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*Gear ratios are a core science behind almost every machine in the modern era. They can maximize power and efficiency and are based on simple mathematics. So, how do they work?*

If you work with gear ratios every single day, this post probably isn’t for you. But, if you want to improve your understanding of this essential element of machine design, keep reading.

Gear ratios are simple as long as you understand some of the math behind circles. I’ll spare you the grade school math, but it is important to know that the circumference of a circle is related to a circle’s diameter. This math is important in gear ratio design.

## The basics of gear ratios and gear ratio design

To begin to understand gear ratios, it’s easiest if we start by removing the teeth from the gears. Imagine two circles rolling against one another, and assuming no slippage, just like college Physics 1. Give circle one a diameter of **2.54 inches**. Multiplying this by pi leaves us with a circumference of **8 inches **or, in other words, one full rotation of the circle one will result in **8 inches** of displacement.

Give circle two a diameter of **.3175 inches**, giving us a circumference of **1 inch**. If these two circles roll together, they will have a gear ratio of **8:1, since** circle one has a circumference **8 times** as big as circle two. A gear ratio of **8:1 means** that circle two rotates **8 times** for every time circle one rotates once. Don’t fall asleep on me yet; we are going to get more and more complex.

Gears aren’t circles because, as you know, they have teeth. Gears have to have teeth because, in the real world, there isn’t infinite friction between two rolling circles. Teeth also make exact gear ratios very easy to achieve.

Rather than having to deal with the diameters of gears, you can use the number of teeth on a gear to achieve highly precise ratios. Gear ratios are never just arbitrary values, they are highly dependent on the needed torque and power output, as well as gear and material strength. For example, if you need a gear ratio of **3.57:1**, it would be possible to design **two compatible gears**, one with **75 teeth** and another with **21**.

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Another big aspect that plays into the use of teeth in gears is manufacturing tolerances. *Most *gears can be built with fairly wide tolerances, and we know that the tighter a tolerance gets, the more expensive it is to manufacture. Teeth allow for the manufacturing of gears with set diameters to be somewhat variant, which means manufacturing is cheaper. Essentially, teeth become a buffer that allows for imperfections in gear manufacturing.

## Calculating gear ratios in machine design

While the basic gear ratio is fairly simple to understand, it can also get much more complicated. Large spans of gears, called gear trains, are often necessary in machine design. These consist of many gears, which are often stacked or laid in succession. Gear trains are necessary to achieve more robust gear ratios, as well as affecting the direction of rotation. Since **two connected** gears will rotate in opposite directions, gear trains are often needed to translate power through specific ratios without affecting rotation.

For example, using a **three-geared gear train, **with a gear ratio of **1:5,** would yield a **2500%** increase in rotation speed, while keeping the output in the same direction as the input. To give a more concrete example, a motor that applied **100 RPM** to the beginning end of this gear train would output **2500 RPM** on the other end in the same direction. You could also reverse where the power is applied and step down a **2500 RPM** motor to an output of **100 RPM**. These changes allow you to adjust both torque and speed.

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More complex combinations of gears and gear ratios yield some interesting machine designs. Theoretically, gear ratios are simple, but as an engineer, you may find yourself involved in complex gearing designs that seem just a little overwhelming. As with other engineering skills, it takes time to fully develop skills in gear ratio design.

## Transmissions - practical applications of gear ratios

Transmissions are some of the best examples of the practical applications of gear ratios. Anyone who has ridden in a car or other motorized vehicle has benefited from transmissions in some form. And every transmission is essentially just a bunch of gears and gear ratios packed closely together. Take a look at the incredibly helpful video from Learn Engineering below to learn more about how manual transmissions work.

It's important to note that while manual transmissions are falling out of favor with automakers, as they are not easy to incorporate in hybrid or electric vehicles, they function almost identically to how automatic transmissions work, as far as gearing goes. The main difference is in how the gears are shifted.

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Manual transmissions will involve action by the user (moving the gear shift and clutch) to shift, whereas automatic transmissions will use input from the car's onboard computer or, in very early models, mechanical input from either the car's speed or the car's engine.

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