How to use the duct size equivalent calculator
- Choose Round for a rectangle or Rectangle for a round.
- Pick inches or millimeters and enter the sizes.
- Add an airflow in CFM if you want the air speed.
- Read the equivalent diameter or side, the areas and the air speeds in each duct.
Formula
Equivalent round diameter De = 1.30 (a b)^0.625 / (a + b)^0.25
Equal-area diameter = sqrt(4 a b / pi)
Air speed = airflow / area
1 CFM = 0.000471947 m3/s
The equation is the Huebscher relation. It gives the round duct that has the same friction loss per length at the same airflow, which is not the same as the round duct with the same area.
Three ducts
An 8 by 8 inch rectangular duct is equivalent to a round duct of 8.745 inches. With 400 CFM the rectangle moves air at 900 ft/min and the round duct at 958.9 ft/min. The round duct with the same area would be 9.027 inches, which has a lower friction loss, so the two are not interchangeable.
A 20 by 10 inch duct is equivalent to a 15.234 inch round duct. In the other direction, a 12 inch round duct with one side of 8 inches needs a rectangle 8 by 15.47 inches, an aspect ratio of 1.93 to 1.
Equal friction versus equal area
A rectangular duct has more wall area for the air to rub against than a round duct of the same cross-section, so it loses more pressure. The Huebscher equation shifts the diameter to account for that. This is why the equivalent round diameter is smaller than the equal-area diameter, and why duct charts that list friction use the equivalent value.
For sizing the airflow itself use the CFM calculator. Related water-pipe friction is in the Hazen-Williams pipe calculator, and light levels in the lighting lumens calculator.
Limits of the method
The equation works well for ducts with an aspect ratio up to about 8 to 1, and the page accepts up to 20 to 1. Tall narrow ducts are noisy and lose more pressure than the equation implies. Fittings, bends and flexible duct add their own losses, and a local mechanical code or a designer should have the final word on the size.
Assumptions and limits
- The equation applies to smooth, straight ducts in air at ordinary conditions.
- Sides may be in inches or millimeters. The air speed is shown in feet per minute and meters per second.
- Rectangle sides must not differ by more than 20 to 1.
- This is a sizing aid, not a design. Fittings, noise and local code are not covered.
Frequently asked questions
How do I convert a rectangular duct to an equivalent round duct?
Use De = 1.30 (a b)^0.625 / (a + b)^0.25. For 8 by 8 inches that gives 8.745 inches. The result has the same friction loss per length at the same airflow.
Why is equivalent diameter not the same as equal area?
Equal area gives the same airspace but not the same friction. A rectangle has more surface for the same area, so a round duct of the same area would have less friction loss.
What airflow should I use?
Use the design airflow for that run in CFM. The page then reports the air speed in the rectangle and in the round duct so you can check against your limits for noise.
What if the other side comes out very long?
Then the sizes you chose are far apart in shape. Pick a side closer to the round size so the aspect ratio stays moderate, within the 20 to 1 limit.