Fluid Flow  Equivalent Diameter
Convert rectangular and oval duct geometry to a equivalent circular diameter  online calculator with imperial and SIunits.
The equivalent diameter is the diameter of a circular duct or pipe that for equal flow gives the same pressure loss or resistance as an equivalent rectangular duct or pipe. A round shape results in lower pressure drops and less fan horsepower to move the air and, consequently, smaller equipment.
The equivalent diameter of a rectangular tube or duct can be calculated as (Huebscher)
d_{e} = 1.30 (a b)^{0.625} / (a + b)^{0.25} (1)
where
d_{e} = equivalent diameter (mm, inches)
a= length of major or minor side (mm, inches)
b= length of minor or major side (mm, inches)
 Hydraulic diameter  the "characteristic length" used to calculate the dimensionless Reynolds Number
Example  Equivalent Diameter
The equivalent diameter of a 300 mm x 500 mm rectangular duct can be calculated as
d_{e} = 1.30 ((300 mm) (500 mm))^{0.625} / ((300 mm) + (500 mm))^{0.25}
= 420 mm
Rectangular to Equivalent Circular Duct Calculator
The calculator below is based on formula (1). The formula is generic and any unit can be used.
Equivalent diameters for some common mm rectangular duct dimensions:
For full table with larger dimensions  rotate the screen!
Circular equivalent diameter  d_{e} (mm)  

Duct side  a  (mm)  Duct side  b (mm)  
100  150  200  250  300  400  500  600  800  1000  1200  1400  1600  1800  2000  
100  109  133  152  168  183  207  227  
150  133  164  189  210  229  261  287  310  
200  152  189  219  244  266  305  337  365  
250  168  210  246  273  299  343  381  414  470  
300  183  229  266  299  328  378  420  457  520  574  
400  207  260  305  343  378  437  488  531  609  674  731  
500  227  287  337  381  420  488  547  598  687  762  827  886  
600  310  365  414  457  531  598  656  755  840  914  980  1041  
800  414  470  520  609  687  755  875  976  1066  1146  1219  1286  
1000  517  574  674  762  840  976  1093  1196  1289  1373  1451  1523  
1200  620  731  827  914  1066  1196  1312  1416  1511  1598  1680  
1400  781  886  980  1146  1289  1416  1530  1635  1732  1822  
1600  939  1041  1219  1373  1511  1635  1749  1854  1952  
1800  1096  1286  1451  1598  1732  1854  1968  2073  
2000  1523  1680  1822  1952  2073  2186 
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Equivalent diameters of some common inches rectangular ducts:
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Circular equivalent diameter (inches)  

Length  b  (inches)  Length  a  (inches)  
4  5  6  8  10  12  16  
4  4.4  4.9  5.3  6.1  
5  4.9  5.5  6  6.9  7.6  
6  5.3  6  6.6  7.6  8.4  9.1  
8  6.1  6.9  7.6  8.6  9.8  10.7  12.2 
10  7.6  8.4  9.8  10.9  12  13.7  
12  9.1  10.7  12  13.1  15.1  
16  12.2  13.7  15.1  17.5 
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Oval Equivalent Diameter (Ellipse)
Flat oval ducts have smaller height requirements than round ducts and retain most of the advantages of the round ducts. Fittings for flat oval ducts are difficult to fabricate or modify in the field.
The equivalent diameter of a oval duct or tube (ellipse) can be calculated as (Heyt & Diaz)
d_{e} = 1.55 A^{0.625 }/ P^{0.25} (2)
where
A = crosssectional area oval duct (m^{2}, in^{2})
P = perimeter oval duct (m, inches)
The crosssectional area of an oval duct can be expressed as
A = π a b / 4
where
a = major dimension of the flat oval duct (m, in)
b = minor dimension of the flat oval duct (m, in)
The perimeter of an oval duct (ellipse) can be approximated to
P ≈ 2 π (1/2 ((a / 2)^{2} + (b / 2)^{2}))^{1/2} (2b)
Oblong Ducts
Equivalent diameters of oblong ducts or pipes can be expressed as
d_{e} = 1.55 (π b^{2} / 4 + a b  b^{2})^{0.625}/(π b + 2 a  2 b)^{0.25} (3)
Hydraulic Diameter
Note!  equivalent diameter is not the same as hydraulic diameter. The hydraulic diameter express the rate between the area section of the duct or tube, and the wetted perimeter of the duct or tube. Hydraulic diameter is used to determine if the flow is laminar or turbulent and to calculate the pressure loss.
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