# Gear Ratio RPM Calculator

Created by Gabriela Diaz
Last updated: Nov 16, 2022

Welcome to our gear ratio RPM calculator! ⚙ This easy-to-use tool will determine the input or output rotational speed in RPM of a two-gear system.

Most likely, you have noticed that gears are everywhere. We can find them in everyday objects like bicycles, cars, or clocks, as well as in industrial settings like gear pumps, wind turbines, and more.

• What a gear ratio is;
• How to obtain it; and
• How to calculate the RPM with the gear ratio.

## What is a gear ratio?

A gear system is a series of two or more gears that transfers motion (speed) or power (torque) from one gear to another. In a two-gear system, one is known as the driver or input gear, and the other is the driven or output gear.

A gear ratio is a mathematical ratio between the number of teeth on two gears that are meshed together. We can determine it by dividing the number of teeth of the input gear by the ones of the output gear, as shown in the following gear ratio formula:

$\footnotesize \text{Gear Ratio} = \cfrac{\text{N° of teeth, input gear}}{\text{N° of teeth, output gear}}$

Note that if the number of teeth of the input gear is larger than the ones of the output one, we'll get values greater than one. These can be expressed as decimal numbers, fractional numbers, or as an ordered pair of numbers separated by a colon, e.g., 4:1. This relationship results in larger speeds and smaller torque in the output gear.

On the other side, if the input gear is smaller than the output one, we'll get a value smaller than one. Similarly, we can express it as a decimal number, fractional number, or in terms of an ordered pair, e.g., 1:4 . In this case, there's a reduction in the output speed and an increase in the output torque. This torque amplification is known as mechanical advantage.

## How do I calculate the RPM from the gear ratio?

Now that we've seen what a gear ratio is and how to calculate it from the number of teeth of the gears, you now might be wondering: can I obtain the RPM of a gear by knowing the gear ratio of the system? and if so, how can I determine it? If this is the case, don't worry, you'll see this is quite simple.

In the previous section, we learned that we can calculate the gear ratio by relating the number of teeth of the input and output gears. However, we may also obtain this ratio by relating the input and output rotational (or angular) speeds, as shown in the following expression:

$\footnotesize \text{Gear Ratio} = \cfrac{\omega_{\text{in}}}{\omega_{\text{out}}}$

where:

• $\omega_{\text{in}}$ - Rotational or angular speed of input gear, in RPM; and
• $\omega_{\text{out}}$ - Rotational or angular speed of output gear.

Visit the angular velocity calculator to read what it is and how to calculate it!

If we already know the gear ratio, we can use the formula below to determine the output gear's rotational speed:

$\footnotesize \omega_{\text{out}} = \cfrac{\omega_{\text{in}}}{\text{Gear Ratio}}$

If the output is known instead, we can use the same formula to determine the input gear's rotational speed.

💡 Keep learning about gear speed calculations with our gear ratio speed calculator!

## How to use the gear ratio RPM calculator

Our gear ratio RPM calculator is an easy-to-use tool that will help you determine your gear system's input or output rotational speed in RPM. To use this calculator, follow these instructions:

1. If you know the gear ratio of your system, input it in the Gear ratio row.
2. If you're unsure about the gear ratio value, the calculator can determine it for you. Simply indicate the Input gear teeth number and the Output gear teeth number in the corresponding fields. The calculator will show the Gear ratio.
3. Now, just enter either the Input rotational speed or the Output rotational speed, and the calculator will display the other one.
4. That's it!

💡 Since all our tools work in any direction, you could also use this tool to figure the Gear ratio from the input and output rotational speeds if these are the known ones instead.

Gabriela Diaz
Input gear teeth number
Output gear teeth number
Gear ratio
:1
Input rotational speed
rpm
Output rotational speed
rpm
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