Pitch Diameter Calculator — Gear Dimensions
Enter the number of teeth and the diametral pitch (imperial) or module (metric) to find the pitch diameter, outside diameter, root diameter, circular pitch, addendum and dedendum instantly.
Gear system
Diameter of the imaginary pitch circle where gears mesh
- 1
Addendum (one tooth height above pitch circle)
1 ÷ 8 = 0.125 in - 2
Pitch diameter
24 ÷ 8 = 3Diameter of the reference circle on which two gears mesh without slipping.
How does this calculator work?
Pitch diameter equals teeth divided by diametral pitch (imperial) or teeth times module (metric). Outside diameter adds two addenda; root diameter subtracts 2.5 addenda each side. Circular pitch is π divided by DP or π times module. These are standard AGMA full-depth involute gear proportions — verify against your design specification.
Formula
How this is calculated
The pitch diameter (PD) is the diameter of the imaginary circle on which two meshing gears roll together without slipping — it is the fundamental reference dimension for all other gear geometry. In the imperial (diametral pitch) system PD = N / DP, where N is the tooth count and DP is the teeth-per-inch of pitch diameter. In the metric (module) system PD = N × m, where m is the module in millimetres.
From the pitch diameter the remaining dimensions follow from standard AGMA full-depth involute tooth proportions. Each tooth projects one addendum above the pitch circle and dips one dedendum below it. The addendum equals 1/DP (imperial) or the module (metric). The dedendum is 1.25 × addendum, providing a small clearance so the tip of one gear's tooth does not bottom out in the root of the mating gear. Outside diameter adds two addenda to PD; root diameter subtracts two dedenda. Circular pitch is the arc length along the pitch circle from one tooth to the next: π / DP or π × m.
These formulas assume standard full-depth involute teeth at a 20° pressure angle (the most common modern standard). Stub-tooth, fine-pitch, or non-standard gears may use different addendum/dedendum ratios. Always verify against your design standard and manufacturing drawings.
Frequently asked questions
Both describe tooth size but in different systems. Diametral pitch (DP) is teeth per inch of pitch diameter — a higher DP means smaller, finer teeth. Module (m) is pitch diameter in mm divided by tooth count — a larger module means larger, coarser teeth. They are related by m = 25.4 / DP.
Standard full-depth teeth have a dedendum of 1.25 × addendum. The extra 0.25 on each side provides a clearance gap so the tip of one gear's tooth does not contact the root of the mating gear, reducing friction and wear.
The pitch diameter formula applies directly to the circular pinion. A rack has an infinite pitch diameter — its teeth are spaced by the same circular pitch, and its module or DP must match the mating pinion. For helical gears the normal pitch differs from the transverse pitch; consult AGMA standards for the full geometry.
Also known as
TG we-Calculate Editorial Team. (2026). Pitch Diameter Calculator — Gear Dimensions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/pitch-diameter-calculator
TG we-Calculate Editorial Team. "Pitch Diameter Calculator — Gear Dimensions." TG we-Calculate. 2026. https://we-calculate.com/calculator/pitch-diameter-calculator.
TG we-Calculate Editorial Team, "Pitch Diameter Calculator — Gear Dimensions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/pitch-diameter-calculator
@misc{wecalculate_pitch_diameter_calculator, title = {Pitch Diameter Calculator — Gear Dimensions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/pitch-diameter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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