# Why 400 CFM per Ton? (Rule of Thumb Explained)

400 CFM per ton is regarded as the standard rule of thumb by many HVAC engineers and technicians for estimating the amount of airflow required based on the cooling capacity of an air conditioner. But, does it always 400 CFM per ton or there is more to it?

First of all, CFM stands for cubic feet per minute, and ton (full form: refrigeration tonnage) is the cooling capacity of an air conditioner expressed in ton, where 1 ton is equivalent to 12,000 btu/hr. So, 400 CFM per ton means a 1-ton air conditioner has or requires 400 CFM of airflow.

Now, the question is: where does this 400 CFM per ton come from? It is always the case or there is a catch to it? Also, when should we use 400 CFM per ton, and what is the range that is feasibly to use for quick estimation?

## Where Does 400 CFM per Ton Come From?

To trace the history of 400 CFM per ton, we need to go back to the enthalpy equation which is expressed as:

Q = mΔh

where,
Q = Coil load, btu/hr
m = Mass flow rate, lb/hr
Δh = Enthalpy difference, btu/lb

Since m = ρV, the equation becomes:

Q = ρVΔh

where,
Q = Coil load, btu/hr
ρ = Density, lb/ft³
V = Volume, ft³/hr
Δh = Enthalpy difference, btu/lb

Since we’re dealing with air, the density of air used here is 0.075 lb/ft³ (though the ISA’s density of air value is 0.0765 lb/ft³). The conversion from ft³/hr to ft³/min (which is the CFM that we want) is multiply by 60. After which, the equation becomes:

Q = 0.075 x 60 x CFM x Δh
Q = 4.5 x CFM x Δh

This is the commonly seen formula we used to calculate coil load or the capacity of the cooling coil in air handling units. I provided a tutorial in my post on how to size AHU cooling coils. Check it out to learn the full procedure.

Since we’re attempting to calculate the CFM per ton, the coil load, Q is 12,000 btu/hr.

Now, the Δh in the equation is the enthalpy difference between the on coil (entering air) and off coil (leaving air) conditions. Both the dry bulb and wet bulb (or relative humidity) must be determined and then we can use the psychrometric chart or an online psychrometric calculator to find the enthalpy value.

For example, given an off coil condition of 52/52°F DB/WB and a room design condition of 75°F at 50% relative humidity. Assuming the on coil condition is the same as the room design condition, the off coil enthalpy is 21.4 btu/lb and the on coil enthalpy is 28.1 btu/lb.

Putting the enthalpy into the equation, we get:

12,000 = 4.5 x CFM x (28.1 – 21.4)
CFM = 12,000 / 30.15
CFM = 398 (~400)

As we can see, the only variable to the CFM per ton value is basically the Δh. Take 400 CFM per ton as an example, to get that, the Δh must be:

12,000 = 4.5 x 400 x Δh
Δh = 6.7 btu/lb

Now, since the enthalpy is based on the on coil off coil conditions, any combination that makes the Δh = 6.7 btu/lb will result in 400 CFM per ton.

## Factors that Affect the CFM per Ton Value

In the above example, a room design condition of 75°F at 50% relative humidity is typical for comfort cooling. For other applications, this room design condition may differ which will change the CFM per ton value.

Also, it is assumed that the on coil condition is the same as the room design condition. However, it is not always the case. Furthermore, if for whatever reason the off coil temperatures are higher or lower, the CFM per ton value will change as well.

So, let’s look at a few examples of factors that could affect the CFM per ton value.

### 1) Low Latent Heat – 450 CFM per ton or more

At 52/52°F DB/WB on coil and 75°F at 50% RH off coil where the result is 400 CFM per ton, the sensible heat ratio (SHR) is about 83% if we plot it in the psychrometric chart (see below).

Now, if there are fewer people in the room, the latent heat ratio will be lower which means the sensible heat ratio will be higher. If the SHR is now 90%, the off coil enthalpy becomes 27.6 btu/lb and the CFM per ton value becomes:

12,000 = 4.5 x CFM x (27.6 – 21.4)
CFM = 12,000 / 27.9
CFM = 430

As we can see, the lower the latent heat, the higher the CFM per ton value. Vice versa, the higher the latent heat, the lower the CFM per ton value.

In data servers or computer rooms where the latent heat is almost 0%, we’re often looking at 450-500 CFM per ton. Contrarily, 300-350 CFM per ton is more likely the range for applications that have high latent heat such as auditoriums and conference halls.

### 2) With Outdoor Air – 300 CFM per ton or less

One critical assumption made to the 400 CFM per ton is that the room design condition is equivalent to the on coil condition. This is mostly applicable to residential buildings where outdoor air is usually not brought in.

However, in commercial buildings, outdoor air is almost always required. Hence, when the return air mixes with the outdoor air, the on coil enthalpy will increase significantly, leading to a lower CFM per ton value.

For example, if 10% of outdoor air is required at an outdoor air condition of 95/86°F DB/WB, the mixed air enthalpy is 30.3 btu/lb (read my post on how to size AHU cooling coil to learn how to find the mixed air enthalpy).

Assuming the same off coil condition, the CFM per ton value becomes:

12,000 = 4.5 x CFM x (30.3 – 21.4)
CFM = 12,000 / 40
CFM = 300

As we can see, when 10% outdoor air is introduced, the CFM per ton value drop significantly. So, when designing for commercial buildings where outdoor air is needed, be very careful of sticking to 400 CFM per ton because that could lead to an oversized system.

In one of my previous projects where I design for navy ships, the AHUs came at around 220 CFM per ton. Not only the people density is high, but the outdoor air requirement also pushed the on coil enthalpy higher, leading to a low CFM per ton value.

### 3) Return Air Heat Gain – 350 CFM per ton or less

Another instance where the on coil enthalpy will increase is when the return air gains a lot of heat due to:

• Return from ceiling plenum – lighting heat gain
• Return duct in unconditioned space – duct heat gain
• Inappropriate return grille location
• Hot air infiltration

For example, if due to whatever reason the return air temperature rises from 75°F to 78°F (sensibly from 50% RH), the on coil enthalpy becomes 29.0 btu/lb, resulting in about 350 CFM per ton given the same off coil condition.

### 4) Low Off Coil Temperature – 350 CFM per ton or less

Most of the time, 52/52°F DB/WB off coil temperatures are achievable for cooling coils. However, depending on the chilled water supply temperature, the off coil temperatures could be reduced to 50/50°F DB/WB. As such, the off coil enthalpy becomes 20.3 btu/lb.

If the on coil condition remain unchanged at 75% and 50% RH, the reduced off coil enthalpy will result in about 340 CFM per ton.

Although each of the above factors increase or decrease the CFM per ton value, they often affect the value together. What I mean is you may have low latent heat, less outdoor air but high return air heat gain. Or, you may have high outdoor air volume but low off coil temperature.

All of these factors may amplify or cancel out each other. The final result could remain at 400 CFM per ton. Only through detailed calculations we can truly know what has been designed and what is the expected outcome.

## Alternate Formula to Get 400 CFM per ton

Other than the Q = 4.5 x CFM x Δh formula, the basic heat transfer equation with ΔT can also be used to get 400 CFM per ton. It is expressed as:

Q = mcΔT and then Q = ρVcΔT

Now, the Q here is the sensible heat. In air conditioners, the cooling capacity is comprised of the sensible portion and the latent portion. See this post for more about sensible cooling capacity and the difference between sensible and latent heat.

The c is the specific heat capacity of air which is 0.24 btu/lb.°F. After which the c is included, the equation becomes the commonly seen:

Q = 0.075 x 60 x 0.24 x CFM x ΔT
Q = 1.08 x CFM x ΔT

Here, the ΔT is the difference between the off coil and on coil temperatures. Using the same value of 52°F off coil, 75°F on coil and 83% SHR, the CFM per ton value is:

Q = 1.08 x CFM x (75 – 52)
12,000 x 0.83 = CFM x 24.84
CFM = 9,960 / 24.84
CFM = ~400

Both equations are viable to use.