Gear is almost everywhere. They are found in both car transmissions and windshield wipers. Bicycles, kitchen appliances such as utensils as the egg beater and even watches are used. At least it used to be like that. A gear is basically a set of gears that are connected together to increase or decrease the speed of rotation of the engine’s drive shaft.

The amount by which a gear system can change the rotational speed is a function of the relative size of the gears and is known as the gear ratio. It seems that the gear ratio formula is very simple. Basically, count the number of drive wheel teeth and divide by the number of drive wheel teeth connected to the engine. Even if your gear system consists of a few intermediate wheels called idlers, this is a simple calculation.

## What is Gear Ratio?

A gear ratio is the ratio of rotation. A gear with fewer teeth must rotate more times when it meshes with a gear that has more teeth. For example, the 15-tooth gear has to rotate 5 times to turn the 75-tooth gear 1 time.

Once you understand the concept of the circumference of a circle, the concept of gear ratio is easy to understand. Note that the circumference of a circle is equal to the diameter of the circle multiplied by pi (where pi is equal to 3.14159…).

So, if you have a circle or gear with a diameter of 1 inch, the circumference of that circle is 3.14159 inches.

Assume you have another circle 0.635″ in diameter (1.27″/2) and roll it. Its diameter is half the circle in the diagram, so you can see that it takes two full turns to cover the same 4-inch line.

This explains why two gears, one half the size of the other, have a gear ratio of 2:1. To travel the same distance as the big gear makes one revolution, the small gear needs two revolutions.

Let’s look at another example. If the drive wheel has 20 teeth and the drive wheel has 40 teeth, the calculation of the 40/20 gear ratio is simplified to 2/1 or 2:1. (The number of teeth of the driven wheel is always above the fraction or the first ratio).

This means that for every revolution of the drive wheels, the drive wheels make two revolutions. Similarly, a ratio of 1/2 indicates that the drive wheels rotate two revolutions for each revolution of the drive wheels. That is, the drive wheel rotates faster than the motor shaft.

Most gears you see in the real world have teeth. Teeth have three advantages.

- It prevents slipping between the gears. So, the axles of the gear are always exactly aligned with each other.
- They allow precise gear ratios to be determined. Just count the number of teeth of two gears and divide. So, if one gear has 60 teeth and the other has 20 teeth, the gear ratio when the two are connected is 3:1.
- They make sure that slight imperfections in the actual diameter and circumference of the two gears do not matter. The gear ratio is controlled by the number of teeth, even if the diameters are slightly apart.

## What is the formula for gears?

Calculate the gear ratio between two gears by dividing the circumference of the input gear by the circumference of the output gear. As you calculate the circumference of a circle, you can determine the circumference of a particular gear. Expressed as an equation, it looks like this:

**Gear ratio **= (π * diameter of input gear)/ (π * diameter of output gear)

Simplifying this equation, we can also obtain the gear ratio when just the gears’ diameters or radii are considered:

**Gear ratio **= (diameter of input gear)/ (diameter of output gear)

**Gear ratio** = (radius of input gear)/ (radius of output gear) The gear ratio I=d2/d1. d1 and d2 refer to the reference diameters of 2 mating gears (gear 1 is the driving gear, and gear 2 is the driven gear).

Similarly, we can calculate the gear ratio by considering the number of teeth on the input and output gears.

**Gear Ratio = Input Gear Teeth Number / Output Gear Teeth Number**

## How to Calculate Gear Ratio?

Calculating a gear ratio can be accomplished in a number of ways. For example:

### Calculating the gear ratio of bevel gears

When referring to bevel gears, we need to consider that it will be equivalent to the number of teeth of the driving gear divided by the number of teeth of the driven gear (RT= Z1 / Z2).

### Calculating the gear ratio of a gear train

For a gear train with two gears, the following steps must be done:

- Count the number of teeth. First, you need to count the number of teeth of the driving gear and the number of teeth of the driven gear.
- Divide the number of drive gear teeth by the number of drive gear teeth. The resulting number is the number of times the small driven gear must rotate to complete one revolution of the large gear.

The gear ratio is equal to the number of teeth on the driving gear divided by the number of teeth on the driving gear.

For gear trains with two or more gears, the following steps should be performed:

- Identify which gear is driven and which gear is driven gear and divide the number of teeth between the first and second gear. Intermediate gears have little effect on the gear ratio in the gear train.
- Follow the same procedure to find the gear ratio for a two-speed gear train.

### Calculating the gear ratio of gears and chain

This type of transmission consists of a chain of two gears and articulated links. In it, the gears rotate in one direction.

It is used to transmit motion between separate parallel shafts. The gear ratio is the result of dividing the number of driver gear teeth by the number of driver gear teeth.