How to use this calculator
- Enter the tooth counts. Enter the driver (input) and driven (output) tooth counts. The ratio is driven ÷ driver.
- Enter the driver speed. Enter the driver-sprocket RPM.
- Enter the chain pitch. Enter the roller-chain pitch (ANSI 40 = 12.7 mm / 1/2 in).
- Read the results. Read the sprocket ratio, driven RPM, chain speed and the two pitch diameters.
How it works
The sprocket ratio is the driven tooth count divided by the driver tooth count:
i = N₂ / N₁
A ratio above 1:1 is a reduction — the output turns slower than the
input but with proportionally more torque. The driven speed is
n₂ = n₁ · N₁ / N₂.
The chain travels along the pitch circle at the pitch-line speed v = N₁ · p · n₁ / 60000 (pitch p in mm, n₁ in
RPM, result in m/s). Each sprocket's pitch diameter — the circle the
chain rollers ride on — is PD = p / sin(180° / N).
After the ratio is set, use the chain length calculator to choose a link count and center distance. If power is known, the roller chain tension calculator converts pitch, teeth, power and RPM into effective tension, design tension and allowable margin. That pull can then be checked as shaft radial load in the overhung load calculator. For general gear or vehicle-speed ratios, use the gear ratio calculator.
Worked example
Verified against the live calculator
A 15-tooth driver sprocket driving a 45-tooth driven sprocket is a
3:1 reduction. At 1,000 RPM in, the output turns about 333 RPM. With
ANSI 40 chain (12.7 mm pitch) the chain speed is
15 × 12.7 × 1000 / 60000 ≈ 3.18 m/s, and the pitch diameters are
≈ 61 mm (driver) and ≈ 182 mm (driven). Those are
the numbers the calculator shows for these inputs.
Frequently asked questions
How do I calculate the sprocket ratio and RPM?
The sprocket ratio is the driven (output) tooth count divided by the driver (input) tooth count: ratio = N₂ / N₁. The driven speed is n₂ = n₁ · N₁ / N₂. For example 45 driven teeth over 15 driver teeth is a 3:1 reduction, so 1,000 RPM in turns the output at about 333 RPM.
What sprocket ratio do I need for more top speed?
For more top speed, lower the ratio: use a larger front (driver) sprocket or a smaller rear (driven) sprocket. That turns the wheel faster per engine revolution. The trade is less torque, so acceleration drops. A smaller front / larger rear sprocket does the opposite — more torque and quicker acceleration, less top speed.
What is the chain or pitch-line speed?
It is how fast the chain travels along the sprocket pitch circle: v = N₁ · p · n₁ / 60000, with the pitch p in mm and n₁ in RPM, giving metres per second. It governs wear and lubrication — most roller chain is rated to roughly 5–8 m/s before special provisions are needed.
How do I calculate a sprocket pitch diameter?
PD = p / sin(180° / N), where p is the chain pitch and N the tooth count. The pitch diameter is the circle the chain rollers sit on — it is theoretical and slightly smaller than the tip (outside) diameter you measure across the teeth.
What are the common ANSI roller-chain pitches?
ANSI 40 (#40) is 12.7 mm (1/2 in), the most common general-purpose size. ANSI 35 is 9.525 mm (3/8 in), ANSI 50 is 15.875 mm (5/8 in), ANSI 60 is 19.05 mm (3/4 in), and ANSI 80 is 25.4 mm (1 in). Bicycle/kart chain is typically #35, #40 or #41.
Does this work in metric and imperial?
Yes — enter the chain pitch in mm or inches and read pitch diameters in mm or inches and chain speed in m/s or ft/min. Toggle SI/Imperial in the header.
Method & assumptions
- No chain slip — a roller chain engages the teeth positively, so the speed ratio is exactly N₁/N₂.
- Pitch diameter
PD = p / sin(180°/N)is theoretical (the pitch circle), slightly less than the measured tip diameter. - Keep at least ~17 teeth on the small sprocket for smooth running and good chain life, then verify chain length and pull with the linked chain tools.