Bicycle Gears

How fast do you ride in each gear? The chainring and the rear sprocket set how far one turn of the pedals takes you; your cadence does the rest.

Machine elementsBicyclesGear ratio

Inputs

Input examples

The wheel circumference includes the tyre: about 2105 mm for a 700×25c road tyre, 2290 mm for a 29×2.2 mountain-bike tyre, 2200 mm for a 28-inch city bike.

The bike

Chainrings (teeth)

Rear sprockets (teeth)

Wheel circumference (mm)

Your gear and cadence

Chainring in use

Sprocket in use

Cadence (pedal turns per minute)

Choosing a Gear

One turn of the pedals turns the rear wheel z_ring/z_sprocket times. A 50-tooth chainring with an 11-tooth sprocket gives 4.5 wheel turns — almost 9.6 metres per pedal stroke — while a 34×28 “granny gear” gives just 2.6 metres, perfect for steep hills.

Most riders are comfortable at 80–95 pedal turns a minute. Cyclists compare gears in development (metres per pedal turn) or in gear inches, a historic unit: the wheel diameter of a penny-farthing that would feel the same.

ring/cogwheel turns per pedal turn

90 rpmcomfortable cadence

gear inchespenny-farthing wheel

overlapmany gears are duplicates

Speed in Every Gear

km/h

big chainring

small chainring

your gear

Result

Enter the values above

Key Relations

Speed

Cadence n in rpm and circumference C in mm.

Example:

Development

The distance travelled for one turn of the pedals.

Gear Inches

The equivalent driving-wheel diameter in inches.

Sources & Verification

References

R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 13 (Gears—General).