# Gear inches

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**Gear inches** is a system that assigns numerical measurements to bicycle gear ratios, to indicate how low or high a gear is.

Gear inches has no current physical significance; it corresponds to the diameter in inches of the main wheel of an old-fashioned penny-farthing bicycle with equivalent gearing. An alternative gearing measurement is **metres of development**, which corresponds to the distance in metres traveled by a bicycle for one rotation of the pedals. To convert from gear inches to metres of development, multiply by 0.08 (more exactly: 0.0798, or precisely: 0.0254π).

## OriginEdit

With old-fashioned "penny-farthing" bicycles, the crankarms were directly attached to the large drive wheel. One turn of the pedals moved the bicycle a distance equal to the circumference of the wheel. The larger the wheel, the farther the bicycle went for each turn of the pedals. The gear-inch system is a holdover from the days of the boneshakers, when wheel diameter determined the bike's "gearing" and was the key measurement on the bike.

Riding in a high gear on a modern bicycle is mechanically equivalent to riding a high-wheeler with a large wheel, where a low gear on a modern bicycle is the equivalent of a smaller wheel on a high-wheeler.

## RatioEdit

Gear inches express gear ratios in terms of the diameter of an equivalent directly-driven wheel, and are calculated as follows:

### DiameterEdit

Diameter of drive wheel in inches × number of teeth in front chainring / number of teeth in rear cog.

gi = Gear Inches

dwd = Drive Wheel Diameter

fct = Front Chainring Teeth

rct = Rear Cog Teeth

For example, suppose the drive wheel is actually 26 inches in diameter. If the front chainring and rear cog have equal numbers of teeth, one turn of the pedals produces exactly one turn of the drive wheel, just as if the pedals were directly driving the drive wheel. That combination of gears and wheel is said to be "26 gear inches." If the front chainring has 48 teeth and the rear cog has 24 teeth, then each turn of the pedals produces two turns of the rear wheel. This is equivalent to doubling the size of the drive wheel; that is, it is like a directly-driven bicycle with a 52-inch wheel. That gear is said to be "52 gear inches."

A bicycle with a 26-inch wheel, a 48-tooth chainring, and a cassette with gears ranging from 11 to 34 teeth has a lowest gear of 26 × 48 / 34 = 36.7 gear inches and a highest gear of 26 × 48 / 11 = 113 gear inches.

For bicycles with 700c wheels, most cyclists quote gear inches based on a nominal wheel diameter of 27 inches, corresponding to the old British tire size of 27 x 1¼" (ETRTO 630). This means that a 48/18 setup is usually considered to be 72". Strictly speaking, the rolling diameter of a 700c wheel is significantly lower, at about 26" for a 20mm tire or 26.3" for a 23mm tire. This means that the true gear on a 700c wheel can be as low as 69", which is the equivalent of only 46/18 on an actual 27" wheel, and can be the source of some confusion when comparing gears unless it is clear whether gear inches have been calculated using the actual wheel size or a conventionalised 27".

The accurate way of calculating true wheel diameter is to take the rim diameter and add twice the tyre diameter. For example, 700c x 23mm. 700c wheels have a rim diameter of 622mm. Add 46mm (2x tyre diameter of 23mm). 622mm + 46mm = 668mm which is equal to 26.3 inches (rounded to 1 decimal place). 26 inch mountain bicycle wheels have a rim diameter of 559mm.

One could also calculate "gear centimetres," but in practice this is not done. An equivalent system customarily used by continental European cyclists is "**metres of development**", and measures the distance travelled with each turn of the crank. That is, metres of development is calculated as:

### CircumferenceEdit

Circumference of drive wheel in metres × number of teeth in front chainring / number of teeth in rear cog.

Thus gear inches and development differ by a factor of π, and English/metric conversion. To convert from gear inches to metres of development, multiply by 0.08 (more exactly: 0.0798, or precisely: 0.0254π). Some bicycles incorporate internally geared hubs, or other components that change the gear ratio and must be taken into account when calculating gearing.

## Gain ratioEdit

Both "gear inches" and "metres of development" are concerned with the distance travelled per **turn** of the pedals, and are ultimately ways of indicating the mechanical advantage of the drivetrain, but neither of them take into account the length of the crankarm, which can vary from bike to bike. The crankarm is a lever arm. If two bicycles have different crank lengths but are otherwise identical, a longer lever arm gives a greater mechanical advantage. To take this into account, Sheldon Brown proposed a gear measurement system called "gain ratio," which is calculated by the distance travelled by the bike divided by the distance travelled by the pedals during one turn of the crank. He argued that it also has the advantage of being a pure number (with no units of measure); the calculation gives the same value whether it is carried out in inches or metres.

## See alsoEdit

## External linksEdit

- Sheldon Brown's gear calculator Online calculator for gear inches, metres development, and gain ratio
- BikeCAD has a graphical means of displaying gear inches as described here
- Gain Ratios—A New Way to Designate Bicycle Gears
- Gain and Watts Calculator
- Interactive Gear ChartAnother gear chart which can be customized with just the cogs and chainrings you want. Outputs gear inches, rollout (development), speed for cadence and other options.