Calculating Rectangular Ducting to Round Ducting

This article will show you how to convert between a rectangular duct and a round duct. When converting these ducts you typically match airflow capacity, not just area. The most common approach uses the equivalent diameter formula based on equal friction loss (more accurate for HVAC design than simple area matching).

De ​= 1.30 × (a+b)0.25 / (a×b)0.625

De being the round ducts diameter 
A&B being the sides of the rectangular duct

This comes from principles in fluid dynamics and is widely used in HVAC sizing.
 

Step by Step

(Example: 20 In x 10In Rectangular duct)

1. ​Identify the values
   a = 20
   b = 10
   
    
2. Use the formula
   De ​= 1.30 × (a+b)0.25 / (a×b)0.625
   
    
3. Multiply A + B
   20 x 10 = 200
   
    
4. Raise to power 0.625
   200^0.625≈27.1 OR 0.625 = 625/1000 = 5/8
   
    
5. Add a+b
   20+10 = 30
   
    
6. Raise to power 0.25
   30^0.25 = 2.34 OR 0.25 = 1/4
   
    
7. Divide
   27.1 / 2.34 = 11.58
   
    
8. Multiply by 1.30
   1.30 x 11.58 = 15.05
    

The end result would be 20 x 10 rectangular duct is the equivalent of a 15" round duct. 

How to solve for round ducting to rectangular

1. A = 3.14D^2 / 4
   
   
    

1. Equivalent diameter formula (rectangular → round)

The standard formula is: