With a 50-tooth chainring and a 20-tooth sprocket, the rear wheel turns 5/2 times, or 2.5, for every turn of the pedals. If the wheel’s circumference is 2.1 m, the bike travels 5.25 m per pedal revolution, and at a cadence of 90 rpm it goes 28.35 km/h (about 17.6 mph). The whole calculation is multiplying and simplifying fractions.
The gear ratio is a fraction of teeth
The ratio is written as chainring over sprocket. The chainring is the large gear at the pedals, which drives the chain, and the sprocket is the small one on the rear axle. The Wikipedia article Bicycle gearing says the gear ratio depends on the number of teeth on the crankset compared with the number of teeth on the rear sprocket (accessed October 17, 2026).
Leaving it as a fraction keeps the exact value. With 34 teeth in front and 28 in back you get 34/28, and dividing both numbers by their greatest common factor (GCF), which is 2, leaves 17/14. As a decimal that is ≈ 1.21, with an error under 0.005. The simplify ratios tool does this reduction for any pair of tooth counts.
A ratio greater than 1 makes the wheel turn more than the pedals. A ratio less than 1 makes the wheel turn less than the pedals.
From tooth counts to kilometers per hour
Development is the distance the bike travels in one full turn of the pedals. The same Wikipedia article describes it as the wheel’s circumference multiplied by the chainring-to-sprocket tooth ratio. On this page the circumference is a working assumption of 2.1 m. Measure your own wheel and substitute that value.
Worked example: 50 chainring, 20 sprocket, 90 rpm
You pedal with a 50-tooth chainring, a 20-tooth sprocket and a wheel with a 2.1 m circumference, at a cadence of 90 rpm. How fast are you going?
- Write and simplify the ratio. 50/20 = 5/2, because the GCF of 50 and 20 is 10.
- Find the development. 2.1 × 5/2 = 21/10 × 5/2 = 21/4 = 5.25 m per pedal revolution.
- Convert to meters per minute. 5.25 × 90 = 472.5 m/min.
- Convert to kilometers per hour. Multiply by 60 minutes and divide by 1000 meters: 472.5 × 60 ÷ 1000 = 28.35 km/h.
Result: 28.35 km/h (17.6 mph).
Check: in one hour that is 90 × 60 = 5,400 pedal revolutions, and 5,400 × 5.25 m = 28,350 m, which is 28.35 km.
The speed, distance and time with fractions guide covers this same change of units in detail.
| Chainring / sprocket | Ratio | Development | Speed |
|---|---|---|---|
| 52 / 13 | 4 | 8.4 m | 45.36 km/h (28.2 mph) |
| 50 / 20 | 5/2 | 5.25 m | 28.35 km/h (17.6 mph) |
| 50 / 25 | 2 | 4.2 m | 22.68 km/h (14.1 mph) |
| 34 / 28 | 17/14 | 2.55 m | 13.77 km/h (8.6 mph) |
| 34 / 34 | 1 | 2.1 m | 11.34 km/h (7.0 mph) |
Each speed comes from multiplying that row’s development by 90 and by 60 and dividing by 1000. Notice that halving the ratio also halves the speed, because the circumference and the cadence do not change.
Different pairs with the same ratio
A 34-tooth chainring with a 17-tooth sprocket gives 34/17 = 2, the same as 50/25. These are equivalent fractions: multiplying or dividing both terms by the same number does not change the quotient. With the same wheel and the same cadence, both pairs give 4.2 m per pedal revolution and 22.68 km/h. To check whether two ratios match, use the equivalent fractions comparison or convert the ratio with ratio to fraction.
What differs between the two pairs is the size of the parts, not the speed. To order ratios that do not simplify to the same number, the compare fractions calculator saves you from doing the divisions by hand.
What you gain and lose with a low ratio
A low ratio like 17/14 moves you forward only a little per pedal revolution: 2.55 m compared with the 8.4 m of a ratio of 4. In exchange, for the same effort at the pedal, the push that reaches the wheel is greater. This follows from spreading the same power over less speed, which is why a low ratio is chosen for climbing. It assumes power and cadence stay the same, which does not always happen on a real climb.
Comparing ratios follows the same logic as other everyday quotients. The unit price ranks offers by dividing, and slope as a fraction measures how much a path rises for each stretch of horizontal distance. In all three cases the result is a quotient read as how much of one thing per unit of another. The ratio, proportion and fraction guide explains why the same rules apply.
Practice
- Simplify the ratio for a 42-tooth chainring with a 28-tooth sprocket.
- With a 2.1 m wheel, how many meters does that combination travel per pedal revolution?
- How many km/h is that at 60 rpm?
Show the answers
- 42/28 = 3/2, with GCF 14.
- 2.1 × 3/2 = 3.15 m.
- 3.15 × 60 × 60 ÷ 1000 = 11.34 km/h (about 7.0 mph).
What the fraction does not measure
The ratio and the development describe the drivetrain. They leave out slope, wind and the rider’s weight, and they assume the chain does not slip. To know how much effort it takes to hold a speed, you need to add those data.
Sources
- Wikipedia, Bicycle gearing: the gear ratio as the number of teeth on the crankset compared with the number of teeth on the rear sprocket, and meters of development as the distance traveled per rotation of the pedals, equal to the wheel’s circumference times the chainring-to-sprocket ratio (accessed October 17, 2026). The 2.1 m circumference used here is an assumption of this page and does not come from that article.