mz and compare the result with a measured pitch diameter or a known module. Use outside diameter only with the correct tooth form and profile assumptions; wear, profile shift and tip relief can make a direct estimate misleading. Confirm dimensions using the relevant inspection method and the manufacturer’s technical documentation.

To use a row, first confirm that the design actually calls for an external spur gear with a standard 20-degree pressure angle and no profile shift. Enter the module and tooth count from the drawing, then compare the calculated reference and outside diameters with the selected design values. Tooth count affects undercut risk, especially for small pinions, and the formulas alone do not establish that a tooth form can be produced without correction. A qualified gear designer should check the mating pair, operating center distance and load case before releasing the dimensions for manufacture.

Use consistent units throughout a calculation. Module is a metric length per tooth, while tooth count is a whole-number input. The example rows are rounded to four decimal places for readability, so a detailed design calculation should retain additional precision until the final drawing values are set. Inspection of an actual gear may require dedicated measuring pins, a span measurement or other methods specified by the applicable standard.

Sources

Equations follow KHK Gears’ Calculation of Gear Dimensions reference for standard spur gears. The displayed rows are original calculations for the stated inputs, not copied standard tolerance data.