Get the pitch diameter, outside diameter, and tooth spacing for a spur gear from its tooth count and diametral pitch.
1. Gear Blank Variables
Enter the number of teeth and the diametral pitch.
Pitch Circle Diameter (PD)
3.000 in
Outside Diameter (OD)
3.250 in
Circular Pitch (CP)
0.3927 in
Standard Center Distance
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How Spur Gear Geometry Works
Diametral pitch describes how many teeth fit per inch of pitch diameter. Pitch diameter is just the tooth count divided by that pitch. Outside diameter adds two more tooth spaces on top of that, since the teeth extend past the pitch circle.) / DP. Circular Pitch (CP) measures the circumferential pitch distance spacing between corresponding profile edges along the arc line, tracking mathematically through the fixed constant ratio matrix: CP = π / DP.
Worked Example
A 24 tooth gear with a diametral pitch of 8 has a pitch diameter of exactly 3.000 inches and an outside diameter of 3.250 inches.
Common Mistakes
Mixing up diametral pitch (teeth per inch of pitch diameter) with module (the metric equivalent, calculated the opposite way); they're not interchangeable without conversion.
Assuming two gears with the same diametral pitch but different tooth counts will mesh at any center distance; spacing still depends on both gears' pitch diameters.
Ignoring pressure angle, a separate spec from pitch and tooth count that also affects whether two gears will mesh correctly.
Frequently Asked Questions
What is diametral pitch?
A measure of tooth size, expressed as the number of teeth per inch of pitch diameter. Higher diametral pitch means smaller teeth.
How is this different from module?
Module is the metric system's equivalent, calculated as pitch diameter divided by tooth count, the inverse relationship of diametral pitch.
Will two gears with the same diametral pitch always mesh?
They need the same diametral pitch and pressure angle to mesh correctly; tooth count can differ between the two gears.
Disclaimer: This tool is provided for educational and informational tracking purposes only. Calculations assume idealized standard 14.5 or 20-degree full-depth involute gear pressure profile settings. True industrial gear cut depths, tooth clearance dimensions, hub spacing configurations, backlash allowances, and profile constraints differ based on raw cutting tooling types and specific mechanical box assemblies. Mating parameters must be manually cross-checked against engineering drawings using formal AGMA standard tables before cutting or casting blank stock materials. The website owner assumes no liability.