How to use this calculator
- Enter tooth count. Enter the sprocket tooth count N.
- Enter chain pitch. Enter the roller-chain pitch p for the chain series.
- Enter RPM if needed. Enter sprocket speed to estimate chain pitch-line speed.
- Read the geometry. Read pitch diameter, pitch radius, chain travel per revolution and tooth pitch angle.
How it works
A roller-chain sprocket pitch diameter is based on the polygon formed by
the chain rollers. The chain pitch p is the chord between adjacent
roller centers, so the pitch diameter is
PD = p / sin(180° / N)
where N is the sprocket tooth count.
The chain does not travel by the smooth pitch-circle circumference. It advances
one pitch for each tooth every revolution, so travel per revolution is
N x p and chain speed is v = N x p x n / 60000 when pitch is
entered in millimetres and speed in RPM.
After the pitch diameter is known, use the sprocket ratio calculator for a two-sprocket speed ratio, the chain length calculator for link count and center distance, and the roller chain tension calculator for power-transfer load. If you already know pitch diameter and power, the chain pull calculator is the shorter force check.
Worked example
Verified against the live calculator
A 15-tooth sprocket on ANSI #40 chain uses a 12.7 mm pitch. The pitch diameter is
12.7 / sin(180° / 15) ≈ 61.1 mm. It advances
15 x 12.7 = 190.5 mm of chain each revolution, so at 1,000 RPM the
chain speed is 190.5 x 1000 / 60000 ≈ 3.18 m/s.
Frequently asked questions
How do you calculate sprocket pitch diameter?
For a roller-chain sprocket, pitch diameter is PD = p / sin(180° / N), where p is the chain pitch and N is the sprocket tooth count. This is the theoretical pitch circle through the roller centers, not the outside tip diameter.
Is sprocket pitch diameter the same as outside diameter?
No. Pitch diameter is the theoretical roller-center circle. Outside diameter depends on the sprocket tooth form and is normally larger. Use manufacturer drawings when measured outside diameter or guard clearance is critical.
How do I calculate chain speed from tooth count and pitch?
A roller chain advances one chain pitch per tooth per sprocket revolution, so travel per revolution is N x p. Chain speed is v = N x p x n / 60000 when p is in mm and n is in RPM, giving m/s.
What chain pitch should I enter?
Enter the chain pitch for the chain series. ANSI #40 chain is 12.7 mm or 1/2 in, #35 is 9.525 mm or 3/8 in, #50 is 15.875 mm or 5/8 in, #60 is 19.05 mm or 3/4 in, and #80 is 25.4 mm or 1 in.
How many teeth should a small sprocket have?
Many roller-chain layouts prefer roughly 17 teeth or more on the small sprocket for smoother action and better chain life. Smaller sprockets can be useful for compact drives, but they raise polygonal action and wear, so verify the chain manufacturer limits.
Does this replace a chain tension or horsepower rating?
No. This page calculates geometry and chain speed. Use the roller chain tension calculator for force from power, and use manufacturer horsepower tables, lubrication guidance and service factors for final chain selection.
Method & assumptions
- Roller-chain sprocket pitch diameter is calculated as
PD = p / sin(180°/N). - Chain speed uses polygon travel per revolution,
N x p, not outside diameter or tip circumference. - The calculator does not derive outside diameter, tooth root diameter, roller seating geometry, wear allowance or chain-series horsepower rating.