Magic gear calculator
Enter your frame's chainstay length and find every chainring and cog pair that fits it with a whole number of chain links: a tight chain with no tensioner and no sliding dropouts. For singlespeed conversions, fixed gear, BMX and track.
Offset is how far the axle would move for that chain to fit exactly: minus means the chain is that much short (tight), plus that much slack. Riders find magic gears go slack as the chain wears, so a slightly tight fit lasts longer. Check with real parts before you cut a chain.
Why some gears are magic
A chain only comes in whole links, usually an even number. On a frame with a fixed chainstay, most chainring and cog pairs need a chain that falls between two lengths: one is too short to fit, the next hangs slack. A magic pair needs almost exactly a whole chain.
For every pair in your ranges, the calculator works out the chain length at your chainstay with the Sprocket Designer's exact model: pitch diameters of 12.7 mm ÷ sin(180°/teeth), straight spans tangent to both, and the chain following each sprocket's pitch polygon. It then finds the nearest allowed chain on each side and the exact centre distance that chain needs, and lists the pairs where that is within your limit of the chainstay.
The result is only as good as your measurement, so measure the frame itself, and expect a few tenths of a millimetre from chain and sprocket tolerances.
Need a size nobody sells? Magic pairs often call for an odd chainring or cog. Every result opens in the Sprocket Designer, which makes a chainring or single-speed sprocket in any tooth count, to print or machine.
Magic gear questions
What is a magic gear (magic ratio)?
A chainring and cog pair that fits a frame's fixed chainstay length with a whole number of chain links, so the chain is tight without a tensioner or sliding dropouts. Riders use them on singlespeed conversions of geared frames, frames with vertical dropouts, and some BMX and track builds.
How do I measure my chainstay length?
Measure from the centre of the bottom bracket spindle to the centre of the rear axle, in a straight line, as precisely as you can: a millimetre matters here. Riders on singlespeed forums note that a frame's published chainstay length is rarely precise enough, so measure the frame itself.
How close does a magic gear need to be?
The offset is how far the axle would have to move for the chain to fit exactly. A negative offset means the chain is slightly short, a positive one slightly slack. Riders report that a magic gear works for a while and then goes slack as the chain wears, so a combination that is slightly tight has more life. Check it with real parts, and keep a tensioner or half-link chain as a fallback.
What does a half-link chain change?
A half-link chain can be any whole number of links, not only even, so twice as many lengths fit and more combinations come out magic. Tick 'Half-link chain' to include odd lengths.
What if the magic combination needs a size I can't buy?
Chainrings and cogs are only sold in some sizes. The Sprocket Designer makes a chainring or single-speed sprocket in any tooth count, to print or machine: every result here opens in it.
Make the chainring or cog
Chainrings on any BCD, single-speed sprockets and BMX drivers, in any tooth count, as STL, STEP, DXF or SVG.