Enter the number of teeth on the chainring and the chain pitch into the calculator to determine the chainring pitch diameter (also called the pitch circle diameter, PCD). This calculator helps in designing and analyzing bicycle gear systems.
Chainring Pitch Diameter (PCD) Formula
The following formula is used to calculate the chainring pitch diameter (pitch circle diameter, PCD).
D = P / \sin(\pi/N)
Variables:
- D is the chainring pitch diameter (PCD) (inches or mm)
- N is the number of teeth on the chainring
- P is the chain pitch (the distance between the centers of adjacent chain pins/rollers, measured along the chain) (same units as D)
To calculate the chainring pitch diameter (PCD), divide the chain pitch by sin(π/N). For large tooth counts, a common approximation is D ≈ (N × P) / π, but the sine-based formula above is the more accurate geometric relationship.
What is a Chainring Diameter?
In chain-and-sprocket geometry, the diameter computed from chain pitch and tooth count is typically the pitch circle diameter (PCD): the diameter of the circle that passes through the centers of the chain rollers as they wrap around the chainring. This is an important dimension for analysis and design because it relates directly to tooth count and chain pitch. Note that the outside diameter of a chainring is larger than the pitch diameter and depends on tooth shape and profile.
How to Calculate Chainring Diameter?
The following steps outline how to calculate the Chainring Pitch Diameter (PCD).
- First, determine the number of teeth on the chainring (N).
- Next, determine the chain pitch (P) in inches (or use consistent units).
- Next, gather the formula from above: D = P / sin(π/N).
- Finally, calculate the Chainring Pitch Diameter (D).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Number of teeth on the chainring (N) = 52
Chain pitch (P) = 0.5 inches
