A bicycle gear is a chainring-and-sprocket pair connected by a roller chain that converts the rider's pedal cadence into rear-wheel rotation at a chosen ratio. The defining component is the chainring-sprocket tooth count pair — the number of teeth on each sets the gear ratio directly, and that ratio decides how much road the bike covers per pedal stroke. The purpose is to keep the rider's legs at an efficient cadence (roughly 80-100 RPM) across wildly different speeds and grades. Outcome: a 50-tooth chainring on an 11-tooth sprocket pushes a road bike past 50 km/h, while a 24×34 combination on a mountain bike crawls up a 15% trail without stalling.
Bicycle Gear Interactive Calculator
Vary chainring teeth, sprocket teeth, and wheel circumference to see gear ratio, wheel rotations, and road development per pedal stroke.
Equation Used
The tooth-count ratio sets how many times the rear wheel turns for each crank revolution. Multiplying that ratio by rolling wheel circumference gives development, the metres of road covered per pedal stroke.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Chain drive has no slip.
- Wheel circumference is rolling circumference under load.
- One pedal revolution equals one chainring revolution.
- Losses, tyre deformation, and drivetrain efficiency are ignored.
Inside the Bicycle Gear
A bicycle gear works by trading rotations for torque. You spin the chainring at the front through the cranks, the chain transfers that motion to one of several sprockets on the rear cassette, and the size difference between the two cogs sets the gear ratio. A 50-tooth chainring driving an 11-tooth sprocket gives a ratio of 4.55, meaning the rear wheel turns 4.55 times for every pedal revolution. Multiply that by the wheel's rolling circumference (about 2.10 m for a 700×25c road tyre) and you get the development — the metres of road covered per pedal stroke. That single number, development, is what your legs actually feel.
The drivetrain is designed around the rider's cadence sweet spot. Most riders are efficient between 80 and 100 RPM, so the gear range exists to keep cadence in that window whether you are climbing at 8 km/h or descending at 60 km/h. The derailleur shifts the chain laterally across cogs, and the cassette's tooth jumps are sized so each shift changes cadence by roughly 8-12% — small enough that your legs do not jolt, large enough that you actually feel the change. Shimano's Hyperglide tooth profiling uses ramped and twisted teeth on the cassette to lift the chain cleanly under load; without that profiling, shifts under power skip and clatter.
If tooth-count tolerances or chain wear go out of spec, the system fails fast. A chain stretched beyond 0.75% elongation (measured with a chain checker) starts riding high on the sprocket teeth, accelerating cassette wear and causing skip under torque. A bent derailleur hanger of just 2-3 mm shifts the chain line off true and you get ghost shifting — the chain hops cogs unprompted. And if you cross-chain badly (big-big or small-small), the chain runs at an angle past 6° and you hear it grinding on the front derailleur cage.
Key Components
- Chainring: The front toothed ring bolted to the crank spider. Common road sizes run 50/34T (compact) or 53/39T (standard); MTB triples historically ran 44/32/22T. Tooth count directly sets the numerator of the gear ratio, and tooth profile (narrow-wide on 1× setups) controls chain retention without a front derailleur.
- Rear Cassette: A stack of 7 to 13 sprockets splined onto the freehub body. Modern road cassettes run 11-28T or 11-34T; gravel and MTB push to 10-52T. The smallest sprocket sets top-end gear, the largest sets climbing gear, and the tooth jumps between them must be 1-2T at the high end and 3-6T at the low end for usable cadence steps.
- Roller Chain: ANSI 40-class roller chain at ½-inch pitch transfers torque between chainring and sprocket. Inner-link width has shrunk from 3/32-inch (8-speed) to 5.25 mm (12-speed) as cassettes added cogs. Chain wear is measured as % elongation — replace at 0.5% on 11/12-speed, 0.75% on 8/9-speed, or you will trash the cassette.
- Rear Derailleur: A spring-loaded parallelogram cage that moves the chain across the cassette and tensions the slack span. The B-tension screw sets pulley-to-cog gap (target 5-6 mm at the largest cog), and the high/low limit screws prevent the cage from throwing the chain into the spokes or off the small cog.
- Front Derailleur: Shifts the chain between chainrings on 2× and 3× drivetrains. Cage height must sit 1-3 mm above the big chainring's tallest tooth, and cage angle must align within 0-5° of the chainring plane. Out of those tolerances, you get dropped chains or refusal to upshift under load.
- Freehub Body: The ratcheting mechanism inside the rear hub that lets the wheel coast while the cassette stays still. Pawl engagement angles range from 10° (cheap hubs, sluggish pickup) down to 0.52° on a DT Swiss 240 EXP — lower engagement angle means quicker power delivery out of corners.
Who Uses the Bicycle Gear
Bicycle gearing is not one design — it splits sharply by use case. Road riders want close-ratio cassettes for cadence stability, mountain bikers want huge ranges for steep terrain, cargo and e-bikes want low gears to move heavy loads, and track bikes want no gears at all. The hardware reflects whichever priority dominates.
- Road Cycling: Shimano Dura-Ace R9200 12-speed groupset with 54/40T chainrings and 11-30T cassette — used in the Tour de France peloton for cadence stability at 45 km/h race pace.
- Mountain Biking: SRAM Eagle Transmission XX SL with 32T chainring and 10-52T cassette — a 520% gear range that lets riders climb 20% grades and pedal out of 60 km/h descents on bikes like the Specialized Stumpjumper.
- Cargo & Utility: Tern GSD S10 cargo e-bike with Shimano Deore 10-speed and a 46T front, 11-42T rear, sized to move 200 kg of payload up urban hills.
- Track Racing: Velodrome bikes at the Lee Valley VeloPark run a single fixed gear — typically 49×14T — with no freewheel and no shifting, optimised for one cadence at one event distance.
- Commuter & Folding Bikes: Brompton's 6-speed system pairs a 2-speed derailleur with a 3-speed Sturmey-Archer hub — chosen because internal gearing survives folding and city grime where exposed derailleurs would not.
- Touring & Bikepacking: Surly Long Haul Trucker with a 3×9 drivetrain (48/36/26T × 11-34T) — the triple chainring stays popular here because loaded touring up alpine passes needs sub-1.0 gain ratios.
The Formula Behind the Bicycle Gear
The number that matters to a rider is development — the metres of road covered per pedal revolution. At the low end of a typical drivetrain (granny gear on a loaded tourer, around 1.5 m development) you climb walls but spin out by 12 km/h. At the high end (53×11 on a road bike, around 9.4 m development) you can push 55 km/h on a flat sprint but cannot hold cadence below 25 km/h without grinding. The sweet spot for steady road riding sits around 6.0-7.5 m development, which keeps a rider at 90 RPM between 32 and 40 km/h.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| D | Development — distance travelled per pedal revolution | m/rev | ft/rev |
| Tchainring | Tooth count on the front chainring | teeth | teeth |
| Tsprocket | Tooth count on the engaged rear sprocket | teeth | teeth |
| dwheel | Effective rolling diameter of the rear wheel + tyre | m | ft |
| v | Resulting road speed at a given cadence | m/s | ft/s |
Worked Example: Bicycle Gear in a Shimano 105 R7100 road bike build
You are speccing the gearing for a Shimano 105 R7100 12-speed road bike intended for a club rider doing rolling 80 km routes in southern Ontario. The build uses a 50/34T compact chainset, an 11-34T cassette, and 700×28c tyres with a measured rolling circumference of 2.136 m. The rider's preferred cadence is 90 RPM. You need to know what road speed each gear delivers and whether the range fits the terrain.
Given
- Tchainring,big = 50 teeth
- Tchainring,small = 34 teeth
- Tsprocket,small = 11 teeth
- Tsprocket,big = 34 teeth
- Cwheel = 2.136 m
- Cadence = 90 RPM
Solution
Step 1 — compute development at the nominal mid-range gear, 50T × 19T (a typical cruising sprocket):
Step 2 — convert to road speed at 90 RPM cadence:
That is exactly where a club rider wants to sit on flat road — legs spinning cleanly, breathing controlled.
Step 3 — at the low end of the typical operating range, 34T × 34T (climbing gear):
At 90 RPM that gives 11.5 km/h — slow enough to crawl up a 10% pitch without stalling. Drop cadence to 70 RPM on a steep ramp and you are at 9.0 km/h, which is realistic for a 200 W rider on a 12% grade.
Step 4 — at the high end, 50T × 11T (top gear):
At 90 RPM that pushes 52.4 km/h. In practice you only spin this gear in a sprint or a tailwind descent — on the flat, holding 52 km/h takes around 400 W, which a club rider cannot sustain. The top gear exists for the 5% of the ride where gravity or wind is helping.
Result
Nominal cruising development comes out at 5. 62 m/rev, giving 30.3 km/h at 90 RPM in the 50×19 gear. The full range spans 11.5 km/h in the granny up to 52.4 km/h in top gear, with the sweet spot sitting in the 50×17 to 50×21 cogs where every shift changes cadence by about 10% — exactly what your legs want. If your measured speed at a given gear runs noticeably below predicted, check three things in this order: (1) actual tyre rolling circumference, because a 28c tyre at 60 psi rolls 15-20 mm shorter circumference than at 90 psi and the error compounds across every gear, (2) cadence sensor calibration if you are running a Garmin or Wahoo — magnet misalignment commonly under-reads by 5-8 RPM, and (3) cassette tooth count if the bike came used, since shop swaps from 11-30 to 11-34 are common and rarely documented.
Bicycle Gear vs Alternatives
Bicycle gearing splits into three architectures: external derailleur systems, internal gear hubs, and continuously variable hubs. They solve the same problem — match cadence to speed — with very different mechanical philosophies, and the right choice depends on terrain, maintenance access, and how much shifting under load you do.
| Property | Derailleur Drivetrain | Internal Gear Hub (Shimano Alfine, Rohloff) | CVT Hub (NuVinci/enviolo) |
|---|---|---|---|
| Drivetrain efficiency at rated load | 96-98% | 90-95% (Rohloff 14-speed) | 87-92% |
| Gear range | Up to 520% (SRAM Eagle) | 526% (Rohloff Speedhub) | 380% (enviolo H-SYNC) |
| Shift under load | Poor — must ease off pedals | Excellent — shifts at standstill | Excellent — fully continuous |
| Service interval | Chain replace every 3,000-5,000 km | Oil change every 5,000 km (Rohloff) | Sealed for life, ~10,000 km |
| Weight penalty (vs derailleur baseline) | Baseline | +1.0 to 1.7 kg | +2.0 to 2.5 kg |
| Cost (groupset/hub only) | $300-$4,000 | $1,500-$1,800 (Rohloff) | $500-$900 |
| Best application fit | Road, MTB, race | Touring, commuter, tandem | Cargo, e-bike, urban hire fleets |
Frequently Asked Questions About Bicycle Gear
That cog is worn faster than its neighbours, almost always because you spent thousands of kilometres in it. The chain has elongated to match the worn tooth pitch on that one cog, and when you shift to a less-used cog the new (or less-worn) chain rides up the teeth under torque and skips.
Quick diagnostic: pull the chain forward off the chainring at the 3 o'clock position. If it lifts more than half a tooth height, the chain is past 0.75% elongation and you needed to replace it 500 km ago. The fix at this point is a new chain AND new cassette — installing only one will cause the same skip immediately.
Narrow-wide chainrings rely on alternating tooth widths matching the chain's alternating inner and outer link plates to hold retention. Two failure modes drop chains here: chainring tooth wear past about 2,000 km (the narrow teeth round off and lose grip), or chainline misalignment beyond about 3 mm between the chainring centre and the middle of the cassette.
Check chainline with a straightedge from the chainring tooth tip to the cassette — it should hit the 5th or 6th cog on a 12-speed. If it hits the 3rd or 9th, you need a different bottom bracket spindle length or a chainring offset change. A clutch derailleur helps but does not fix a misaligned chainline.
Compute the lowest gear you actually need, then work up. For a loaded gravel rider on 10-12% pitches, you want a gain ratio around 1.0 or below. A 1× with 40T × 10-44T gives a low gain ratio of about 1.45 — fine for fit riders on moderate climbs, painful with bags on steep stuff.
A 2× with 46/30T × 11-34T gives a low gain ratio of 0.65, which crawls up anything. The penalty is a front derailleur, an extra shifter, and more chainline angles to manage. If your rides have sustained 8%+ climbs with luggage, take the 2×. For race-pace gravel under 6% average, 1× wins on simplicity.
Yes, and it is the fundamental compromise of wide-range 1× cassettes. An 11-speed 11-32T has tooth jumps of 1-2-2-2-2-3-3-3-4-4. A 12-speed 10-52T has jumps of 2-2-3-3-4-5-6-7-8-9. The big-cog jumps are 15-20% cadence steps, which feel jarring on a sustained climb because you cannot find the right cadence — you are either spinning out or grinding.
If that bothers you, run a 2× setup or fit a tighter-range cassette like 10-36T and accept losing some climbing gear. There is no way to get both wide range and tight steps from a single cassette — the geometry forbids it.
Either the low limit screw is backed too far out, or the derailleur hanger is bent inboard. The low limit screw (marked L) physically stops the parallelogram from moving past the largest cog — turn it clockwise in quarter-turns until the cage just clears the spokes by 1-2 mm.
If the limit screw is already correct and the cage still hits, sight along the hanger from behind. A bent hanger of even 3-4 mm inboard will throw the chain into the spokes. Hangers bend from drive-side falls and shipping damage; you need a hanger alignment gauge (Park DAG-2.2) to straighten it, or just replace the hanger — they are designed to be the sacrificial part.
Drivetrain efficiency drops in extreme gear combinations. A straight chainline (50×17 on a road bike) runs at about 97% efficiency. Cross-chained at 50×34, the chain is angled 6-7° and efficiency drops to roughly 92% — you are losing 15-20 W of a 300 W effort to friction in the chain articulation.
Pulley wheel size and chain wear amplify this. Worn 11-tooth jockey wheels and a chain past 0.5% elongation can cost another 3-5 W. If your power is honest but the bike feels sluggish, look at chainline first, chain cleanliness second, and pulley wear third.
References & Further Reading
- Wikipedia contributors. Bicycle gearing. Wikipedia
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