How bicycle gears work
Follow a chain-drive cutaway to see why gear ratios trade wheel speed for torque, and what an easier gear changes.
Reviewed 2026-10-23
What does an easier gear change?
Gears change how many wheel turns you get per pedal turn, trading rotation rate against turning force.
Literal chain-drive teaching cutaway, laid flat on a bench. The 6- and 12-tooth sprockets are compact teaching hardware; the presets are separate rebuilt assemblies.
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What this guide explains
We follow the drive while pedalling with the rear hub engaged. The rear sprocket and wheel turn together. A real bicycle can freewheel while coasting; this bench does not model that decoupling or the derailleur's shifting mechanism.
The teeth pull one linked chain
The front sprocket advances the chain; the same chain drives the rear sprocket and engaged wheel hub.
The connected crank, sprockets and chain are emphasized. Near-side link plates are removed so the individual rollers and pin heads remain visible.
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The chain does not divide into two speeds
Both straight runs belong to the same closed loop. In a steady ideal drive, the same number of chain pitches passes each sprocket in the same time. An uncrossed chain makes the two sprockets turn in the same direction.
What carries torque
Under load, a difference between tight-run and slack-run chain tensions transmits torque. The picture shows engagement and pitch, not a calculated tension distribution or a fully loaded moving chain.
Front teeth divided by rear teeth
A full front-sprocket turn advances one chain pitch for every front tooth. Divide that count by the rear tooth count.
Compare the visibly different 12/6 and 6/12 sprocket assemblies. Each uses the same 18-pitch chain loop; the ratio follows tooth counts, not drawn diameter.
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Read a ratio in both directions
12 ÷ 6 = 2 wheel turns per crank turn. Reversing the sprockets gives 6 ÷ 12 = 0.5: one wheel turn takes two crank turns. Real combinations such as 48/24 and 24/48 have those same ratios, despite their different absolute sizes.
Why the pitch matters
Every neighboring pin centre in the bench is one equal chain pitch apart. Sprocket pitch radii use the chord relation p/(2 sin(π/N)), where p is pitch and N is tooth count. Small sprocket diameters therefore need not have the same proportion as their tooth counts.
The same cadence can move you farther
Wheel rpm equals cadence times gear ratio. Wheel circumference converts that wheel rate into an ideal road speed.
The bench stays at an fixed rest pose. The cadence calculator changes the shared-scale rate comparison and calculated outputs; it does not animate a rotating chain.
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Keep the comparison controlled
Change cadence while holding the selected gear fixed, then compare the gear presets at the same cadence. A higher ratio gives a faster wheel rate and more distance per pedal revolution. It does not guarantee that a rider can sustain that cadence under a particular load.
What the speed leaves out
The calculation assumes a 2.1 m wheel circumference, pure rolling and steady engaged drive. It omits tyre deformation, wind, slope, rider power limits and drivetrain losses. It illustrates kinematics rather than forecasting a ride.
More wheel turns mean less wheel torque
At the same crank torque, a lower ratio produces more wheel torque and fewer wheel revolutions. Ideal power stays the same.
Compare fixed 20 N·m crank torque in both assemblies. The same ideal model calculates wheel torque, both rotation rates and the equal ideal powers.
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Torque is not a force
Torque describes a turning effect. A 0.17 m crank needs about 118 N of perpendicular pedal force to make 20 N·m. At the wheel, ground-driving force equals hub torque divided by wheel radius; a larger wheel needs more hub torque for the same ground force.
Why power is conserved here
Rotational power equals torque × angular speed. A ratio of 2 doubles output rotation rate and halves output torque. A ratio of 0.5 halves output rotation rate and doubles output torque. Real friction makes output power lower than input power.
An easier gear lowers required pedal force
For the same required wheel torque, a lower ratio needs less crank torque, but more pedal turns cover the same distance.
A separate load comparison holds required wheel torque at 20 N·m and crank length at 0.17 m. It does not calculate a particular hill or rider's performance.
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How this relates to a hill
Climbing generally demands more wheel torque than level riding at a similar steady speed. A lower ratio lets the rider supply a given wheel torque with less crank torque. The price is less distance per pedal turn, so matching the old road speed would require a higher cadence.
How a real bicycle changes ratio
With the front chainring unchanged, choosing a larger rear cog lowers the ratio. With the rear cog unchanged, choosing a smaller front chainring also lowers it. This bench swaps both sprockets for a compact comparison; a derailleur uses other sprockets and manages chain slack.
Which change makes this climb easier?
A bicycle has a 36-tooth front chainring and an 18-tooth rear cog. Apply the ratio and torque tradeoff to a new choice.
Keeping the 36-tooth front chainring and wheel fixed, which rear cog needs less crank torque for the same required wheel torque?
- A 27-tooth rear cog, because it lowers the front/rear ratio
- A 12-tooth rear cog, because a smaller rear cog takes less effort
- Either cog, because the chain transfers the same power
Read the answer
36/27 is about 1.33, below the original ratio of 2. The needed crank torque falls in proportion to the ratio; distance per pedal turn also falls.
Count, choose cadence, compare torque
Front ÷ rear gives wheel turns per pedal turn. Lower ratios trade distance and wheel rate for greater wheel torque at equal crank torque.
Return to the same chain drive and compare both presets once more. Use the final navigation action to finish, or choose an earlier slide to revisit the tradeoff.
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Three questions for any gear
First, what is front teeth ÷ rear teeth? Second, what wheel rate does that give at the chosen cadence? Third, for the load at the wheel, what crank torque is required? A gear changes those relationships; it does not create energy.
Apply it outside the bench
On a bicycle with one front chainring, identify a larger and a smaller rear cog. Predict which gives more distance per pedal turn and which needs less crank torque for the same wheel torque. Finish this guide, or revisit the ratio comparison to check your reasoning.