What this calculator does
Pitch diameter is the diameter of the imaginary circle on a gear where its teeth are considered to mesh with a mating gear, and it is the reference dimension every other gear measurement is built from. It is not the outer diameter of the gear, which is slightly larger to accommodate the tips of the teeth.
Imperial gears are specified by diametral pitch, the number of teeth per inch of pitch diameter, while metric gears use module, the pitch diameter in millimetres per tooth. This calculator handles both conventions, since the two describe the same underlying geometry with different reference units.
The formula
For imperial gears, divide the number of teeth by the diametral pitch to get the pitch diameter in inches. For metric gears, multiply the number of teeth by the module to get the pitch diameter in millimetres. Both are simple, exact relationships once the gear standard being used is known.
| Term | Meaning |
|---|---|
| Pitch diameter | The diameter of the reference circle where two meshing gears effectively contact each other. |
| Diametral pitch | Teeth per inch of pitch diameter, the imperial gear-sizing convention: a higher number means finer, more closely spaced teeth. |
| Module | Pitch diameter in millimetres divided by tooth count, the metric gear-sizing convention: a higher number means larger, coarser teeth. |
The inputs explained
| Field | What to enter |
|---|---|
| System | Choose imperial (diametral pitch) or metric (module) depending on which standard the gear is specified in. |
| Number of teeth | The number of teeth on the gear. |
| Diametral pitch (teeth per inch of pitch diameter) | Diametral pitch, only used in imperial mode: teeth per inch of pitch diameter. |
| Module (mm) | Module in millimetres, only used in metric mode: pitch diameter per tooth. |
When to use it
Specifying a replacement gear
Matching a replacement or mating gear requires the same pitch diameter as the original, which this calculator gives directly from the tooth count and pitch or module printed on a parts diagram.
Checking two gears will actually mesh
Two gears can only mesh correctly if they share the same diametral pitch or module; comparing their resulting pitch diameters and centre-to-centre spacing confirms a design will fit.
Converting between imperial and metric gear specifications
A gear specified in one convention can be checked against a catalogue using the other convention by working out the pitch diameter in both systems and comparing.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How pitch diameter changes with tooth count at a fixed diametral pitch
A fixed diametral pitch of 8 teeth per inch, across a range of tooth counts.
| Number of teeth | Pitch diameter | Same, in millimetres |
|---|---|---|
| 12 | 1.500 in | 38.100 mm |
| 18 | 2.250 in | 57.150 mm |
| 24 | 3.000 in | 76.200 mm |
| 36 | 4.500 in | 114.300 mm |
| 48 | 6.000 in | 152.400 mm |
| 60 | 7.500 in | 190.500 mm |
How pitch diameter changes with module at a fixed tooth count
A fixed 24-tooth gear, across a range of common metric modules.
| Module | Pitch diameter | Same, in inches |
|---|---|---|
| 1 mm | 24.000 mm | 0.9449 in |
| 1.5 mm | 36.000 mm | 1.417 in |
| 2 mm | 48.000 mm | 1.890 in |
| 2.5 mm | 60.000 mm | 2.362 in |
| 3 mm | 72.000 mm | 2.835 in |
| 4 mm | 96.000 mm | 3.780 in |
Questions
Is pitch diameter the same as the outer diameter of a gear?
No. The outer diameter is larger, since it includes the addendum, the height the teeth project beyond the pitch circle. Pitch diameter is the reference circle used for meshing calculations, not the physically largest measurement on the gear.
How does pitch diameter relate to gear ratio?
Gear ratio is set by the ratio of tooth counts between two meshing gears, and because meshing gears share the same diametral pitch or module, that tooth-count ratio is also the ratio of their pitch diameters. See the gear ratio calculator for the speed and torque that follow from that ratio.
Can two gears with different diametral pitch or module mesh together?
No. Two gears can only mesh correctly if they share the same diametral pitch (imperial) or the same module (metric); mismatched gears will not engage properly even if their tooth counts happen to be compatible.
Why do some drawings specify module instead of diametral pitch?
Module is the metric convention and diametral pitch is the imperial one; which appears on a drawing usually just reflects which measurement system the design originated in, though the two describe the same underlying pitch-circle geometry.
For the speed and torque that follow once two gears are meshed, see the gear ratio calculator.