# Calculating Output Speed Using Pulley Diameters and Input Speed

Knowing the correct shaft speed of both shafts on a belt-driven machine is important when performing machinery diagnostics. Ideally you would do this by first identifying the input and output speeds using a strobe light, photo tach or laser tach. Once you know the accurate speed of both components, use this formula to determine the multiplication factor:

**RPM Output/RPM Input = Multiplication Factor **

On a belt-driven fan the two primary speeds required are the RPM of the Motor and the RPM of the fan. For example, if you know the motor speed is 1778 rpm and the fan speed is 944 rpm the multiplication factor would be:

**944/1778 = .5309 **

The multiplication factor is input into the Nest when building a machine.

If you can’t get to the fan shaft to strobe it but you do know the pulley diameters here is how you can determine the output speed and the multiplication factor.

**Formula **

** RPM Input/RPM Output = Diameter Out/Diameter In**

Fan sheave diameter = 11.5 inches Motor sheave diameter = 6.5 inches

Output RPM = ? Input RPM = 1773

**Formula**

**RPM Input/RPM Output = Diameter out/Diameter In**

1773/RPM Output = 11.5/6.5

(RPM Output) (11.5) = (1773)(6.5)

(RPM Output) (11.5) = 11,524.5

**RPM Out = 1,002.13 **

This number does make sense since the fan will be running slower since it has the bigger pulley.

**Multiplication Factor = RPM Out/RPM In = 1002.13/1773 = .5652**

Input .5652 as the multiplication factor in the Nest.

Here are some video’s that discuss the importance of 1X and how to enter a multiplication factor into the Nest when analyzing belt driven machinery.

The importance of finding 1X: https://www.youtube.com/watch?v=ZWxjWiuQpv0

Entering Multiplication Factors into the Nest: https://www.youtube.com/watch?v=ugYyfdvwmf4

## 14 Comments

I would like to know how that above mentioning formula is derived

Laksan,

These formulas are in a variety of engineering texts/reference guides. My typical source is the “Marks Standard Handbook for Mechanical Engineers.”

The input speed of a transmission with a ratio fo 3.5:1 is 3600 RPM. What is the expected output speed? I couldn’t figure it out.

Andrew, A 3.5:1 gear ration means that the smaller gear needs to rotate 3.5 times to make the larger gear rotate once.

So for 3600 RPM input it would be 3600/3.5 = 1028.57

Regards,

Michael

I have a question. I have a air compressorand the pump is required to run 1050rpm. My motor runs 1375rpm and I have 6in pulley on motor and pump came with a 14in. I’m thinking I’m way under 1050rpm. More like 600rpm. Am I on the right path? I need to get at least 1000rpm thx

Good lord just do this (6.5) / (11.5) = _____- x rpm of motor.. How simple…..

If don’t know both input or output RPM and diameter of both pulley are known

Then how to find speed

Karim,

Hopefully you can see one or both of the shafts. If so you can use a strobe or a tach to get the speed of at least one of the shafts and then do the math as appropriate. If you can get to both shafts then use the strobe/tach and get the actual speeds on each and then compute the ratio.

Jesse,

I understand and thanks for the comment!The reason I wrote it that way is because we get questions with any combination of unknowns. Wasn’t trying to confuse folks but maybe I did!

Thanks for reading and we would love it if you would like to submit a post.

I have a 9″ pulley on furnace blower and 3 1/2″ on motor. 9″ pulleys are no longer available and I can only get an 8″ pulley. What combination of pulleys can I use to have same fan speed?

Lou,

Your current ratio is 3.5/9 = .388 so any combination of pulleys that provides that ratio will maintain the speed. If you use an 8″ pulley on the fan than a 3″ pulley on the motor will be close. 3/8 = .375 ratio.

If the motor is 1800 rpm your current fan speed is 1800(.388) = 698 rpm. A 3″ to 8″ pulley would give you 1800(.375) = 675

If my pump rotating at 100 rpm per min,,, how can i reduce the rpm to 25rpm per minute

if we have input rpm and output rpm so how do we calculate diameter of pulley for output and input

I have a 2.25 motor pulley and 3.25 fan pulley motor is single phase 3600 rpm what is the fan rpm?