Bicycles/Maintenance and Repair/Freewheels and Cassettes

A typical nine-speed rear wheel. The large bulge at one end of the hub identifies it as a freehub. This, and the size of the cluster means that the cogs are supplied as a cassette.

A cassette cog-set and its splined (grooved) freehub. The splines allow alignment of the cogs and prevent their rotation in use. The ratchet is in the wheel's hub.

A freewheel cog-set and its threaded hub. The freewheel itself contains both ratchet and cogs. Individual cogs are threaded onto the freewheel itself and the entire freewheel assembly is threaded onto the hub.

General

The freewheel is the ratchet device on the rear wheel that makes it possible to roll without pedaling, for example, when free-wheeling down a hill. It operates whenever the wheels are going faster than the drive-force, in this case the pedals and chain. The term is also used to describe a bicycle component that combines both a ratchet and a cog-set in one single screw-on assembly, and this is the most commonly used meaning. The alternative way of installing a cog-set is to use a cassette, a stack of cogs that slides onto a splined hub. Whether a freewheel or a cassette is used on the rear hub of the bike, there is always a ratchet; in the case of a freewheel assembly the ratchet is unscrewed with the cogs, whereas a cassette is merely a stack of cogs, and the ratchet is within the freehub of the wheel. Cog pitch (here is means inter- cog center-to-center spacing) is the main consideration for shifting and apart from the restricted choice of freewheels, it is unimportant to the derailleur whether a freewheel or a cassette is installed, provided that the spacing between the cogs is right.

Bikes without gear-changing exist, so-called fixed-gear bikes or fixies. They have one chain-ring and one rear cog. Although such bikes are not technically prevented from having a ratchet device, they usually have none, so that the rider's legs will be forced to rotate whenever the bike is moving. Some new riders of such bikes can find the experience disturbing.

The threaded hub of the freewheel installation is clearly different from the splined freehub of the cassette installation and the cog-set of one type cannot be installed onto the other. When an upgrade from freewheels to cassettes is to be made, it is most convenient to do so by changing the rear wheel for one with a freehub and cassette already installed. Examples of a freehub and of a threaded hub can be seen clearly in the adjacent photographs.

Both freewheels and cassettes exist in a variety of cog combinations, and because chains are all half-inch spaced, cogs can be defined entirely by their numbers of teeth. For example, an 11T cog has eleven teeth, and a cog-set with a range of 11T-30T might have say, seven cogs, the smallest having eleven teeth and the largest thirty. Because cog-sets have been in use for a long time, the most useful sets have been identified by code letters, for example, the above set is designated 'am'.

For those who need more than seven rear cogs, a bike with a cassette becomes the choice. This is because bikes are rarely made with freewheels of more than seven cogs. Larger numbers of gears can be obtained even with a seven speed freewheel or cassette by simply having more front chainrings. For example, the combination of three front chainrings and seven rear sprockets provides 21 gear combinations (3 X 7), and enjoys the wider working tolerances of seven speed shifting at the rear.

This page explains how to remove and fit cassettes and freewheels and provides links for further information on that subject. An introduction to the principles of indexed shifting is given, and notes on the complexity of gear-shifting standards is provided with the help of tables.

Cog-set Standards.

Complexity

The hub of a rear wheel has an extension on it, and this is threaded or splined to fit either a freewheel or a cassette respectively. Extensions differ in length, according to the number of cogs to be installed, but to maintain reasonable chain alignment and reduce the stresses on the hub, there is a limit to the extension that can be considered. So, when a number of cogs greater than say, seven, is crammed into a set, the teeth and spacers need to be made thinner. In this way the space or pitch between the cogs can be reduced. (See the table in the drop box below for a summary on cog-pitch.) A narrower chain is also needed for a narrower cog-pitch.

Although cassette cogs and most freewheel cogs can be replaced individually, doing so favors cassettes. Freewheel cogs need two chain-whips to remove them from the cluster after the freewheel itself if free of its hub, one to unscrew the cog and another to prevent the freewheel from rotating; anyway, individual replacement cogs for freewheels are now hard to find. Freewheels rarely exist beyond 7-speeds, while cassettes exist in up to 11-speeds. Cassette cogs are easier to remove, are abundant in supply, and offer the greatest scope for modification.

Cog pitch (here means inter-cog spacing), cog thickness, and spacer thickness differ greatly for the various bike types, (see Sheldon Brown's Cribsheet on Spacing for detailed lists), not only for different sizes of cog-sets, but between different manufacturers for the same size of cog-set. As a result, the derailleurs and shifters used differ greatly as well. When the different shift ratios of derailleurs, cable-pull-lengths of shifters, and the pitch (inter-cog spacing) of cog-sets are considered together, it becomes clear that arbitrarily selected drive components will hardly ever work well together.

Examples of the various manufacturers' cog-pitches and the expected results of mixing drive gear can be found in the drop-box below. For the full description upon which these notes were based, see CTC on Rear Shifting. In the way of relief, some notes on the more common ground are given in the next section.

Pitch for Rear Cog-sets and Predicted Shifts for Mixed Drive-gear The tables give an introduction to the complexity of drive gear. Detailed lists for particular cog-sets are best found from manufacturers, or possibly on the late Sheldon Brown's page, Cribsheet on Spacings. Cassette Sprocket Pitch and Other Data by Size and Manufacturer Credit due to CTC, the UK's national cyclists' organisation. Note: The term pitch in these tables means inter-cog center-to-center spacing. Cassette Sprocket Pitch Code Sprocket Thickness Spacer Thickness Stack Width   mm.   mm. mm. mm. All 5 and 6-speed 5 - 5.50 S5/6     23.2 - 29.5 All standard 7-speed 5.00 S7     31.5 - 32.4 Shimano Hyperglide 7-speed 5.00 S7 1.85. 3.15 31.9 Campagnolo 8-speed 5.00 C8 1.9 3.1 36.9 Shimano 8-speed 4.80 S8 1.8 3.00 35.4 SRAM 8-speed 4.80 S8 1.8 3.00 35.4 Campagnolo 9-speed 4.55 C9 1.75 2.8 38.2 Shimano 9-speed 4.35 S9 1.78 2.56 36.5 SRAM 9-speed 4.35 S9 1.8 2.54 36.5 Campagnolo 10-speed 4.15 C10 1.7 2.42 38.8 Shimano 10-speed 3.95 S10 1.6 2.35 37.2 SRAM 10-speed 3.95 S10 1.6 2.35 37.2 Campagnolo 11-speed 3.85 C11 1.6 2.25 40.1* *Large stack is accommodated by an unique small-cog overhang that requires extra attention in any adaptation. Predicted cog-shifts for variously mixed bicycle drive-gear Credit due to CTC, the UK's national cyclists' organisation. Note: The term pitch in these tables means inter-cog center-to-center spacing.   Rear Mechanism Shimano old Dura-ace Hubbub New Campagnolo Old Campagnolo SRAM (1:1) Derailleur Actuation Ratios 1.7   1.9   1.6   1.5   1.4   1.1   Shifter Cable Pull Pitch Code Pitch Code Pitch Code Pitch Code Pitch Code Pitch Code   (mm) (mm)   (mm)   (mm)   (mm)   (mm)   (mm)   Shimano 6 3.2 5.5 S5/6 6.07   4.98 S7/C8 4.76 S8 4.56 C9 3.54   Shimano 7 2.9 5.0 S7 5.52 S5/6 4.53 C9 4.33 S9 4.14 C10 3.22   Shimano 8 2.8 4.8 S8 5.30   4.35 S9 4.16 C10 3.98 S10 3.09   Shimano 9 2.5 4.35 S9 4.80 S8 3.94 S10 3.77   3.60   2.80   Shimano 10 2.3 3.95 S10 4.36 S9 3.58   3.42   3.27   2.55   Campagnolo 8 3.5 6.03   6.66   5.47 S5/6 5.22   5.00 S7/C8 3.89 S10 Campagnolo old 9 3.2 5.49 S5/6 6.06   4.98 S7 4.75 S8 4.55 C9 3.54   Campagnolo new 9 3.0 5.26   5.80   4.76 S8 4.55 C9 4.36 S9 3.39   Campagnolo 10 2.8 4.79 S8 5.29 S5/6 4.34 S9 4.15 C10 3.97 S10 3.09   Campagnolo 11 2.6 4.48 S9 4.94 S7/8 4.05 S10 3.85 C11 3.70   2.83   SRAM (1:1) 7 4.5 7.76   8.56   7.03       6.43   5.00 S7 SRAM (1:1) 8 4.3 7.45   8.22   6.75   6.45   6.17   4.80 S8 SRAM (1:1) 9 4.0 6.75   7.45   6.12   5.84   5.59   4.35 S9 SRAM (2:1) 7 2.9 5.0 S7 5.52 S5/6 4.53 C9 4.33 S9 4.14 C10 3.22   SRAM (2:1) 8 2.8 4.8 S8 5.30   4.35 S9 4.16 C10 3.98 S10 3.09   SRAM (2:1) 9 2.5 4.35 S9 4.80 S8 3.94 S10 3.77   3.60   2.80   COLOR CODE Designed to Match These Match Well Needs Shortened Cassette The above tables give the means to predict whether or not rear-gear shifting will work with various combinations of shifters, derailleurs, and cogs. Because of the size limitations and difficulty in modifying freewheels, these tables refer in the main to CASSETTES. The emphasis here is on closeness of pitch, and other practical factors might still need to be considered. The pitch of common cog-sets is given in one table and the derailleur shift data is given in another. The shift data is divided into four main categories: GREEN Colors These show the resultant derailleur shift in millimeters when the shifter, derailleur, and cogs of one manufacturer are used together. This is the ideal situation. For example, the Shimano 10-speed shifter with a cable pull of 2.3mm is applied to a Shimano derailleur with an actuation ratio of 1.7, resulting in a shift (2.3mm x 1.7) of 3.91mm. Allowing for the precision of the available data this fits the Shimano 10-speed cog-set pitch of 3.95mm well, and the shifting is considered to be ideal. YELLOW Colors These give the resultant derailleur shift in millimeters when other than the ideal combination is used, and are characterized by having an intact set of cogs, but unused positions on the shifter when the modification is complete.(But see Campagnolo 'old and new'). The pitch that is produced works well enough with the alternative cog-set. For example, the Campagnolo 10-speed shifter with a cable pull of 2.8mm is applied to a Shimano derailleur with an actuation ratio of 1.7, resulting in a shift (2.8mm x 1.7) of 4.76mm. Allowing for the precision of the available data this fits the Shimano 8-speed cog-set pitch of 4.80mm well. That is to say, the Campagnolo 10-speed shifter could be used with the Shimano derailleur provided that there was an 8-speed Shimano cog-set installed. The other two positions on the shifter would remain unused, excluded by adjusting the limit stops of the derailleur. RED Colors These give the resultant derailleur shift in millimeters when other than the ideal combination is used, and although the shifter range will be correct, they need some cogs to be left off the cassette assembly. The pitch that is produced works well enough with the specified cog-set. For example, the Campagnolo 8-speed shifter with a cable pull of 3.5mm is applied to a SRAM (1.0) derailleur with an actuation ratio of 1.1, resulting in a shift (3.5mm x 1.1) of 3.85mm. Allowing for the precision of the available data this fits the Shimano S10 cog-set pitch of 3.95mm well. That is to say, the cog-set can be assembled using eight of the Shimano 10-speed cogs and seven of its spacers. OTHER Shift Data Data other than those with green, yellow, or red coloring would not index correctly. That said, there are some other Shimano combinations that can be applied to a Shimano 7-speed freehub. The set can be extended to eight cogs if S9 cogs form the cassette, and a 9-speed shifter and chain are used. Similar results can be obtained for nine cogs on a 7-speed freehub if S10 is used for the assembly, and a 10-speed shifter and chain are used. In each of these two cases the unused positions on the shifters are blocked by the adjustment of the derailleurs' limit stops. 7 August 2011

To avoid most compatibility problems, stick to one manufacturer's components for the cog-set, derailleur, shifter, and chain. Even then, since some manufacturers make items for more than one shift ratio, it is wise to make sure that the derailleur and shifter combine to produce the cog-pitch that is intended. The tables in the above drop-box explain the indexing principles, and the calculation of derailleur capacity based on the cog-set is given elsewhere on this page.

General Rule

A close-up of cogs clearly showing their ramps

Consistencies

Although complexity is the rule as opposed to the exception, there are some consistencies in manufactured goods. Examples include manufacturers who produce components that suit the drive-trains of others, a tendency to standardize spline patterns for cassettes on the most popular brand name, and the standardized pitch (inter-cog spacing) for 7-speed cog-sets.

Some SRAM shifters, for example, GripShift types marked as MRX, are suitable for Shimano systems, since these shifters suit the so-called 2 : 1 family of Shimano derailleurs; in fact their shift ratios are not exactly 2 but 1.7. (Shift ratio is the reciprocal of actuation ratio which is itself the ratio of input change to output change, so here, one length of cable pull causes a transverse movement that exceeds it by 1.7 times). Other shifters by the same SRAM manufacturer, are suited to the 1:1 family of derailleurs; (with exact 1.1 shift ratios), and so these do not match the Shimano derailleurs. The subject of compatibility in drive-train gear has received much attention over the years and despite the complexities involved, it has been found that some mixed systems can work well enough provided that there is careful selection. (See the examples in the drop-box of the above section).

Cassette spline patterns for Shimano freehubs fit a number of other makes of cassette, and within its own products is the same for virtually every type of cassette. With minor exceptions, the SRAM manufacturer has used the same sprocket pitch (inter-sprocket spacing) and spline pattern as Shimano, so that their products are used interchangeably, (with the possible exception of cog ramping functions). The tool used to remove Shimano cassette locking-rings will unlock them for all of their modern cassettes, and in addition, the cassette locking-rings of SRAM, SunRace, SunTour, Chris King and various others. A similar situation exists for freewheel removals, with the Shimano freewheel tool unlocking all of its own and Sachs, Aris, and Sun Race freewheels besides. As far as is known, the Campagnolo cassette removal tool is intended only for its own locking rings, though some report that a Shimano tool is a (risky?) 'near fit'. The Shimano standards for spline-fittings come closest to an informal industry standard.

Seven-speed sprocket pitch is almost always 5mm , so shifter/derailleur combinations that are designed for seven-speed use can be made to work on all seven-speed sprocket sets, (subject to any frame fitting constraints). Consideration of the mixed shifts and pitches given elsewhere on this page will emphasize how unusual this fortunate situation is. The main consideration is that the shifter's cable-pull suits the derailleur's shift ratio so that between them they make the necessary 5mm gear shifts. How the necessary shift is accomplished is of no concern. For example, a Shimano 7-speed shifter pulls the cable by 2.9 mm while the derailleur has a shift ratio of 1.7. The resulting product, (2.9 mm x 1.7 = 4.93 mm), is about 5mm so the combination works well. Another shifter and derailleur combination, say SRAM, also produces the necessary 5mm derailleur shift using 4.5 mm of cable pull and a derailleur shift ratio of 1.1. (4.5mm x 1.1 = 4.95mm = approx 5mm). There is little cross-manufacturer consistency for the pitch of the larger sprocket-sets, so the mixing of components for these larger cog-sets needs more care. See CTC on Rear Shifting for more on mixing components of the drive system.

Freewheel threads on modern bikes are the same. Regardless of where in the world the bike is made, the standard (ISO) for freewheel mounting threads is 1.375 inches in diameter and 24 threads per inch. This means that any modern freewheel is likely to fit a standard threaded hub. This is not necessarily the case for older bikes, and the details for these can be found at Sheldon Brown's Freewheels. There are a number of other ISO standards in use for bikes; see Sheldon Brown's ISO Standards for Bikes.

Removal and Replacement

A cassette's locking ring removal tool. This is typical of the tool used for Shimano freehubs. It has twelve splines.

A typical removal tool in place over a cassette's locking ring. The skewer cap is not shown.

A chain whip tool shown wrapped onto a cog.

A torque wrench with a detachable socket. Twisting the handle sets a pointer at the required torque. When the torque on the nut is reached, the ratchet slips to avoid over-tightening.

Loose cogs and a locking ring or final gear

The tools needed to remove and replace cassettes differ according to the manufacturer. The most commonly used tools include a locking ring remover (see the image), shaped for the lock ring in use, and a chain-whip (see the image), a tool that engages with the cogs to prevent turning while the locking ring is being unscrewed. (A chain-whip is needed only for cassette removal). Because the locking ring remover is merely a tool-end, an extension arm or a long adjustable spanner is needed to provide the necessary torque. An external page that describes the different removal tools of various manufacturers is provided at Park Tool's Cassette and Freewheel Removal, along with other practical advice.

The tools needed for the removal of freewheels have similar appearance to those for cassettes, though the removal tools might not always be interchangeable. The effort in removing a freewheel is likely to be greater than that for a cassette's locking ring owing to the freewheel's self-tightening during normal cycling.

The removal of cassettes and freewheels that have been in use require considerable force, and under force the tool might tend to slip, possibly damaging the tool or its receptacle. For this reason some mechanics modify the simple procedures below by fastening the tool in position with the reassembled quick-release wheel skewer. When this is done the skewer springs are omitted and the skewer cap is tightened against the removal tool to take up the slack. The tool must not exceed one turn with the skewer still in place, and must be removed before completing the removal of the cassette or freewhweel.

Tools required

• Cassette locking ring or freewheel removal tool for the product in use.
• Adjustable wrench, about one foot long, or specific tools with similar leverage.
• A chain whip, for cassette removal only.
• Torque wrench, in a range that includes 30 ft.lbs: Mainly for cassette locking ring replacement, (optional).
• Bench with a secure vice, (optional).

Few riders are lucky enough to own expensive torque wrenches for their bikes, so it might be as well to get the assistance of the bike shop for work that requires their use. That said, many are known to approximate the necessary torques by judging the force applied to a wrench lever of known length. That is to say, torque is just the product of force and length. For example, a 30 ft.lb torque is applied when a thirty pound force is applied at right angles to the end of a one foot wrench. The accuracy of this method is as good as the user's ingenuity at judging or measuring the applied force. Formulas for converting to other torque designations: in.lb = ft.lb x 12 in.lb = Nm x 8.851 in.lb = kgf.cm / 1.15

Technical Note:

Cassette Removal

Howsoever the effort is eventually applied or from what angle, these directions are made assuming that the cogs of the wheel are facing you.

• Remove the rear wheel from the bike.
• Unscrew and remove the skewer assembly from the wheel.
• Fit the correct locking ring removal tool against the locking ring. Some removal tools have their own guide rods that feed through the middle of the hub.
• Apply a chain whip to the cogs to pull them clockwise, to prevent them from turning anti-clockwise during removal.
• While holding the cogs firmly with the chain whip, turn the removal tool with the wrench or lever-arm anti-clockwise to release it. Slackening requires considerable force, so a longer lever arm or pipe extension might help. It is usual to hear a clicking noise as the ring is initially released. Note that the torque wrench should never be used for heavy work of this kind.
• The cluster of cogs can then be removed. Note the alignment and sequence of the parts for reassembly before splitting up the cog-set. Consider stringing them together, since the spacer thicknesses might differ within the cluster. The smallest cogs will be noted to have built-in spacers, and perhaps shims.

For those who have a bench fitted with a suitable vice, fit the tool into the cassette in the usual way and if possible use the skewer and its cap (no springs) to set it in position. Having done so, and with the wheel flat and the cog-set on the underside, grip the flats of the removal tool in the vice. Hold the cogs in the chain-whip and with it, turn the cogs anti- clockwise, (looking down on top of the wheel), to release the ring. Do not turn the wheel to make this release, but use only the chain-whip, letting the wheel turn with the cogs.

Further details on the subject of cassette removal can be found at Park Tool's Cassette and Freewheel Removal. A video that clearly shows the unlocking of a typical cassette is available at FR-5 Lock-ring video.

Cassette Replacement

The replacement of a cassette does not require the use of a chain whip, and the process is otherwise just a reverse of the removal. The procedure is as follows:

Howsoever the effort is eventually applied or from what angle, these directions are made assuming that the cogs of the wheel are facing you.

• Clean the cassette and oil-wipe the cogs of the cluster. Grease the threads of the locking-ring and its receptacle.
• Fit the cassette cogs onto the freehub splines with the correct orientation. While manufacturers attempt to ensure that only one working alignment can exist, there will no doubt be exceptions. In addition, take care that the cassette spacers are in the correct sequence, since they are not always identical.
• Screw on the locking ring loosely into position.
• Turn the tool on the locking ring clockwise with a wrench, (no chain whip needed), to establish the manufacturer's recommended torque. In the absence of data, aim for about of 360in.lbs, (40N.m), (30 ft.lbs).

Freewheel Removal

Howsoever the effort is eventually applied or from what angle, these directions are made assuming that the cogs of the wheel are facing you.

• Remove the rear wheel from the bike.
• Unscrew and remove the skewer assembly from the wheel.
• Fit the correct removal tool into the recess in the hub. Some removal tools have their own guide rods that feed through the middle of the hub.
• Turn the removal tool with the wrench or lever-arm anti-clockwise to slacken the freewheel. Slackening requires considerable force, so a longer lever arm or pipe extension might help. Consider the use of a bench and vice if it is available. Note that the torque wrench should never be used for heavy work of this kind.
• The freewheel cluster can then be removed as a complete unit.

If a bench-vice is to be used, then first set the removal tool in the wheel and if possible use the skewer and its cap (no springs) to set it in position. Place the wheel, cogs down with the flats of the tool in the vice. Turn the wheel anti-clockwise, (looking down on top of the wheel), to unscrew the freewheel. An inflated tire gives the best grip.

Freewheel Replacement

Howsoever the effort is eventually applied or from what angle, these directions are made assuming that the cogs of the wheel are facing you.

• Unscrew the skewer assembly from the wheel.
• Clean the freewheel, oil-wipe the cogs, and grease both its threads and the threads on the hub.
• Fit the freewheel onto the hub threads until it is hand tight. Tighten the freewheel further using the wrench and tool in a clock-wise direction, to obtain the torque recommended by the manufacturer. In the absence of data, aim for about of 240 in.lbs, (27 N.m), (20 ft.lbs). The freewheel will tighten in use in any case; the above figure is given to avoid uncertainty at the point of delivery.

There is little advantage in making use of a vice for the freewheel fitting, but for those who intend to do so, they can find a method at Park Tool's Cassette and Freewheel Removal.

Gearing Calculations

This section provides the rudimentary calculations associated with bicycle gearing.

Distance Shifted

In all indexed shifting, (as opposed to friction shifting), there is a fundamental relation to describe the transverse distance that a derailleur cage shifts across the cog-set or chainrings. The transverse distance shifted is equal to the product of the shifter's cable pull and the derailleur's shift ratio. In practice, the distance shifted must equal the center to center spacing of the cogs, (or chainrings). Most modern rear-shifting is indexed, and some front-shifting is indexed (for example, Shimano). See Gear Changing Dimensions for a selection of such data.

Transverse Distance of Derailleur Cage = Shifter Cable Pull   x   Derailleur Shift Ratio

For example:   For a seven-speed rear cogset, a Shimano rear derailleur, and a SRAM MRX twist 7-speed shifter; we have;
Transverse Distance of Derailleur Cage = 1.7 ratio  x   2.9mm cable pull    =    4.93mm    Approximately 5mm
This suits all seven speed center to center spacings since they are all set at 5mm centers.
 

Derailleur Capacity

When a rear-derailleur is planned or when an existing chain ring or cogset is changed, the required total capacity of the derailleur needs to be checked. The total capacity refers to the ability of the derailleur to take up slack across the entire range of gear combinations. Since the gear combinations are affected by the range of both the chain rings and the rear cogset, these are both represented in the calculation. The required capacity of the rear derailleur becomes:

Minimum Required Capacity = (Largest cog - Smallest cog) + (Largest chainring - Smallest chainring)

For example:   For a cogset 11T - 30T with only one chainring of 38T; we have;
Minimum Required Capacity = (30T - 11T) + (38T - 38T) = 19T    The 'total capacity' spec for the derailleur must be at least 19T.

Another example:  For a cogset 11T - 28T and chain rings 20, 30, and 42; we have;
Minimum Required Capacity = (28T - 11T) + (42T - 20T) = 39T    The 'total capacity' spec for the derailleur must be at least 39T. 

Other consideraions within a derailleur's specification sheet include front chain ring tooth difference and smallest and largest rear cog sizes. This latter requirement ensures that as the derailleur traverses the cogs on its in-built gradient, the clearance of the cage, as set by the 'b-height' adjustment, is reasonably consistent. Attention should also be paid to the number of gears for which the derailleur is intended, and whether or not the shifter is compatible with its shift ratio.

Gear-Inches and Ground Covered

Gear inch calculations are used by those who plan the design of cycle gearing, and are useful when a new bike is being considered. They allow a tabular layout where the gears associated with adjacent chain rings can be studied for their overlap and convenience, and allow a purchaser to predict whether or not an intended ride will have a similar sweet spot, or feel, like their existing bike. Multiplying the gear-inch figure by the constant pi (approximately 3) gives the distance covered by one complete turn of the pedals. Calculations are made for each gear combination of front chain ring and rear sprocket. The formula for any one combination is just:

Gear Inches = Outside Inch-Diameter of driven Bicycle Wheel   X  (Size front chain ring / Size rear sprocket)

For example:   For an 11T rear sprocket and a 38T chain ring, with a 26 inch rear wheel diameter, we have:
Gear Inches   =   26   X   (38T / 11T)   =  89.8

and the distance covered in one turn of pedals is:
Distance (inches)   =   ''gear-inches  X  pi''   =   89.8   x   3.142   =   282.2 inches   =   23.5 feet for one turn of the pedals. 

It is usual to make a table of the gear inches and then possibly another table showing the change in gear inches between adjacent gears. This permits an understanding of the relative effort required in the use of adjacent gears. An on-line calculator that saves some work can be found at Gears by Sheldon Brown. A typical gear-inch table is shown below, and although it is not entirely obvious in this example, for convenient arrangements, the top figure of each column is most usually found in the middle of the next column to its right.

Gear Inches for 11T-30T cogs, 20T,30T,38T chain rings, and 26 inch wheels

Gear Inches	20T Chain Ring	30T Chain Ring	38T Chain Ring
11T cog	47	71	90
13T cog	40	60	76
15T cog	35	52	66
18T cog	29	43	55
21T cog	25	37	47
24T cog	22	33	41
30T cog	17	26	33

See also

• Gear-changing Dimensions  : A page devoted to the dimensions of gear shifting

External links

• Park Tool Repair Help
• Cassettes & Freehubs by Sheldon Brown
• Gears by Sheldon Brown: A gear-inches calculator using wheel diameter; see below for wheel circumference.
• Spacing Cribsheet by Sheldon Brown: Details of many cogsets, with pitch, cog thickness, and spacer thickness given, as well as overall hub use.
• Rear Shifting (Mixing Systems) by CTC - the UK’s national cyclists’ organisation.
• Gearing 101 by The Cycling Site
• SRAM Service Page Links by SRAM
• SRAM Tech Manual 2010 by SRAM
• SHIMANO techdocs links by Shimano
• Campagnolo Technical Documentation by Campagnolo
• Campagnolo Gear-Inches Calculator by Campagnolo: Uses wheel circumference.