Machine Design 101: Gear Ratios

Gear ratios are a core science to 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 even just a little in the essential machine design realm of gear ratios, keep reading. Gear ratios are simple if you understand how circles work. I’ll spare you the grade school math, but the circumference of a circle is related to a circle’s diameter. This math plays right into gear ratio design.

To begin to understand gear ratios, it’s easiest if we remove the teeth from the gears. Imagine 2 circles rolling against one another, assume no slippage, just like college Physics 1. Circle one will have 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 circle one will result in 8 inches of displacement. Circle two will have a diameter of .3175 inches, giving us a circumference of 1 inch. These two circles will roll together and have a gear ratio of 8:1 since circle one is 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, 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 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 needed torque and power output weighed with gear and material strength. If you need a gear ratio of 3.57:1, it would be possible to design 2 compatible gears, one with 75 teeth and another with 21.


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 zone for gear manufacturing imperfections.

The basic gear ratio is fairly simple to understand, but as you likely no, nothing is ever just that simple. Large spans of gears, called gear trains, are often necessary in machine design. These  consist of many gears that are often stacked or laid in succession. Gear trains are necessary to achieve more robust gear ratios as well as paying attention to the direction of rotation. Since 2 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 3 geared gear train with the gear ratios of 1:5 would yield a 2500% increase in rotation speed, while keeping the output in the same direction as the input. To give more concrete numbers to this abstract setup, a motor that applied 100 RPM to the beginning end 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. In these ways, you can adjust torque, and speed.


More complex combinations of gears and gear ratios yield some interesting machine designs. Ultimately, understanding gear ratios means understanding ratios themselves. Theoretically, gear ratios are simple, but you may find yourself in complex gearing designs that seem just a little overwhelming. Like with all of your other engineering skills, it will take time to refine your gear ratio prowess.

Sources: How Stuff WorksPractical MachinistWind Power EngineeringMachine Design

Images: [1], [2], [3]

Profile photo of Trevor English
Trevor is a civil engineer by trade with an extensive background in internet media and marketing. He loves finding new and interesting topics and bringing them to the rest of the world.

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