# Gear Inches: Understanding the Historical Significance and Practical Application

If you've ever looked into bicycle gearing, you've probably come across the term "gear inches." It's a common imperial measure that gives a rough idea of how far a bike will travel for each revolution of the crank. In this article we'll explain where this term came from and what it actually means when used to express gear ratios.

## The origin of gear inches

In the 1870s and 1880s, most bicycles were penny-farthings. These bikes had a huge front wheel with the crank connected directly to the hub. With each revolution of the crank, the wheel went around exactly one time. The larger the front wheel, the faster a penny-farthing would travel if pedaled at a constant cadence.

Therefore, penny-farthings were commonly described by the measured diameter of their wheel. A 54-inch penny-farthing would generally have a higher max speed than a 52-inch version, but would be slightly harder to ride up hills.

Another unfortunate characteristic of the penny-farthing was that the larger the wheel, the higher the center of gravity, and as a result, the bike was more dangerous to ride. Over time, innovations were made that made them safer to ride. Chain drives and different sized gears at the crank and hubs enabled smaller wheels to be spun at a faster rate than the pedals.This allowed for a smaller, safer bike that performed as well as the largest penny-farthings available.

These geared bikes required new terminology to help people understand how they compared in performance to their traditional penny-farthings. If a bike with 28-inch wheels traveled at the same speed as a 56-inch penny-farthing when pedaled at the same cadence, it was said to be geared at 56 gear inches.

The tradition of using inches to express bicycle gearing started as a way to make comparisons with penny-farthings easier.

## Measuring wheel rotations

To understand how gear inches work in practice, we need to calculate the distance a wheel travels for each rotation. This is determined by multiplying the wheel's diameter by π (approximately 3.14) to find the circumference of the wheel.

```
wheel circumference = π * wheel diameter
```

Using this formula, we can calculate how far different sized wheels will travel with each rotation. For example, a 28-inch wheel has a circumference of 28 times 3.14, which gives us approximately 87.92 inches.

With every rotation, a 28-inch wheel will roll forward roughly 87.92 inches.

## Comparing bikes

We can now think through how bike comparisons were made to penny-farthings as a way to determine gear inches.

Consider two bikes.

First, a modern bike with 28-inch wheels. It's geared so that the rear wheel will rotate twice with one turn of the pedals.This means it has a 2:1 gear ratio. We can derive how far it will travel with a single pedal rotation by taking double the wheel's circumference (because it rotates twice), which is around 175.84 inches.

The second bike is an old 56-inch penny-farthing where one turn of the pedals turns the wheel a single time. This is a 1:1 gear ratio. It will travel the wheel's circumference, which is roughly 175.84 inches, with one turn of the pedals.

Both of these bikes will travel the same distance with each turn of the pedals. By comparing our modern, geared bike to a hypothetical penny-farthing, we can determine that it has a 56-inch gear.

## More on gear ratios

In our above example, we stated that our modern bike had a 2:1 gear ratio. It's important to understand that this can result from many different gear combinations. For example, you could have a 40-tooth front chainring with a 20-tooth rear sprocket (40:20). Another possibility is a 50-tooth front ring and a 25-tooth rear (50:25). Both of these combinations are equivalent to a 2:1 ratio.

Gear ratios are calculated as the number of teeth on the front chainring divided by the number of teeth on the rear sprocket. So, our 40-tooth chainring with a 20-tooth rear sprocket results in a gear ratio of 2 or 2:1.

```
gear ratio = front teeth / rear teeth
```

Understanding gear ratios allows us to calculate how many times the rear wheel of a bike will turn with each pedal rotation, regardless of the combination of gears used.

## Calculating gear inches

Bringing all this together, we can now derive a formula for calculating the gear inches for any bike with any gear combination.

If you know the number of teeth on the front chain ring, the number of teeth on the rear sprocket, and the diameter of the rear wheel, you can determine how far it will travel with each turn of the pedals. To do this, calculate your gear ratio and your wheel circumference, then multiply them together.

```
distance = front teeth / rear teeth * π * wheel diameter
```

We can equate this distance to a hypothetical penny-farthing with an unknown wheel diameter. This diameter is the gear inches we're solving for. It's the diameter of a wheel that will travel the same distance as our bike with one rotation.

```
distance = π * gear inches
```

Since both of these equations are equal to the same distance, we can set them equal to each other.

```
π * gear inches = front teeth / rear teeth * π * wheel diameter
```

We can simplify this by dividing both sides by π. This gives us the formula for gear inches.

```
gear inches = front teeth / rear teeth * wheel diameter
```

With this formula, you can calculate gear inches for every gear combination of any bike. It's simply the teeth on the chain ring divided by the teeth on the sprocket, multiplied by the diameter of the wheel.

## Comparing gears

Calculating gear inches allows you to understand your bike and its gears. You can then compare the gear inches of each combination of gears possible on your bike against each other.

For example, if your bike had a 1x gravel bike with a 42T chainring, 10-44T rear cassette, and 700c wheels (~28-inch tire diameter), you can determine that it has a lowest gear of 26.7 inches, a highest gear of 117.6 inches, and gear range of 440%.

You can determine how big the steps are between sequential gears by comparing them. You'll find that as sprockets get larger, bigger jumps in the number of teeth are needed to keep the relative distance between the gears consistent.

They help us navigate the endless drivetrain options available for today's bikes, just as people in the late 1800s used gear inches to understand how new styles of bicycles would perform and feel.

The old penny-farthing lives on as a baseline to compare our modern machines against.