How to Use Pitch Circle Diameter Calculator
The Pitch Circle Diameter Calculator supports three modes that cover the most common engineering scenarios.
- Pick a mode — Metric gear, imperial gear or bolt circle.
- Choose a unit — mm, cm or inch.
- Enter the inputs — module and teeth, or teeth and DP, or holes and chord spacing.
- Read the result — The calculator displays PCD and the underlying formula expanded with your numbers.
Formula & Theory — Pitch Circle Diameter Calculator
The Pitch Circle Diameter Calculator is grounded in classic gear and circle geometry:
Metric gear: PCD = m × Z
Imperial gear: PCD = N / DP
Bolt circle: PCD = s / sin(π / n)| Symbol | Meaning |
|---|---|
| m | Module of the gear (mm) |
| Z, N | Number of teeth |
| DP | Diametral pitch (teeth per inch) |
| s | Chord between adjacent bolt holes |
| n | Number of bolt holes |
For bolt circles, the chord-to-PCD relationship comes from the law of sines applied to the isosceles triangle formed by two adjacent holes and the centre.
Pitch circle and meshing
When two gears mesh correctly, their pitch circles roll without slipping. PCD therefore determines centre distance: C = (PCD1 + PCD2) / 2.
Use Cases for Pitch Circle Diameter Calculator
- Gear design — Quickly verify that a chosen module / tooth combination produces the desired PCD and centre distance.
- Wheel manufacturing — Calculate bolt-circle dimensions for wheels, hubs and brake rotors.
- Flange design — Lay out bolt circles for piping, machinery couplings and pressure vessels.
- Reverse engineering — Given a measured chord between two holes, recover the original PCD.
- CNC programming — Generate hole-centre coordinates by combining PCD with start angle.
- Education — Students explore relationships between module, teeth and pitch circle through hands-on examples.
From classroom problems to production drawings, the Pitch Circle Diameter Calculator delivers the number you need with zero ambiguity.