Calculate chainring pitch diameter, chain pitch, or tooth count from the other two values in inches or mm for bicycle chainrings using any two inputs.
Chainring Pitch Diameter (PCD) Formula
The calculator uses the relationship between the number of teeth, chain pitch, and the pitch circle diameter of the chainring. Enter any two values to calculate the third.
- D = chainring pitch diameter, or PCD
- P = chain pitch
- N = number of teeth
- pi = 3.14159…
To solve for chain pitch:
To solve for number of teeth:
- Calculate PCD: use the number of teeth and chain pitch to find the chainring pitch diameter.
- Calculate chain pitch: use the number of teeth and PCD to find the chain pitch.
- Calculate number of teeth: use the chain pitch and PCD to estimate the tooth count. Since teeth must be a whole number, the calculator rounds the result to the nearest whole tooth.
- Unit handling: inches and millimeters are converted internally so you can enter pitch and diameter in different units.
Common Chain Pitch Values
Chain pitch is the distance from one chain pin center to the next. Bicycle chainrings commonly use 1/2 inch pitch, but other chain systems may use different pitches.
| Chain pitch | Decimal inches | Millimeters | Typical use |
|---|---|---|---|
| 1/2 in | 0.500 in | 12.70 mm | Most bicycle chains |
| 3/8 in | 0.375 in | 9.525 mm | Small chain drives and specialty uses |
| 1/4 in | 0.250 in | 6.35 mm | Small mechanical chain systems |
Typical PCD Results for 1/2 Inch Bicycle Chain Pitch
| Number of teeth | PCD in inches | PCD in millimeters |
|---|---|---|
| 28 | 4.468 in | 113.49 mm |
| 32 | 5.101 in | 129.57 mm |
| 36 | 5.737 in | 145.72 mm |
| 42 | 6.690 in | 169.93 mm |
| 52 | 8.282 in | 210.36 mm |
Example
Example 1: Calculate chainring PCD
You have a 36-tooth chainring and a 1/2 inch chain pitch.
The result is approximately 5.7369 in, or 145.72 mm.
Example 2: Calculate chain pitch
You have a 42-tooth chainring with a PCD of 169.93 mm.
The result is approximately 12.70 mm, which is 0.5 in.
FAQ
Is chainring PCD the same as bolt circle diameter?
No. In this calculator, PCD means the pitch diameter of the chain teeth, which is the diameter of the circle passing through the chain pin centers as the chain wraps around the chainring. Bolt circle diameter, often called BCD, is the circle through the chainring mounting bolts.
Why does the tooth count result get rounded?
A real chainring can only have a whole number of teeth. The formula can return a decimal tooth count when the entered pitch and diameter do not match an exact chainring size, so the calculator rounds to the nearest whole tooth.
Why is 1/2 inch pitch common for bicycle chainrings?
Most bicycle chains use a 1/2 inch pitch, equal to 12.7 mm. If you are calculating a standard bicycle chainring, 0.5 in or 12.7 mm is usually the correct pitch to enter.
