Last updated: Jul 31, 2024

Gear Ratio RPM Calculator

Q: What is the gear speed of 30 rpm in rad/s?

The gear speed in rad/s is π . To obtain gear speed in rad/s from rpm: multiply the gear speed in rpm by 2π and divide by 60 .

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Table of contents

What is a gear ratio?What is the difference between gear rpm and gear speed?How to use our gear ratio rpm calculator?More gear related calculators FAQs

Are you wondering how to find the rpm of your gear system? Don't fret! Our gear ratio rpm calculator will help you do that in a flash!

After reading the article below, you'll have learnt more about:

The relation between the gear ratio and the gear speed in rpm; and
How to use our gear ratio rpm calculator.

What is a gear ratio?

Gears are ubiquitous mechanisms, and you can find them in watches, bicycles, cars, etc. The gear ratio is an important parameter that describes the characteristics of a gear system.

The gear ratio is the ratio of the number of teeth of the driver gear to the number of teeth of the driven gear.

Now that we know what does gear ratio mean, the relationship between gear ratio and gear rpm is given as:

\footnotesize \text{Output gear rpm} = \frac{ \text{Input gear rpm} }{ \text{Gear ratio} }

Using the above relation, we can calculate the gear rpm by using the gear ratio.

What is the difference between gear rpm and gear speed?

The gear rpm and gear speed are the quantities used to represent how fast an object rotates.

Gear speed indicates how much angle is spanned by a rotating object per second. To convert from gear rpm to gear speed in $\text{rad}/\text{s}$ : multiply gear rpm by $\pi/30$ .
Gear rpm indicates how many rotations a rotating object makes per minute. To convert from gear speed in $\text{rad}/\text{s}$ to gear speed in rpm: multiply gear speed in $\text{rad}/\text{s}$ by $30/\pi$ .

💡 If you'd like to learn what RPM (revolutions per minute) are and how to calculate them, you can check our RPM calculator to read more!

How to use our gear ratio rpm calculator?

To use our calculator, use the following guidelines:

First, you must know about the number of teeth present in your gear system. The gear system includes the input (driver) and output (driven) gear. Input gear is the gear that drives the output gear.
Insert the number of teeth for input and output gear in Input gear teeth and Output gear teeth fields.
Right after you insert the teeth information, you will obtain the Gear ratio.
Now enter the rpm of your input gear to obtain the output gear rpm.

Great! Now you know how to use our calculator to find output gear rpm quickly.

FAQs

What is the gear speed of 30 rpm in rad/s?

The gear speed in rad/s is π. To obtain gear speed in rad/s from rpm: multiply the gear speed in rpm by 2π and divide by 60.

How to calculate the output torque from gear ratio?

To calculate the output torque from the gear ratio, use the following guidelines:

Obtain the information about the number of teeth present in the input and the output gears;
Take the ratio of the number of teeth of the output gear to the number of teeth of the input gear to find the gear ratio; and
Find output torque by multiplying the input torque by the gear ratio.

Awesome, now you know how to find the output torque given you know the gear ratio and input torque of the gear system.

How do I find the gear speed in rpm given its speed in rad/s ?

To calculate the gear speed in rpm, use the following steps:

Multiply the gear speed in rad/s by 60;
Now divide the obtained quantity from step 1 by 2π to obtain the gear speed in revolution per minute (rpm); and
Cool!, Now you can easily convert the gear speed in rad/s to rpm.