Pitch Diameter Calculator

Pitch diameter is the diameter of an imaginary circle where mating gear teeth theoretically roll together without slipping. It is one of the central dimensions in spur gear design because center distance, speed ratio, and tooth spacing all relate to the pitch circles. The physical gear has an outside diameter at the tooth tips and a smaller root diameter at the bottoms of the tooth spaces, but the pitch circle lies between those visible boundaries. For a metric spur gear, pitch diameter equals module multiplied by the number of teeth. Module expresses tooth size in millimeters of pitch diameter per tooth, so gears that mesh must normally share the same module and pressure angle. This calculator also finds circular pitch as pi multiplied by module. Circular pitch is the distance along the pitch circle from one tooth to the corresponding point on the next tooth, and dividing it approximately in half gives the standard tooth thickness at the pitch circle before backlash modifications. The outside diameter shown uses the common full-depth standard relation of module multiplied by tooth count plus two. The root diameter uses module multiplied by tooth count minus two-and-a-half, reflecting a one-module addendum and a 1.25-module dedendum. Base diameter is pitch diameter multiplied by the cosine of the pressure angle. The involute tooth profile is generated from this base circle, making pressure angle important even though it does not alter the pitch diameter itself. These formulas describe an unshifted external standard spur gear. Profile shift, nonstandard addendum, internal gears, helical gears, backlash adjustments, protuberance cutters, and tip relief require additional calculations. A low tooth count may also suffer undercut unless a suitable pressure angle or positive profile shift is used. The displayed root diameter is therefore a nominal design value, not a substitute for the actual cutter geometry or manufacturing drawing. Use the calculator for preliminary layouts, center-distance checks, classroom problems, and quick verification of catalog data. Two mating external gears have a nominal center distance equal to half the sum of their pitch diameters, while their speed ratio is the inverse ratio of tooth counts. Final production work should follow the relevant ISO, AGMA, DIN, or company standard and include tolerances, quality grade, material, heat treatment, face width, load capacity, lubrication, and inspection requirements.