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# The relationship between bicycle gear ratio, cadence and speed

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Mar. 23, 2021

Since the engine is a human being, the bicycle seems to be able to go infinitely fast, but in fact, the gear ratio and cadence roughly determine the maximum speed. In this article, we'll take a look at the relationship between gear ratio, cadence, and speed.

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## When you buy a bicycle, your maximum speed is almost always determined.

It may come as a surprise to you, but it’s not an exaggeration to say that the maximum speed you can ride a bicycle at is almost decided when you buy it.

This is because the speed of a bicycle is determined by “energy! or “momentum! or “momentum!” (although of course there is no such factor at all), but it is calculated by a proper calculation.

The calculation of the speed of a vehicle using gears, not just a bicycle, is simple.

Gear ratio x Average cadence (rpm) x Tire size

The above formula can be used to calculate.

In simple terms, it is as follows.

- With tires that go forward XX cm in one rotation
- In gears that make the rear wheel rotate X number of times in one pedal stroke
- How many times you turn the pedals per minute

It’s simple.

### The only thing that changes after purchase is the “cadence (number of revolutions)

Of these, the only thing that will change after purchase is “how many times you pedal per minute,” in other words, the only thing that is up to you is “cadence.

In this sense, “energy!” or “momentum!” can be said to have something to do with it. However, there is a limit to the cadence that a human being can achieve, so you can’t go beyond the gear ratio x tire size barrier.

## Let’s actually calculate the speed of a bicycle.

This calculation assumes that you are riding on a flat road. In particular, please keep in mind that the conditions will be different on a slope.

### Tire (Wheel) Size

Tire size and tire circumference vary depending on what is mounted on the bicycle.

For example, a typical 700 x 23C tire size for a road bike will go 2.09 meters per revolution. Naturally, the larger the diameter of the tire and the thicker the tire, the longer the distance travelled per revolution.

### Gear ratios

The most difficult thing to understand is the gear ratio.

A bicycle moves forward by combining the gear on the side you pedal (chain ring) with the gear on the rear wheel (sprocket). The ratio of the number of teeth in the front and rear gears is called the “gear ratio.

For example, if the front gear has 50 teeth (labeled 50T) and the rear gear has 25 teeth (25T), the ratio would be “50T / 25T = 2.0 (gear ratio),” meaning that when you pedal and the front gear turns once, the rear gear turns twice.

The larger the gear ratio, the faster the bike will go, so the fewer teeth in the rear gear, the faster the bike will go. This is why heavier gears are smaller.

For your information, a typical city bike (so-called mamachari) has 32 teeth in the front gear and 14 in the rear gear, with a gear ratio of 2.285 being the most common. If you are using a road bike or a cross bike, the gear ratio would be around 2nd or 3rd gear.

#### Tire circumference x gear ratio = distance traveled in one revolution

Once you have these numbers, you can calculate the distance traveled by one rotation of the front gear.

For example, if you are running on 700 x 23C tires with a gear ratio of 2.0 (50T / 25T), the distance travelled by one rotation of the front gear will be “2.09m x 2 = 4.18m”.

### What is Cadence (RPM)?

Once you have calculated the distance you can go in one revolution of the front gear, it is now up to you to decide how much you want to revolve (pedal).

The number of revolutions of the front gear is called the “cadence”. Cadence is expressed in “rpm (rotations per minute). This is the same not only for bicycles but also for automobiles.

The cadence depends on the power of the person pedaling. If you are just riding around town, the average cadence is about 40-50 rpm. If you are a professional athlete, you will be able to maintain an average of 80 rpm or higher, and if you are serious before the goal, you can exceed 120 rpm.

Once you have your cadence, you can finally calculate your speed. Using the example above with 700 x 23C tires and a gear ratio of 2.0 (50T / 25T), we get the following.

Average Cadence | Calculation Formula (Tire circumference x Gear ratio x RPM x 60min) | Speed |
---|---|---|

50rpm | 2.09 x 2 x 50 x 60 = 12,540m | 12.5km/h |

60rpm | 2.09 x 2 x 60 x 60 = 15,048m | 15.1km/h |

70rpm | 2.09 x 2 x 70 x 60 = 17,556m | 17.6km/h |

80rpm | 2.09 x 2 x 80 x 60 = 20,064m | 20.1km/h |

90rpm | 2.09 x 2 x 90 x 60 = 22,572m | 22.6km/h |

100rpm | 2.09 x 2 x 100 x 60 = 25,080m | 25.1km/h |

120rpm | 2.09 x 2 x 120 x 60 = 30,096m | 30.1km/h |

200rpm | 2.09 x 2 x 200 x 60 = 50,160m | 50.2km/h |

In other words, if the tire circumference is 700 x 23C, which is common for road bikes, even city bikes can go over 50km/h (although a cadence of 200rpm is not realistic).

## The relationship between cadence and gear ratio

### What happens when you change gears at the same cadence?

Now let’s see how much the speed changes when changing gears at the same cadence.

For reference data, let’s assume that the front gear of Giant’s ESCAPE R3 cross bike is fixed to the outer gear and the rear gear is changed.

The ESCAPE R3, a cross bike, has slightly thicker tires than a road bike for speed, with a size of 700x30C, a tire circumference of “2.14m”, and a cadence of 60 rpm.

Gear | Tire circumference | Gear ratio | Cadence(rpm) | Speed |
---|---|---|---|---|

48T-32T | 2.14 | 1.50 | 60 | 11.5km/h |

48T-28T | 2.14 | 1.71 | 60 | 13.2km/h |

48T-24T | 2.14 | 2.00 | 60 | 15.4km/h |

48T-21T | 2.14 | 2.29 | 60 | 17.6km/h |

48T-18T | 2.14 | 2.67 | 60 | 20.5km/h |

48T-15T | 2.14 | 3.20 | 60 | 24.6km/h |

48T-13T | 2.14 | 3.69 | 60 | 28.4km/h |

48T-11T | 2.14 | 4.36 | 60 | 33.6km/h |

A cadence of 60 rpm is about as fast as you can go on a leisurely pottering trip, so even on a pottering trip you can go 33.6 km/h in top gear. That’s more than the speed limit for mopeds on a cross bike.

On the other hand, at a low gear and a cadence of 60 rpm, no matter how much you ride your $300 Giant cross bike, you can still be passed by those $100 city bikes.

Also, at a cadence of 60 rpm, you can only increase your speed by about 2 to 3 km/h even if you go up one gear. When you are pedaling a bicycle, you will feel “quite heavy” when you go up about 3 gears, but in reality, you can only go about 6km/h faster by maintaining the same cadence.

### How much does the cadence change the speed?

Now, let’s look at the speed of the ESCAPE R3, also a Giant cross bike, by increasing the cadence.

First, let’s increase the cadence to 80 rpm.

Gear | Tire circumference | Gear ratio | Cadence(rpm) | Speed |
---|---|---|---|---|

48T-32T | 2.14 | 1.5 | 80 | 15.4km/h |

48T-28T | 2.14 | 1.71 | 80 | 17.6km/h |

48T-24T | 2.14 | 2 | 80 | 20.5km/h |

48T-21T | 2.14 | 2.29 | 80 | 23.5km/h |

48T-18T | 2.14 | 2.67 | 80 | 27.4km/h |

48T-15T | 2.14 | 3.2 | 80 | 32.9km/h |

48T-13T | 2.14 | 3.69 | 80 | 37.9km/h |

48T-11T | 2.14 | 4.36 | 80 | 44.8km/h |

In first gear, the speed increased to 15km/h, and the maximum speed was about 45km/h.

Next, at 100 rpm.

Gear | Tire circumference | Gear ratio | Cadence(rpm) | Speed |
---|---|---|---|---|

48T-32T | 2.14 | 1.5 | 100 | 19.3km/h |

48T-28T | 2.14 | 1.71 | 100 | 22.0km/h |

48T-24T | 2.14 | 2 | 100 | 25.7km/h |

48T-21T | 2.14 | 2.29 | 100 | 29.4km/h |

48T-18T | 2.14 | 2.67 | 100 | 34.3km/h |

48T-15T | 2.14 | 3.2 | 100 | 41.1km/h |

48T-13T | 2.14 | 3.69 | 100 | 47.4km/h |

48T-11T | 2.14 | 4.36 | 100 | 56.0km/h |

In top gear, the speed was 56km/h. That’s about the same as a car on a regular road.

Finally, 120 rpm.

Gear | Tire circumference | Gear ratio | Cadence(rpm) | Speed |
---|---|---|---|---|

48T-32T | 2.14 | 1.5 | 120 | 23.1km/h |

48T-28T | 2.14 | 1.71 | 120 | 26.3km/h |

48T-24T | 2.14 | 2 | 120 | 30.8km/h |

48T-21T | 2.14 | 2.29 | 120 | 35.3km/h |

48T-18T | 2.14 | 2.67 | 120 | 41.1km/h |

48T-15T | 2.14 | 3.2 | 120 | 49.3km/h |

48T-13T | 2.14 | 3.69 | 120 | 56.9km/h |

48T-11T | 2.14 | 4.36 | 120 | 67.2km/h |

At 120 rpm, the speed exceeds 30 km/h even in 3rd gear, and about 67 km/h in top gear.

Again, a cadence of 120 rpm is at the level of a professional athlete, so conversely, even if a professional athlete were to ride the Giant ESCAPE R3 cross bike, he or she would only be able to reach a maximum speed of 70 km/h. Moreover, a cadence of 120 rpm in top gear is quite heavy and can only be sustained for a few minutes.

In other words, it is theoretically impossible to ride over 80km/h on a road bike like the one in the manga, when riding on flat roads with this bike.

We have looked at the relationship between the gear ratio, cadence, and speed of a bicycle.

When riding a bicycle, you don’t necessarily need to be concerned about speed, but for long rides such as cycling, you can get an approximate cruising speed based on your bicycle, the gears you can physically handle, and your cadence.

When choosing a bicycle, please consider what tire size and gear configuration is best for you.