I have a friend who has a 'trick'. Give him any date and he'll tell you what day of the week it is... For example if you say to him 5th of March 2001, he'll reply "Wednesday"... That example is probably not correct so don't bag me out for getting it wrong!!!

He says its easy and just a mathermatical formula...

Anyway, I was just wondering if anyone knows the mathematical fomula for gear inches. So if someone were to say "48/18" I could reply with a smartass "72". Or "50/15" - "92".

Sheldon Brown has an online calculator. I could work it out on a calculator. But I want to be able to do it mentally... Does some clever b*****d know this? It'd have to be real simple....

(Chainring/Cog) * 27 will get you close enough for road wheels.

Thats the normal formula. Not easy to do mentally though.... But thanks anyway

If you need anything simpler that that, you'll have to carry a calculator or a friend with an operating brain.
The actual formula is way more complicated, taking into account rim size, tyre and crank arm size. You can't go any simpler than Chainring/cog multiplied by something.

If you want to know how a modification changes the feel of your own bike, that's simpler. E.g. if you put on a 48 chainring instead of the 44 you have now, the gear will get 48/44 your current one, i.e. 9% higher. 18 instead of 16 cog=> 16/18, i.e. 11% lower gear

If you want to mess around with both chainring and cog, then memorize the ratio of your current combo. 44/16 is 2.75. If you go 55/20, that's also 2.75=> same gear. 48/14=3.43, which is wicked high, of course.

Just tire diameter and ratio. Crank arm size is part of Sheldon's exclusive Gain Ratio formula.

on a somewhat related note, are there opinions about running larger vs smaller chainrings/cogs in the same ratio? such as a 48/18=2.667=72 inches vs a 45/17=2.65= 71.5 inches. Roughly the same, but does the larger cog in the rear (in the first example) give you better torque or is it offset by the smaller chainring in the front in the second example?

Yeah. I thought it was the other way round.

The larger set will give you a smoother, and slightly more efficient drivetrain. (though the increase is efficiency won't be noticible). You will also have better drivetrain wear with the larger set. The smaller set will be lighter and be harder to fine tune as dropping one tooth in the rear will be a larger change than dropping one tooth off the larger cog.

I have a very nice Casio scientific calculator strapped to my bars. I can work out any gear formula while out on a ride.

I dont think theres an easy way. At the track, I see the record-holding coaches reach for their gear inch chart when they need to know.

I might have to do it the old 'repetition arithmetic' way. You know, saying out loud 2x2 is 4, 2x4 is 8 etc.

Rear cog 11 to 20, chainring 46 to 50. Thats only 50 numbers to memorise... Shouldn't be too hard... Hmmmm.

Although the brain aint what is used to be at school...

just invest in a quality timepiece. like mine.

If you're just wanting to impress people, you could just memorize the most common ratios per wheel size. Just pretend like you're doing calculations in your head