's Forum Archives - Components

Archive Home >> Components(1 2 3 4 5 6 7 8 9 10 )

Gear Ratios --> what is the math behind it?(7 posts)

Gear Ratios --> what is the math behind it?jimsawino
Feb 12, 2003 2:20 PM
Currently, I have a 39/53 crank and a 12-23 cassette (dura ace, if that matters). I think the gears are 12, 13, 14, 15, 16, 17, 19, 21, 23 (9-speed). What is the formula to find the ratio? Thanks in advance.
re: Gear Ratios --> what is the math behind it?DougSloan
Feb 12, 2003 2:23 PM
Here's a spreadsheet that is easier than calculating:

# front teeth/# rear teeth x tire diameter in inches = "gear inches"

"ratio" is simply front divided rear
circumference instead of diameter? Or measure your rolloutSpunout
Feb 13, 2003 4:19 AM
I mostly use ratios, that is front/rear. If you switch wheel sizes alot, the development (rollout) will be different, so there is that to think about.
You might find this formula useful as well...joekm
Feb 13, 2003 5:44 AM
If you have a typical 700x23 tire then, according to the documentation that came with my bike computer, that's a 2105 cm circumference. So, with a little playing with numbers, you can get this formula.

1 mph = 12.82 rpms at the rear wheel


Speed X 12.82 X (# teeth in chainwheel)/(# teeth in cog) = CADENCE

...adapt as req'd if you're not running a 700x23 tire.
Correction to above....joekm
Feb 13, 2003 5:47 AM
Sorry about that, it's

(# teeth in COG)/(# teeth in CHAINWHEEL)

....I really should refrain from math until after I've had my morning coffee... ;)
Make it easy.MR_GRUMPY
Feb 13, 2003 8:49 AM
Use this: Front chainwheel/ Rear cog X 27 = Gear inches. An example would be: 53 X 12 = 119.3 Gear inches. Another example would be: 39 X 23 = 45.8 Gear inches. If you have a Mtn bike, just use 26 instead of 27. Yes, I know that some tires are fatter than others, but the difference is ignored in calculations.
re: Gear Ratios --> what is the math behind it?jimsawino
Feb 14, 2003 7:47 PM
all this infor has been very helpful to me. i like having more to think about than the girl on my stem when i'm on the trainer (i live in ohio - for now). thank you all.