If you want to replace rectangular ducts with round ducts, you will have to use the rectangular to round duct transformation formula. This formula determines the needed round duct diameter you need to match the rectangular duct airflow.
In HVAC, this is known as equivalent diameter. You will need a sufficient diameter of round ducts to keep the same CFM airflow running through the ducts.
Example: Let’s say you currently have a 6×7 inch rectangular duct that can handle 200 CFM airflow. What size round duct do you need to replace the 6×7 inch rectangular duct? Using the rectangular to round duct transformation formula will tell you that you need a 7.1-inch round diameter duct. This round duct size can handle 200 CFM airflow.
First, let’s look at the formula that translates rectangular duct size to round duct size. We will also look at a square to round duct transformation formula.
The easiest way to do this transformation is to consult the pre-calculated rectangular to round duct chart that tells you what size round ducts have an equivalent diameter to different rectangular duct sizes (with CFMs included):
Rectangular To Round Duct Transformation Formula
To determine the size of round duct you need to replace rectangular ducts, we have to account for two factors:
- Primary factor: Cross-section area of rectangular and round ducts. That simply means the area of the round duct through which the air is going to flow should match the area that was available in the case of rectangular ducts. This gives us a very good approximation of round duct diameter (below 10% deviation).
- Secondary factor: Ducts friction loss. To calculate the size of the round duct precisely, we need to take into account ducts friction loss. Due to different shapes of ducts, the friction fast-moving air makes with the duct, is different. This is not an overly significant factor and can be omitted (especially with low-CFM ducts).
Here is a visual representation of the cross-section of rectangular and round ducts:
To transform the area (A) of a rectangular duct to the area of round duct (circle A), we have to use this equation:
a × b = π × r2 and r = d/2
If we do little math on this equation and express d (equivalent diameter of the round duct), we get rectangular to round duct transformation formula:
That means that the equivalent diameter of a round duct is calculated as a square root of the length of rectangular duct (b) multiplied by the width of rectangular duct (a) and multiplied by a factor of 4 and divided by π (3.14). This is quite a mouthful.
Note: In the case of converting square to round ducts, both a and b are the same. Example 8×8-inch square duct has a length of 8-inches (a) and a width of 8-inches (b).
Here is an example of how you can use this formula (it’s not all that complicated). Let’s use our example from above (6×7 inch rectangular duct with 200 CFM airflow) and calculate the equivalent diameter of the round duct like this:
d = √((4×6-inches×7-inches)/π) = 7.31 inches
Now, from the chart below we see that the actual result should be 7.1 inches, not 7.31 inches. Have we calculated wrong? No. We have only accounted for the primary cross-section factor. That means we made an approximation with 3% deviance from the actual result (hence below 10% deviance).
To get the 7.1 inches, we have to account for the secondary duct friction loss as well. Here is the formula for calculating the friction loss in galvanized steel circular ducts with the turbulent flow:
Friction Loss Per 100 Ft = 0.109136 × q1.9 / d5.02
This is quite a complicated formula. q stands for airflow (measured in CFM) and d is the equivalent diameter.
Accounting for the friction loss is extremely complex. You have to account for Reynolds number (laminar vs. transient vs. turbulent flow), length of the ducts, the shape of the ducts, duct material, and so on.
The easiest way to account for the friction loss between rectangular and round ducts is to consult the pre-calculated values (chart, if you will).
Here is this chart from 80 CFM to 2,000 CFM airflow:
Rectangular To Round Duct Chart
|Duct Airflow (CFM):||Rectangular Duct Size (Inches):||Round Duct Size (Inches):|
|80 CFM||3 x 7, 4 x 5||4.9 Inch Diameter|
|100 CFM||4 x 6||5.33 Inch Diameter|
|120 CFM||4 x 7, 5 x 6||5.7, 6.0 Inch Diameter|
|140 CFM||4 x 8||6.09 Inch Diameter|
|150 CFM||3.5 x 10||6.26 Inch Diameter|
|160 CFM||4 x 9, 5 x 7, 6 x 6||6.4 Inch Diameter|
|180 CFM||4 x 10||6.74 Inch Diameter|
|200 CFM||6 x 7||7.1 Inch Diameter|
|230 CFM||4 x 12||7.31 Inch Diameter|
|250 CFM||6 x 8||7.55 Inch Diameter|
|270 CFM||4 x 14||7.81 Inch Diameter|
|300 CFM||5 x 12, 6 x 10, 7 x 8||8.3 Inch Diameter|
|400 CFM||7 x 10, 8 x 9||9.1 Inch Diameter|
|480 CFM||8 x 10, 9 x 9||9.8 Inch Diameter|
|600 CFM||8 x 12, 10 x 10||10.8 Inch Diameter|
|750 CFM||8 x 14, 9 x 12, 10 x 11||11.5 Inch Diameter|
|800 CFM||8 x 15, 10 x 12||11.8 Inch Diameter|
|1,000 CFM||10 x 14, 12 x 12||13.0 Inch Diameter|
|2,000 CFM||10 x 25, 12 x 20, 15 x 16||16.9 Inch Diameter|
With this chart, you can adequately replace existing rectangular (or squared) ducts with appropriately sized round ducts.
Example: Let’s say that you have 10×10-inch square ducts that allow for 600 CFM. What size round ducts should you replace it with?
Just check the chart above and you see that the equivalent diameter for a 10×10-inch rectangular duct is a 10.8-inch round duct.
In such a way, you can confidently replace any rectangular duct with a round duct. We hope this helps you make your decision and calculations easier.
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4 thoughts on “Rectangular To Round Duct Transformation (Formula + Chart)”
I’m attempting to change ductwork in my 1978 Hillcrest mobile home.
It’s 14” wide X 3 1/2” wide.
My question is what is the proper size in round ductwork?
Also what’s recommended in a job like this rigid or flex? Thank you!
Hi Dave, the simplest idea here is that the cross-section of the rectangular duct and round duct should be the same. By using the equivalent diameter and inserting 14-inch x 3.5-inch rectangular duct dimensions, you get the diameter: 7.9 inches. Basically, you need an 8-inch round duct. For confined spaces, flex ducts are preferrable. Seems like a better option here than rigid. Hope this helps.
I would like to change the existing galvanized rectangular duct size (310mmHx510mmWx27mLx3mm thickness) to round pipe (duplex 2205 sch10s).
what diameter of round pipe size should I choose? thank you and await for your reply.
Hi Han, alright, you have to calculate the equivalent diameter here. Here is the cross-section of your rectangular duct: 310mm × 510mm = 158,100 mm2. To calculate the diameter of an equivalent round pipe you can use this equation d = square foot of (4 × 310 mm × 510mm / 3.14). The resulting diameter in your case is 44.88 mm. So, practically, you should get the 45 mm diameter round pipe. Hope this helps.