Chain Sprocket Ratio and Chain Length Calculator

How is the sprocket ratio calculated?

In a chain drive the ratio is the ratio of tooth counts: i = z₂ / z₁. The driven speed is n₂ = n₁ / i. Because the chain engages the teeth there is no slip and the ratio is exact. The larger sprocket turns more slowly and multiplies torque by the same factor.

Chain speed and sprocket diameter

For each turn of the sprocket the chain advances by as many links as there are teeth. The speed is v = z₁ × p × n₁, where p is the pitch and n₁ is in revolutions per second. The pitch diameter of a sprocket follows from d = p / sin(180° / z).

Chain length

Chain length is specified in links, not millimetres: X = 2C / p + (z₁ + z₂) / 2 + ((z₂ − z₁) / 2π)² × p / C. The result is rounded up to an even number, because an odd number of links needs an offset link.

Example

Sprockets with 19 and 57 teeth, a 12.7 mm pitch chain and a centre distance of 500 mm give a ratio of 3. With the driver at 300 rpm the output runs at 100 rpm and the chain speed is 1.21 m/s. The chain length works out at 117.7 links, so 118 links are chosen, which is 1498.6 mm.

Limits

The tool gives ratio, speed and length only. The power a chain can carry depends on pitch, speed, the tooth count of the small sprocket and lubrication, and is selected from the power tables in the manufacturer's catalogue. Fewer teeth on the small sprocket mean more polygon effect and wear.