Calculate gear pitch circle diameter, number of teeth, or diametral pitch with inch, cm, mm, and meter unit conversions for gears.
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Pitch Circle Formula
The pitch circle calculator uses the relationship between pitch circle diameter, number of teeth, and diametral pitch. Choose the quantity to solve for, then enter the two known values. Use diameter and diametral pitch in the same reference plane; diametral pitch is teeth per unit of pitch diameter.
- D = pitch circle diameter
- N = number of teeth
- P = diametral pitch
The calculator converts diameter values to inches and diametral pitch values to teeth per inch before applying the formula. It then converts the result back to the unit you selected.
- To calculate pitch circle diameter: the calculator divides the number of teeth by the diametral pitch.
- To calculate number of teeth: the calculator multiplies pitch circle diameter by diametral pitch.
- To calculate diametral pitch: the calculator divides the number of teeth by the pitch circle diameter.
Common Pitch Circle Unit Conversions
These conversions match the unit handling used by the calculator.
| Input Type | Unit | Base Conversion |
|---|---|---|
| Diameter | Inches | 1 inch = 1 inch |
| Diameter | Centimeters | 1 cm = 1/2.54 inches (exactly) |
| Diameter | Millimeters | 1 mm = 1/25.4 inches (exactly) |
| Diameter | Meters | 1 m = 1/0.0254 inches (exactly) |
| Diametral Pitch Unit | Base Conversion |
|---|---|
| Teeth per inch | 1 tooth/inch = 1 tooth/inch |
| Teeth per centimeter | 1 tooth/cm = 2.54 teeth/inch |
| Teeth per millimeter | 1 tooth/mm = 25.4 teeth/inch |
| Teeth per meter | 1 tooth/m = 0.0254 teeth/inch |
Example Pitch Circle Calculations
Example 1: Calculate pitch circle diameter
You have a gear with 48 teeth and a diametral pitch of 12 teeth per inch.
The pitch circle diameter is 4 inches.
Example 2: Calculate diametral pitch
You have a gear with 60 teeth and a pitch circle diameter of 5 inches.
The diametral pitch is 12 teeth per inch.
FAQ
What is a pitch circle?
The pitch circle is an imaginary circle used to define the working size of a gear. Gear teeth are spaced around this circle, and the pitch circle is used when calculating gear ratios, tooth spacing, and diametral pitch.
Is pitch circle diameter the same as outside diameter?
No. Pitch circle diameter is measured at the theoretical pitch circle, where gear teeth effectively mesh. Outside diameter is measured across the outer tips of the gear teeth. For standard gears, the outside diameter is usually larger than the pitch circle diameter.
Why does the calculator need exactly two values?
The formula has three related variables: pitch circle diameter, number of teeth, and diametral pitch. Choose the unknown and enter the other two. A noninteger theoretical tooth count does not describe a buildable gear without changing diameter or pitch; the calculator does not silently round that result. Actual tooth counts entered into the other modes must be positive whole numbers.
