Enter the sprocket ratio and the input velocity into the calculator to determine the output velocity.

## Sprocket Speed Formula

The following formula is used to calculate a sprocket speed with a given sprocket ratio and output speed.

V2 = V1 / (T1/T2)

• Where V2 is the output velocity
• V1 is the input velocity
• T1/T2 is the sprocket ratio. The sprocket ratio is typically expressed as 1:X where 1 is T1 and X is T2

## Sprocket Speed Definition

A sprocket speed is defined as an output velocity, typically represented in RPM, of a bike or gear system that has a given input velocity and sprocket ratio.

## Example Problem

How to calculate a sprocket speed?

1. First, determine the sprocket ratio.

For this example problem, we will be looking at a bike with a sprocket ratio of 100 teeth in the rear and 20 teeth in the front. This is simplified to 20:100 = 1:5.

2. Next, determine the input velocity.

On this particular bike, the biker is able to push the petals to a velocity of 50 RPM (rotations per minute).

3. Finally, calculate the output velocity.

Using the sprocket ratio and input velocity from steps 1 and 2 above, the output velocity can be calculated using the formula V2=V1/(T1/T2) = 50/(1/5) = 250 RPM.

## FAQ

How does sprocket size affect speed?

A sprocket size is directly proportional to the output speed. That is the greater the ratio of the sprocket i.e. 1:10, the greater the output speed with a given input. This can be seen in the formula T1/T2 = V1/V2, where T1/T2 is the sprocket ratio.

Which sprocket is fast?

A 1:10 sprocket will be faster than a 1:5 sprocket when the input velocity stays constant. In real-world cases, keeping the same input velocity with changes in sprocket ratio is more difficult because more force is required to keep the same velocity input.

Can sprockets reduce speed?

Just as sprockets can increase speeds as mentioned above, they can also reduce speeds if the number of teeth in the input is less than the number of teeth in the output.