Enter Gear Data
Formula Used
Pitch diameter from module: d = N × m
Pitch diameter from diametral pitch: d(in) = N / P
Module from diametral pitch: m = 25.4 / P
Circular pitch: p = π × m
Outside diameter: OD = d + 2m
Root diameter estimate: RD = d - 2.5m
Base diameter: BD = d × cos(pressure angle)
Center distance: C = (d1 + d2) / 2
Tangential force: Ft = 2T / d, where diameter is in meters.
Example Data Table
| Teeth | Module mm | Pitch Diameter mm | Outside Diameter mm | Circular Pitch mm |
|---|---|---|---|---|
| 20 | 2.00 | 40.00 | 44.00 | 6.2832 |
| 40 | 2.50 | 100.00 | 105.00 | 7.8540 |
| 60 | 3.00 | 180.00 | 186.00 | 9.4248 |
| 80 | 4.00 | 320.00 | 328.00 | 12.5664 |
How to Use This Calculator
- Enter the number of teeth on the gear.
- Select the known input type.
- Enter module, diametral pitch, circular pitch, or pitch diameter.
- Add pressure angle for base diameter calculation.
- Enter mate gear teeth to estimate center distance.
- Add torque and service factor for force checking.
- Press the calculate button.
- Use CSV or PDF buttons to save the results.
Gear Pitch Diameter Guide
What Pitch Diameter Means
Pitch diameter is a key gear size. It describes the theoretical circle where two gears roll together. It is not the outside size. It is not the root size. It sits between both. This circle controls speed ratio, center distance, and tooth engagement. A correct value helps gears mesh smoothly. It also reduces noise and wear.
Why It Matters in Engineering
Gear design depends on accurate geometry. The pitch diameter links tooth count with module or diametral pitch. In metric work, module is common. In inch based work, diametral pitch is common. Both describe tooth size. A larger module creates larger teeth. A higher diametral pitch creates smaller teeth. This calculator converts between these systems and keeps the results clear.
Related Gear Dimensions
A useful design check should show more than one number. This tool also estimates outside diameter, root diameter, base diameter, addendum, dedendum, circular pitch, and tooth thickness. These values help with drawing, layout, inspection, and early part selection. The base diameter uses the pressure angle. That value affects involute tooth action. Twenty degrees is common, but the field can be changed.
Center Distance and Pair Checks
A gear normally works with another gear. When mate gear teeth are entered, the calculator estimates the second pitch diameter. It also gives the center distance. This helps during gearbox layout. The gear ratio is also shown. It compares driven gear teeth with driver gear teeth. Use that ratio when checking speed reduction or speed increase.
Torque and Force Review
The calculator can estimate tangential force from torque. It first applies the service factor. Then it uses pitch diameter in meters. This gives a practical load estimate for early checks. It is not a full strength rating. Final gear design should also review material, heat treatment, lubrication, quality grade, bending stress, contact stress, and safety factor.
Best Practice
Use consistent units. Check every input twice. Compare results with supplier data or design standards. Keep enough face width for load sharing. Avoid very small tooth counts unless undercut is reviewed. Export the report when the result will be shared with a machinist, designer, or reviewer.
FAQs
1. What is gear pitch diameter?
Gear pitch diameter is the theoretical rolling diameter of a gear. It is used to define tooth spacing, gear ratio, and center distance between mating gears.
2. Is pitch diameter the same as outside diameter?
No. Outside diameter is larger than pitch diameter for standard external gears. It includes the addendum above the pitch circle.
3. How is pitch diameter calculated from module?
Multiply the number of teeth by the module. For example, a 40 tooth gear with 2 mm module has an 80 mm pitch diameter.
4. How is pitch diameter calculated from diametral pitch?
Divide the tooth count by diametral pitch to get inches. The calculator also converts that value to millimeters for easier comparison.
5. What pressure angle should I use?
Twenty degrees is common for many modern spur gears. Use the value required by your gear standard, cutter, catalog, or existing mating gear.
6. Can this calculator estimate center distance?
Yes. Enter the mate gear teeth. The tool calculates the mate pitch diameter and divides the sum of both pitch diameters by two.
7. Does this replace full gear strength design?
No. It supports geometry and early force checks. Final design should include stress, material, lubrication, manufacturing quality, and safety factor review.
8. Why is circular pitch useful?
Circular pitch shows the arc distance from one tooth to the next on the pitch circle. It helps compare tooth spacing directly.