Bicycle Chain Length Calculator and Gear Range

Derailleur sizing

The requested classic approximation is $L=2C+F/4+R/4+1$ inches, using the chainstay $C$ and the largest tooth counts $F,R$. Its dimensional implementation is $L=2C+p(F+R)/2+a$, where chain pitch $p=12.7\,\mathrm{mm}$ and the classic allowance $a=25.4\,\mathrm{mm}$. The custom approximation substitutes the entered allowance. For these two options, $N=2\lceil L/(2p)\rceil$ half-inch pitches, including the connector. Rounding upward is this tool's conservative policy; the classic approximation is kept distinct from the physical sizing procedure.

Park wide-range 1× follows the sequence in Park Tool, Chain Length Sizing, section 5: first establish the shortest joinable big-big wrap with the derailleur bypassed, then add four half-inch pitches (two inches). Numerically this is

Here $L_w$ is the smooth-chain direct-wrap geometry below. Rounding the simple loop approximation with a two-inch allowance can miss a link-pair boundary, so it is not used for this option. For the independent review's 425 mm chainstay, 30-tooth ring and 52-tooth rear cog, the wrap rounds to 110 pitches and the finished estimate is 114 links.

Park Tool section 4 describes a one-inch physical allowance for cogs up to 36 teeth; section 5 describes the four-pitch wide-range method for dedicated 1× systems with cogs of 42 teeth or more. The classic formula is an approximation, not an exact simulation of either joinable reference. Consult the maker for other arrangements and physically establish the joinable reference before cutting. The numerical wrap remains a smooth-chain estimate rather than a polygonal model of the fitted chain.

Two-sprocket geometry and single speed

The direct wrap is the smooth, taut loop around two circles. With equivalent radii $r_f=pF/(2\pi)$, $r_r=pR/(2\pi)$ and $d=r_f-r_r$, its length is

This is equivalent to equation (2) in Matto's original Bike Chain Math derivation (2021). The radii preserve chain pitch along an arc; they are not exact polygonal sprocket pitch radii. Horizontal mode rounds $L_w$ upward to an even-link chain, then solves for the corresponding taut centre distance by bisection. Its axle movement is a geometric starting point, not the final tension setting. Unlike Park Tool's wheel-removal procedure, this shortest-chain mode adds no automatic spare inch. Pulley mode first adds the entered routing allowance; maximum take-up is evaluated at the shortest centre distance.

Capacity and gearing

Total tooth capacity is (F_\max-F_\min)+(R_\max-R_\min), following Sheldon Brown's Capacity worked example. Maximum cog clearance is checked separately against the entered rating. Gear ratio is front teeth divided by rear teeth. Sheldon Brown's Gain Ratios, printed p. 30, defines gear inches as wheel diameter in inches times this ratio, and development as $\pi D$ times the ratio, with $D$ in metres. Speed is development times crank revolutions per minute, converted to the displayed speed unit. Overall range is 100\,g_\max/g_\min percent; 100% means a single ratio.

Gear inches is displayed as the conventional inch-based index (equivalent geared wheel diameter divided by one inch). Its numerical definition stays fixed when the metric/US switch converts physical lengths, development and road speed.

• New, conventional half-inch-pitch chains with alternating inner and outer links. A displayed link is one 12.7 mm pitch; two make a one-inch pair. Connector length is included in the finished estimate.
• Tooth counts are entered for the actual components; default derailleur ratings are illustrative input values, not a specification for a named product.
• Ordinary direct-chain layouts without idlers, eccentric suspension routing or internally geared hub ratios. No half-link connector is modelled.
• The suspension input is an increase in centre distance, not shock stroke. The maximum must be established from the frame maker's procedure across the full travel.
• Wheel diameter means effective rolling diameter. No slip, tyre growth or drivetrain loss is included in the kinematic speed calculation.
• The direct wrap assumes a smooth, taut chain and concentric sprockets. Real chains form polygons and require running slack; tensioner geometry must be checked on the bicycle.

Use this tool for planning chain purchases and comparing external gearing. The numerical input ranges are editing limits, not component compatibility guarantees. The schematic deliberately shows a direct sizing wrap with the derailleur bypassed, rather than the installed chain route.

Before cutting, use the physical big-big method and the exact chain, derailleur and frame instructions. Check big-big reach and small-small tension after normal routing. Capacity and largest-cog checks do not establish indexing, chain width, mounting, B-gap, front derailleur or chainline compatibility. Do not shorten a chain to compensate for inadequate derailleur capacity.

Full Mount/T-Type, high-pivot idler frames, oval chainrings, unusual guides, half-link chains, chain wear and internal hub ratios require their own treatment. A custom allowance does not make these systems covered.

In horizontal-dropout mode, the solved position is theoretically taut: leave the prescribed slack, inspect tight spots through a crank revolution, and ensure the wheel can be removed. A pulley tensioner requires an adequate wrap and travel range; do not use a sprung pulley tensioner for fixed-gear or coaster-brake drives. Installation and suspension work belong to a qualified bicycle mechanic when the user lacks the required competence and equipment.