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# Explanation of Bicycle Gear-to-Sprocket Ratios

by
Claire Lunardoni
Claire Lunardoni has written for LIVESTRONG.COM and eHow since 2009. She is an American College of Sports Medicine-certified personal trainer and a fitness instructor who trains endurance athletes for IntEnd: Integrated Endurance in San Francisco. She holds a Bachelor of Arts in language studies from University of California in Santa Cruz.
A bicycle chain and sprocket. Photo Credit: TeerawatWinyarat/iStock/Getty Images

Most bicycles have multiple gears that make pedaling easier or harder, depending on the front and back gear combinations. The large gears in the front, or chainrings, make big changes in pressure needed to turn the pedals; the cluster of gears in the back make fine gearing adjustments. The skill of bicycle riding lies in a combination of leg strength, to power you through the higher gears, and finding the right gear combination and pedaling cadence to reach your destination as quickly and efficiently as possible.

## The Origins of Gearing

In Victorian times, bicycle pedals were affixed directly to the front wheel; the bike covered a distance equivalent to the wheel’s circumference with each pedal stroke. The only way to go faster was to pedal faster or make a bigger wheel, which led to bikes with oversized front wheels. In 1905, a cycling advocate popularly known as Velocio used two gears of varying sizes to adjust the distance that his wheel traveled per pedal stroke, which also changed the pressure needed to turn the pedals. According to cycling historian Ken Kefir, a woman on Velocio’s geared bike beat a champion racer on a high-wheeler in an uphill race.

## Explanation

Using the example of a bike with a gear ratio of 50 to 25 -- in which the front chainring has 50 teeth and the rear sprocket has 25 teeth -- you can calculate the number of wheel revolutions per pedal stroke by dividing the number of front teeth by the number of rear teeth. With one full revolution of the pedals, the chain moves over 50 teeth in the front. The chain then transfers that power to the rear wheel, where the 25-tooth cog must spin twice to pass the same number of chain links. If the rear wheel has a diameter of roughly 700 cm -- the size of a standard road bike wheel -- then you will travel 4.2 meters or twice the wheel’s circumference of 2.1 meters with each pedal stroke.

Your bike’s actual speed depends on both the gear ratio and the rate at which the pedals are turning. You achieve the same speed by pedaling a 54-to-11 gearing at 40 rpm as a 36-to-25 gearing at 136 rpm. The heavy resistance in the former gear and the fast pedal turnover in the latter will tire you out quickly. In an article in “European Journal of Applied Physiology,” exercise physiologists found that professional cyclists preferred a high cadence to heavy gears on long mountain passes.

## Uses

Gearing is particularly important for touring cyclists and single-speed riders. Cyclotourists need a very low gear to push their heavy bike loads up steep hills without exhausting their legs. Single-speed riders need a gear ratio that allows them to both push uphill and maintain a decent pace on flat roads.

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