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Sprockets
There is not much to say about BMX sprockets. Small and thick for Street, tiny and thinner for Flatland (starting from 16T) pretty much sums it up. The bigger the sprocket the harder it is to accelerate, but the faster is your maximum speed.
Sprockets FAQSprockets stuff
Sprockets FAQ
Axle diameter
Almost every BMX Crank has a 19mm or 22mm axle. You should take a look at the diameter of the BMX sprocket. A lot of sprockets come with a corresponding spacer.
Spline Drive
BMX sprockets with Spline Drive require no sprocket bolt. Its built-in steel insert has 48T which fits only on 19mm spindles with 48T. That allows using smaller BMX sprockets, which fit precisely onto your BMX crank.