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).
Worked example
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.
Related calculators
- Pulley Calculator — Pulley ratio, driven RPM and belt speed from pulley diameters.
- Belt Length Calculator — Two-pulley belt length and wrap angle from center distance and diameters.
- Chain Length Calculator — Roller-chain length in links and mm from sprocket teeth and center distance.
- Bearing Life (L10) Calculator — Basic L10 rating life in revolutions and hours from load, speed and rating.