Bicycle Gear Ratio and Speed Calculator
Enter the teeth on the chainring and the sprocket to get the gear ratio, then add the tire circumference and cadence (pedal revolutions per minute) to get the theoretical speed.
Formulas
- Gear ratio = teeth on the front chainring ÷ teeth on the rear sprocket. One turn of the pedals turns the rear wheel that many times.
- Distance per pedal revolution (m) = gear ratio × tire circumference (m)
- Theoretical speed (km/h) = distance per pedal revolution (m) × cadence (rpm) × 60 ÷ 1,000
- Cadence needed (rpm) = speed (km/h) × 1,000 ÷ (60 × distance per pedal revolution (m))
The distance per pedal revolution is what Sheldon Brown calls "development": wheel diameter × π × front teeth ÷ rear teeth (circumference = diameter × π). The speed and cadence formulas follow from that distance by simple unit conversion. The calculation uses exact fractions, and the result is rounded once, when it is displayed.
Entering the tire circumference
You enter the circumference yourself, in mm or m (1 m = 1,000 mm). The calculator does not work out a circumference from a tire size marking such as ETRTO. To find it:
- Measure how far the bike rolls in one turn of the rear wheel with the tire inflated and a rider on the bike (a "rollout" measurement).
- Use the circumference given in the tire maker's documentation.
- If you know the outer diameter, use circumference = diameter × 3.14159… (the Circle Calculator can do this).
Sheldon Brown's gear calculator page notes that a rollout varies with air pressure and tread type, and that deep, knobby tread typically measures about 1% smaller than thin tread. If accuracy matters, measure it yourself.
Examples
- 52/13 (ratio 4.000), circumference 2,096 mm, 90 rpm: 8.384 m per revolution, speed about 45.27 km/h (about 28.1 mph).
- 39/25 (ratio 1.560), circumference 2,096 mm, 80 rpm: about 3.270 m per revolution, speed about 15.69 km/h.
- 50/20 (ratio 2.5), circumference 2.1 m, 60 rpm: 5.25 m per revolution, speed 18.9 km/h.
- Working backward: 52/13, circumference 2,096 mm, 30 km/h: cadence needed about 59.6 rpm.
Limits
- The number of teeth must be a whole number from 1 to 200 (0, negative numbers and decimals give an error).
- The circumference must be greater than 0 and at most 10 m (10,000 mm).
- The cadence is from 0 to 999 rpm (at 0 rpm the speed is 0). If the cadence needed is above 999 rpm, the result is flagged as a value nobody can actually pedal.
Things to know
- To convert speeds between units, use the Speed Converter. For running pace, use the Running Pace Calculator.
- The theoretical speed differs from the real speed. Gear choice, the road surface, wind and slope are not included.
Source
- Sheldon Brown, "Gain Ratios": https://www.sheldonbrown.com/gain.html (checked November 1, 2026; the definition of development) and "Gear Calculator": https://www.sheldonbrown.com/gear-calc.html (checked November 1, 2026; the notes on rollout). Neither page gives a formula for speed from cadence; that part is derived here.
Frequently asked questions
What is a gear ratio?
The number of teeth on the front chainring divided by the number of teeth on the rear sprocket. The larger it is, the farther the bike moves per pedal revolution (a "harder" gear).
What is a good cadence?
It depends on the rider and the way they ride. This calculator does not suggest a target value.
Why does my bike computer show a different speed?
The circumference setting, the real circumference of the tire and slip can all differ from the values entered here.