Sprocket ratio calculator

Enter the tooth counts and driving speed to calculate reduction ratio and theoretical driven sprocket RPM.

Formularatio = driven teeth ÷ driving teeth; driven RPM = driving RPM ÷ ratio

The larger driven sprocket turns more slowly

A 15-tooth driving sprocket and 45-tooth driven sprocket produce a 3:1 reduction. At 3,000 driving RPM, the driven sprocket turns at 1,000 RPM.

The result excludes the rest of the system

Tire diameter, other transmission stages, chain pitch, center distance, load, losses and component speed ratings are outside this calculation.

Why one front tooth is worth about three at the back

From a standard 15 and 45, dropping the front sprocket to 14 gives a ratio of 3.21, a 7.1% change. Going the other way and fitting a 48-tooth rear gives 3.20, 6.7%. One tooth at the front is close to three at the back, because the front sprocket has so few teeth that each one is a large fraction of the total.

That makes the front sprocket the cheap, coarse adjustment and the rear the fine one. It also explains why a single front tooth can be too much: the same change that transforms a bike off the line drops top-gear cruising speed and raises revs on the motorway by the same 7%.

Frequently asked questions

Which sprocket should I change for more acceleration?

Either a smaller front or a larger rear shortens the gearing, and both trade top speed for pull. A tooth off the front is the cheapest experiment and the biggest single step. Two or three teeth on the rear is the finer adjustment and keeps the chain run closer to standard.

Does changing sprockets upset the speedometer?

On most bikes yes, because the sensor reads from the gearbox output rather than the wheel. Shorter gearing then makes the speedometer read high. Where the sensor sits on the wheel or in the ABS ring, sprockets make no difference. Check which yours has before assuming the error.

Will I need a different chain?

Often. A larger rear sprocket needs a longer chain, usually two links per couple of teeth, and even where the length works the adjusters may run out of travel. Replace the chain and both sprockets together as a set when they are worn: a new chain on old sprockets wears out quickly.

What do 520, 525 and 530 mean?

They are chain sizes. The first digit gives the pitch in eighths of an inch, so all three are 5/8-inch pitch, and the rest describes the roller width. A 520 is narrower and lighter than a 530 and is a common weight saving, but the sprockets must match the chain, and the chain must be rated for the power going through it.

Does this work for anything other than motorcycles?

Yes, any chain drive with two sprockets: go-karts, minibikes, industrial reduction stages, bicycles if you enter chainring and cog teeth. The arithmetic only cares about tooth counts and the input speed. What it does not know is the rating of your chain, sprockets and bearings at the resulting speed.