# Calculating CFM

If an air compressor generates 4 CFM of compressed air at 90 PSI, how much does it generate at 50 PSI, for example? That's what this page is all about. Calculating CFM output at various pressure levels for air compressors!

Over the years, I have received many requests for information about calculating CFM at different pressures. Almost all compressor manuals that have compressed air output information provide it at 90 PSI and sometimes at 40 PSI. Knowing the air compressor output at 90 PSI output is good, since many air tools are rated on their air consumption at that pressure.

But, what if you want to know how much air your compressor puts out at 55 PSI or 20 PSI? Turns out this isn't all that easy to figureusing the math, yet I've tried to help as much as possible below.

Calculating CFM is complex. An anonymous contributor provided the following insight regarding calculating cfm at different pressures. The anonymous contributor is not certain of the pinpoint accuracy of his formula. To paraphrase the contributor...

### Calculating CFM

"it's a very coarse" calculation. But, at least, using the formula, you can get some idea of how much compressed air your air compressor will provide at a variety of pressures. The contributor writes (I have re-formatted somewhat)...

"Having not been able to find a conversion table, I had to rely on the Ideal Gas Law:

### PxV = nRT

• where P = pressure
• V = Volume
• T = Temperature
• n is the amount of gas present
• and R is a constant depending on the units used for the other variables

Air is a mixture of gases and water vapor so would deviate from this law based on humidity and the molecular properties of the gases present. This law is also net generally applied to a flowing gas.

Assuming constant temperature, a simple interpretation of this law is that pressure is inversely proportional to volume.

So, for example, with a compressor rated to output 24 cfm at 175 psi, I got a result of 52.5 cfm at 80 psi. I consider this a very rough approximation."

I was finding this puzzling for my limited math skills so I asked the contributor: "Thank you! Would you mind explaining the steps? If I have a compressor rated for 5 CFM at 90 PSI, what would be the output flow, approximately, of that same air compressor at 35 PSI?"

Here was the response.

"Based on physical gas law, common sense, decreased volume results in increased pressure (and also temperature).

• P= pressure
• V= volume
• K= constant

So:

• P=K*(1/V)
• 90psi=K*(1/5cfm)
• Solving for K, we get a value of K= 450
• V=K*(1/P) so V=450*(1/35psi)= 12.86 cfm

**Very coarse approximation."

I sure hope that the above provides some assistance, folks. Algebra and me never got along, so I have never been able to solve for "X", or for "K" as this formula requires. Good luck to you. And thank you again to the anonymous contributor.

### Use a Flow Meter?

With my decided lack of math skills, it's my opinion that knowing how much CFM an air compressor is generating at any pressure, and if knowing this is critical to your use of the comressed air, then the first choice is acquiring an air flow meter. For compressed air use knowing the amount of flow out of the fitting and the pressure of the air in that flow is what we want.

The pressure of the air in the flow to be tested is controlled by the regulator at the compressor discharge. If there were a long air line between the on-compressor regulator and the point of air use, I would be inclined to install the regulator at the air tool end, ensuring the pressure of the flow at that point.

Between that regulator and the point of use, install an in-line flow meter. There are many makes and manufacturers out there, so Google compressor air flow meter and find one that suits your needs.

Another visitor offered the following information in the quest to figure out the best way of calculating CFM.

### An Engineer Comments on Calculating CFM

"Hi Bill, Just found randomly your page about Calculating CFM and I think you should correct it because the entire idea exposed there is wrong.

The key factor here is that the capacity of a compressor is always expressed at atmospheric pressure, not discharge pressure. A capacity of 20 cfm means that the compressor can suck up 20 cubic feet of air at atmospheric pressure every minute. Then it will compress this volume to the final operating pressure. So if the manufacturer indicates a capacity of 18 cfm, it will always be that, no matter the operating pressure.

But actually, this is not completly true because there will be a slight variation due to volumetric efficiency loss. As you increase operating pressure, the temperature rises into the pump and volumetric efficiency decreases, leading to a little decrease in capacity. This is why some manufacturers will post for example a capacity of 20 cfm at 90 psi and 18 cfm at 125 psi for the same compressor.

You cannot calculate it, you must measure it. So if you ask yourself "How much cfm my compressor will deliver if I use it at 50 psi and the manufacturer posted a capacity of 20 cfm at 90 psi?" Then... it will be quite the same capacity, maybe few cfm more. Hope this info useful."

Source: Alexandre Pare, ing., Conseiller technique, www.airindustriel.com

### Yet Another Perspective On Calculating CFM

"Hi Bill:

Ok, I have it. Here's the basics --- the air flow and CFM are based upon three things:

• 1: The larger the tank, the greater the supply of air (longer supply of CFM for a more gradual drop in pressure). This is the "capacitor" or "flywheel" in the system. However, this is only the "time" relationship. If you know your pressure and just want CFM, you don't care about the tank size.
• 2: Separate the Tank from the compressor (ie, compressor is off). The relationship between CFM and PSI is just linear. Ie, if you charge to 120 psi, and pull the electrical plug....if you get 8 CFM at 120 psi, you will get 4 CFM at 60 PSI. The pressure just "pushes" the air out, and with half the "push" you get half the air flow.
• 3: The motor and compressor. Assume the compressor to be 100% efficient, and the motor to be 80% efficient. A general rule of thumb is that a 5hp motor can produce 10 CFM at 100psi. The BEST way to determine your compressor-only CFM vs PSI is to know the steady state running current of your motor. Ie, my old 2hp 20 gall compressor pulls about 6.5 amps at 240VAC. Thats a power pull of 1560 watts. At about 746 watts per HP, that's 2.1 HP. 80% efficiency brings it to 1.7 true HP for compressing air. Going through a bunch of math, the flows I get for my compressor at 80/70/60/50/40/30 psi are: 4.9/5.6/6.5/7.8/9.7/12.9 CFM respectively.

Then, what you do is combine 2 and 3 above for a graph. More basically, if I know I need to blow out my sprinkler system with 50 PSI and 20 GPM, that's 50 PSI and about 3 CFM. If my air reservoir is being depleted and the compressor turns on, I will WORST CASE still get 7.8 GPM at 50 PSI.

Ideally, one would like a spreadsheet that gave CFM per PSI based on true HP. This would not include a third axis (time) which would include bleed-out based on tank size.

Best Regards, Greg"

Thanks Greg. I appreciate the contribution to this seemingly increasingly complex issue which is important to all air compressor users.

Are they right... can you or can you not use math to calculate the CFM of different air compressors at different output pressures, or is a flow meter your only option?

### Another perspective, from Lukas

Because some of the data on Lukas did not convert to Html satisfactorily, I've converted his document to a PDF. Please open Lukas' formula for calculating CFM here.

Here's a blog post from Exair that offers a formula to calculate CFM at any pressure!

Thanks for those that offered their guidance. If you have further insight, please add a comment.