# Formula to calculate Single Speed Chain Length from Chainring Size, Cog Size, and Chainstay Length

I've seen formulas to calculate chain length for multi-speed bikes, but I need something for single speed.

Example: 42T Chainring 17T Cog 406mm (16") Chainstay Length

The answer in this case should come to ~94L.

• I have made a strikingly question before, although I wanted to find chainstay length while you want to find number of chain links. Should this count as a duplicate? bicycles.stackexchange.com/q/8608/2355 May 7, 2013 at 3:28
• And if you want a still more technical explanation: math.stackexchange.com/q/123361/27435 May 7, 2013 at 3:30
• And, just in case you want to find the "magic gear" for a vertical dropout bike, I think it's risky, since minor variations on the parts themselves can make the chain become too tight or too slacky... Not to mention the ideal length will quickly vanish as the chain wears out. (well, just a thought) May 7, 2013 at 3:34
• I did see the other similar question but as you mentioned it would have to be re-worked to solve for chain length. I'm not competent enough to understand how to do that unfortunately! May 7, 2013 at 4:13
• The formula I would use, to get the practical length (i.e. the one that is known to work) - wrap a chain around the cogs and match up one end to the link that it meets when tight, count the links.... Or were you wanting the theoretical value. May 8, 2013 at 4:32