Bicycle Gear Mechanism Explained: Drivetrain Parts, Gear Ratio Formula, Diagram and Calculator

How bicycle chain gearing works

The crank turns the chainring. Chain links engage successive teeth and carry motion to the rear sprocket, which drives the rear wheel while the freewheel is engaged. A larger chainring or smaller rear sprocket increases wheel revolutions per crank revolution. The ideal wheel torque changes inversely.

The animation shows one selected pair. It does not show a derailleur shifting or solve chain length for a real frame. Smooth pitch-circle motion neglects the small chordal speed variations of a discrete chain. The drawn tooth counts follow the inputs; tooth profiles are illustrative.

Parts in the drawing

The crank and pedal rotate about the bottom bracket, the chain runs around both sprockets, and the rear sprocket rotates with the wheel. The bicycle frame holds the shaft centres. A real multi-speed drivetrain also needs the appropriate derailleur, chain tension and component compatibility.

Comparing bicycle gearing

Use the calculator to compare selected ratios for road, utility, mountain, cargo or track bicycles. Lower ratios trade road distance per revolution for greater ideal wheel torque. Internal hub gears introduce another ratio that is not included here.

Gear ratio and development

r = Tf / Tr; D = r C; Twheel / Tcrank = 1/r for ideal transmission. Tf and Tr are tooth counts and C is rolling wheel circumference in metres. D is metres per complete crank revolution.

At cadence n in crank revolutions per minute, speed would be D n / 60 metres per second. This kinematic relation does not calculate aerodynamic resistance, tyre losses, power, traction or sustainable climbing speed.

Worked example

With a 50-tooth chainring, 11-tooth sprocket and 2.10 m wheel circumference: r = 50/11 = 4.545, D = 4.545 × 2.10 = 9.545 m per crank revolution. Ideal wheel torque is 11/50 = 0.22 times crank torque.

Changing the rear sprocket to 25 teeth makes r = 2.0, D = 4.20 m/rev and torque factor 0.50. At the same crank torque, ideal wheel torque increases, while distance per revolution decreases. Neither combination guarantees a particular hill-climbing performance.

What this comparison does and does not cover

Tooth-count ratios make direct gearing comparisons straightforward. A real drivetrain must also satisfy chainline, chain length, derailleur capacity and component compatibility. This calculator does not prescribe compatible parts, maintenance intervals, service adjustments or efficiency values.

Frequently asked questions

Why are gear ratio and wheel revolutions the same number?

For the modeled direct rear-hub connection, the ratio is exactly the number of wheel revolutions for one crank revolution. They are two descriptions of the same relationship.

Does a bigger wheel change the tooth-count ratio?

No. It changes distance travelled per wheel revolution, so development increases while the sprocket ratio stays unchanged.

Why does a low gear have more torque?

Ignoring losses, the same transmitted power at a lower output rotational speed corresponds to greater output torque. The torque factor is the reciprocal speed ratio.

Does the chain keep turning while coasting?

On a freewheel-equipped bicycle the wheel can overrun the sprocket while coasting. This animation shows continuous pedalling with the drive engaged, not coasting.