Transverse contact ratio estimates how many pairs of standard spur-gear teeth are in contact, on average, as the gears rotate. A higher value generally means that tooth load is shared across more than one pair for more of the mesh cycle. It is one useful geometry measure, but it does not determine whether a gear set is strong, quiet or suitable for a particular machine.

The table compares selected standard external spur-gear pairs at module 2 mm. It varies pinion tooth count, uses either a 1:1 or 2:1 tooth-count relationship, and compares 20° and 25° pressure angles. The values are calculated from the standard path-of-contact relation and displayed to six decimal places for comparison. The examples assume unshifted, full-depth teeth with a common module and the same pressure angle on both gears.

What the calculation represents

The reference diameter of each gear is half the module multiplied by its tooth count. Adding one module gives the standard addendum radius, and multiplying the reference radius by the cosine of the pressure angle gives the base radius. The path of contact is the sum of the involute contact lengths at the two addenda, less the projection associated with center distance and pressure angle. Dividing that path by base pitch gives transverse contact ratio.

Base pitch is the distance between corresponding tooth profiles measured along the line of action. Because it depends on module and pressure angle, changing the pressure angle changes both base pitch and path of contact. The table makes that comparison while holding module and the selected tooth counts constant. Results are geometric calculations, not measured performance data.

Comparing tooth counts and pressure angles

Within these examples, increasing tooth counts at the same ratio changes the contact ratio because the addendum and base-circle geometry changes. The 2:1 pairs also have a different path of contact from the 1:1 pairs. The numerical differences should be interpreted only within the assumptions shown; a profile shift, altered addendum, center-distance change or different tooth system would change the result.

The 20° and 25° rows illustrate the effect of pressure angle for these standard geometries. Do not use the ratio alone to choose a pressure angle. Pressure angle also affects radial force, tooth size at the base, undercut limits, bearing loads and other aspects of the gear design. The mating parts must have compatible geometry and manufacturing specifications.

Limits before selecting a gear set

These examples do not check tooth bending strength, surface durability, interference, undercut, backlash, accuracy grade, noise, lubrication, temperature or service life. They assume standard unmodified geometry; no profile shift or special tooth proportions are included. The 20-tooth pinion examples are not intended to imply that every material, cutter or tooth system avoids undercut or interference.

For a real design, use the applicable gear rating method and verify loads, duty cycle, materials, heat treatment, face width, quality, shaft alignment, bearing arrangement and lubrication. Confirm the actual center distance and manufacturing tolerances. If the operating conditions require profile correction or a nonstandard tooth form, recalculate the path of contact with that geometry.

Use the table to compare a small, clearly defined set of baseline geometries. It can help with early sizing and education, while the complete gear design remains dependent on the application and its governing design method.

The path-of-contact definition and contact-ratio relationship are described by KHK Gears; an independent gear technical reference is available in KG Gear’s technical data. The displayed rows are calculations from the assumptions stated above.

For a practical comparison, for example, the equal 20-tooth pair at 20° has a calculated contact ratio of about 1.557, while a 20/40 pair at the same pressure angle is about 1.635. This comparison isolates geometry; it does not predict the gear pair’s rated load or service life.