# Calculating CFM

Calculating CFM; if your air compressor generates 4 CFM of compressed air at 90 PSI, how much does it generate at 50 PSI, for example?

Over the years, I have received many requests for information about calculating CFM at different pressures. It seems important for folks to be able to figure out, for a given air compressor, its flow ratio.

Just so we are clear what I mean by that, if a compressor of yours is producing 3 CFM of air flow at 90 PSI, what would that same air compressor discharge if you reduced the outflow to 80 PSI, or 60 PSI, or whatever?

Calculating CFM at different pressures has been a problem for me, I admit it.

Recently, however, an anonymous contributor provided the following insight regarding air compressor flow rates and air pressures.

I am not certain, nor is the contributor it seems, of the pinpoint accuracy of the formula. To paraphrase the contributor, "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.

Since I was finding this puzzling for my math skills, to say the least, 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.

• P= pressure
• V= volume
• K= constant
Based on physical gas law, common sense, decreased volume results in increased pressure (and also temperature).

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 this 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.

### An Engineer Comments on Calculating CFM

And a recent visitor offers the following:

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.

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

### And I Say

Is it true then... if I buy an air compressor that has a discharge flow of 5 CFM at 90 PSI, and I need compressed air at only at 40 PSI, is there no way that I can tell what that same compressor output will be at the lower pressure?

### 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 depleated 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.