Bicycle gearing is the aspect of a bicycle drivetrain that determines the relation between the cadence, the rate at which the rider pedals, and the rate at which the drive wheel turns.
On some bicycles there is only one gear and, therefore, the gear ratio is fixed, but most modern bicycles have multiple gears and thus multiple gear ratios. A shifting mechanism allows selection of the appropriate gear ratio for efficiency or comfort under the prevailing circumstances: for example, it may be comfortable to use a high gear when cycling downhill, a medium gear when cycling on a flat road, and a low gear when cycling uphill. Different gear ratios and gear ranges are appropriate for different people and styles of cycling.
A cyclist's legs produce power optimally within a narrow pedalling speed range, or cadence. Gearing can be optimized to use this narrow range as efficiently as possible. As in other types of transmissions, the gear ratio is closely related to the mechanical advantage of the drivetrain of the bicycle. On single-speed bicycles and multi-speed bicycles using derailleur gears, the gear ratio depends on the ratio of the number of teeth on the crankset to the number of teeth on the rear sprocket (cogset). For bicycles equipped with hub gears, the gear ratio also depends on the internal planetary gears within the hub. For a shaft-driven bicycle the gear ratio depends on the bevel gears used at each end of the shaft.
For a bicycle to travel at the same speed, using a lower gear (larger mechanical advantage) requires the rider to pedal at a faster cadence, but with less force. Conversely, a higher gear (smaller mechanical advantage) provides a higher speed for a given cadence, but requires the rider to exert greater force or stand while pedalling. Different cyclists may have different preferences for cadence, riding position, and pedalling force. Prolonged exertion of too much force in too high a gear at too low a cadence can increase the chance of knee damage; cadence above 100 rpm becomes less effective after short bursts, as during a sprint.
Measuring gear ratios
Methods
There are at least four different methods for measuring gear ratios: gear inches, metres of development (roll-out), gain ratio, and quoting the number of teeth on the front and rear sprockets respectively. The first three methods result in each possible gear ratio being represented by a single number which allows the gearing of any bicycles to be compared regardless of drive wheel diameter; the numbers produced by different methods are not comparable, but for each method the larger the number the higher the gear. The third method, gain ratio, also takes the length of the crankarm into account, which can vary from bike to bike. The fourth method uses two numbers and is only useful in comparing bicycles with the same drive wheel diameter. In the case of road bikes, this is usually around 670 mm. A 700c "standard" wheel has a 622 mm rim diameter. The final wheel diameter depends on the specific tire but will be approximately 622 mm plus twice the tire width.
Front/rear measurement only considers the sizes of a chainring and a rear sprocket. Gear inches and metres of development also take the size of the rear wheel into account. Gain ratio goes further and also takes the length of a pedal crankarm into account.
Gear inches and metres of development are closely related: to convert from gear inches to metres of development, multiply by 0.08 (more exactly: 0.0798, or precisely: 0.0254π).
The methods of calculation which follow assume that any hub gear is in direct drive. Multiplication by a further factor is needed to allow for any other selected hub gear ratio (many online gear calculators have these factors built in for various popular hub gears). Gear inches = Diameter of drive wheel in inches × (number of teeth in front chainring / number of teeth in rear sprocket). Normally rounded to nearest whole number. Metres of development = Circumference of drive wheel in metres × (number of teeth in front chainring / number of teeth in rear sprocket). Gain ratio = (Radius of drive wheel / length of pedal crank) × (number of teeth in front chainring / number of teeth in rear sprocket). Measure radius and length in same units.
Both metres of development and gain ratios are normally rounded to one decimal place.