How Are Gear Ratios Traditionally Expressed in Written Form?

Ever since their invention and refinement by the ancient Greeks and Chinese, gears have been an integral part of technology. Many types of gears are used to help drive cars, operate pulleys, work clocks, and do all sorts of other useful things.

But if you’ve ever looked at a gear diagram, you’ve probably seen how confusing the numbers and letters look. How do you calculate gear ratios when working with multiple gears?

Read on for everything you need to know about gear ratios, how they’re calculated, and their proper notation!

What Are Gear Ratios?

Essentially, the gear ratio is the expression of the size of one gear compared against the size of another. A smaller gear can turn a larger gear if you want to increase your torque. A larger gear can then turn a smaller gear if you want to lose torque but increase your output speed.

A gear ratio can quickly tell someone in the manufacturing process how much relative torque the driving gear applies to the driven gear, as well as how much relative speed the gears have.

Basically, it lets you take your input torque and speed, and quickly find the output torque and speed of your gears. This is important when working on your own projects, as well as for people working in the manufacturing industry.

Even if there are multiple gears in your setup, your gear ratio can help you quickly see the input to output ratio. This is very useful when looking at how much work you need to do or how much speed you’ll get out of your gears!

How Are They Calculated?

A gear ratio is calculated by looking at the number of teeth in your driving (or input) gear and comparing it against the number of teeth in your driven (our output) gear.

If your input gear has 30 teeth and your output gear has 60, you’ll need to turn your input gear twice to turn the output gear once. This gives you a gear ratio of 2:1.

But what does this ratio of 2:1 mean? In practical terms, it means your torque has been doubled, but your speed has been cut in half, assuming you have proper gear lubrication and that everything fits properly. In a motor, you’d double its initial torque value but halve the speed coming from the motor.

For example, if you have a sequence of self lubricating gears, you can find the total gear ratio by multiplying each individual gear ratio together. For example, if you had three gear ratios of 10:1, 2:1, and 3:1, your total gear ratio would be 60:1, or 10x2x3.

How Should Gear Ratios Be Expressed?

So if that’s how you calculate gear ratios, how should you express them in written form? There are a few standards that you should follow as you’re calculating and writing your gear ratios to ensure there’s no confusion.

The first thing to know is that your ratio is always expressed with a 1 in the denominator, even if that makes the numerator have a decimal. The denominator represents your input gear, and the numerator is your output gear. You can express it with a colon, as shown earlier, or as a fraction like 3/1.

Second, you can use the letter “u” to denote gear ratio and the letter “i” to denote total transmission ratio. This means that in the above equation with a 60:1 ratio, you could also write it as i=60.

Learn More Great Tech Facts

While they can be a headache at times, calculating gear ratios is an important and rewarding process. Combined with using the best gears for the job, you’ll save a lot of time and effort when you calculate your ratios properly!

If you’d like to learn more about automobiles and tech, be sure to check out the rest of our blog! We have plenty of great articles to help you stay informed on a wide range of subjects.