Gearing in Inches On Video

In previous posts I have alluded to bicycle "gearing inches" and now I can give you a couple examples of the process of calculating (or describing) gear ratios.

First we take a tape measure and determine the outer circumference of the tire. You can do this with math but it's more accurate to measure. I'm not going to bother about the millimeters (you can if you wish). Tape on the tire to show where we are measuring. Let's assume the middle of the tape is on zero.

We then roll the bike forward along the tape measure until our marker shows 82 5/8" (210 cm). That's the circumference of the bike wheel, or the distance it travels for each revolution of the wheel. 

This distance is INDEPENDENT of the gearing on the bike. One wheel's revolution ON MY BIKE is always the same distance traveled unless I have a flat tire. Your bike will vary somewhat, as your wheels and tires are different from mine.

Now we can think about gearing. To measure the range of gearing on my Paramount, we put the bike in the lowest gear. Large 26-tooth cog in the rear and smallest 42-tooth chainring in the front.

We stand the bike up and move it along the tape measure until the crank has turned one complete revolution. To measure precisely you should also have a plumb line showing the exact point at which to measure both the crank and the wheel. So forgive me if we are off a smidge.



You can line the crank arm up with the seat post or try to make it vertical. Then check the distance traveled on the tape measure. Most of the time, the wheel position will NOT be where the duct tape mark is located. Here we've gone about 136 inches or 345 cm.

Repeating the procedure now, we move the chain to the smallest 13-tooth cog in the rear and the largest 52-tooth chainring in the front.

We roll the bike along the tape measure again, turning the crank one time.



The distance traveled in one crank revolution is equal to the length of my 24 foot (288") tape measure PLUS 43 inches, for approximately 331 inches or 841 cm.

Notice the tape on the tire? The wheel revolved about 4 times. The large chainring has 52 teeth, and the smallest cog has 13 teeth (1/4th the number). So one revolution of the pedals means 4 revolutions of the little cog AND the big wheel to which it's firmly attached. The distance traveled may vary from bike to bike with tire variations, but with 4:1 gearing, the revolutions per turn stay the same.

Now what have we learned?

In English standard units

low gear 42:26 = 1.6 multiply by a nominal 27" (actual 26.3" for my bike) to get a "42 inch low gear"
high gear 52:13 = 4.0 multiply by 26.3 to get a "105 inch top gear"

These numbers don't give us the distance traveled, they only give us a relative comparison of the gear ratios. To get distance traveled, we have to multiply by pi or 3.14.

42 x 3.14 = 135 inches traveled in low gear
108 x 3.14 = 330 inches traveled in high gear

In metric units 

Low gear = 3.31 meters per revolution also called meters of development
Top gear = 8.41 meters per revolution

Yes, this is all academic and a nuisance. But it's convention in the bicycle world. It doesn't help you to get up a hill but it does allow you to spec a bike the way you want it.