What the inputs mean
- Chainrings: the teeth on each front ring, for example 50/34.
- Cassette: the teeth on every rear cog, smallest to largest.
- Tire size: the ETRTO size on the sidewall (28-622 means 28 mm wide on a 622 mm bead seat) or a common marking such as 700x28c. The tool turns it into an approximate outside diameter. See the bike tire size chart for how markings map to rims.
- Crank length: center of the bottom bracket to center of the pedal axle, usually stamped on the inside of the crank arm. Only the gain ratio uses it.
The formulas
outside diameter ≈ bead seat diameter + 2 × tire widthgear ratio = chainring teeth ÷ cog teeth
gear inches = outside diameter (in) × chainring ÷ cog
development (m) = π × outside diameter (m) × chainring ÷ cogGear inches is the diameter of a wheel that, pedaled directly, would move the bike as far per crank turn. Development is the distance the bike rolls per crank turn.
Gain ratio is not in our tire source, so we define it here from first principles: the distance the bike moves divided by the distance your foot travels around the pedal circle. That works out to:
gain ratio = (wheel radius ÷ crank length) × chainring ÷ cogIt has no units, and it is the only one of the four that changes with crank length.
Worked example
A 50/34 compact with an 11 to 32 cassette on 700x28c tires (28-622). The outside diameter is about 622 + 2 × 28 = 678 mm, or 26.69 in.
- 50 × 11: 26.69 × 50 ÷ 11 = 121.3 gear inches, π × 0.678 × 4.545 = 9.68 m of development, and with 172.5 mm cranks a gain ratio of 339 ÷ 172.5 × 4.545 = 8.93.
- 34 × 32: 28.4 gear inches, 2.26 m, gain ratio 2.09.
The spread is 121.3 ÷ 28.4 = 428%. Some gears repeat: 34 × 11 gives 82.5 gear inches and 50 × 16 gives 83.4, only 1.1% apart. With a 2% threshold the grid marks those cells, so you can see which shifts across the front give you nothing new.
Comparing two setups
Fill in setup B to see both on one scale. The dots show where each setup has gears, where one reaches lower or higher, and where the gaps between gears are wider. For motorcycle chain drives, use the motorcycle gear ratio calculator. To turn gears into road speed, go to the bike speed calculator.
Questions
How do you calculate gear inches on a bike?
Multiply the wheel's outside diameter in inches by the chainring teeth and divide by the cog teeth. A 50 × 17 gear on a 700x28c tire (about 26.69 in) gives 26.69 × 50 ÷ 17 = 78.5 gear inches.
Does tire width change gear inches?
Yes, a little, because a wider tire makes the wheel taller. The same 50 × 17 gear gives 78.5 gear inches on 28-622 (678 mm) and 77.8 on 25-622 (672 mm).
What is the difference between gear inches and development?
Gear inches is an equivalent wheel diameter; development is the distance rolled per crank turn. Development = gear inches × π, converted to meters: 121.3 gear inches is 9.68 m.
Why does crank length only change the gain ratio?
Gear inches and development describe the bike only. Gain ratio compares the bike's travel with your foot's travel, and a longer crank moves your foot farther per turn. For 50 × 11 on 678 mm, 165 mm cranks give 9.34 and 175 mm cranks give 8.81.