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Rectangular to Round Duct Equivalent Calculator

Find the round duct that has the same friction loss as a rectangular or flat oval duct — or the rectangular width that matches a round duct at the height you have room for.

Method reviewed October 26, 2026. Version 1.0.0. How it works

Your inputs

Unit system

Result

Equivalent round diameter
11.46in

A 14 × 8 in rectangular duct is equivalent to a 11.46-inch round duct.

  • Equivalent means the same friction loss per foot at the same airflow — not the same area. The non-round section has more area, so its velocity is lower.
Aspect ratio (long side ÷ short side)
1.75
Next standard round size
12in
Area of the equivalent round duct
103.1in²
Area of the rectangular duct
112in²

Velocities at your airflow

Velocity in the rectangular duct
771fpm
Velocity in the equivalent round duct
838fpm
Show the working
  1. Huebscher: De = 1.30·(a·b)^0.625 / (a + b)^0.25
    1.30 × (14 × 8)^0.625 / (14 + 8)^0.25 = 11.46 in
  2. Velocity = CFM ÷ area
    600 CFM: 771 fpm in the rectangular section, 838 fpm in the round

What “equivalent” means

Two ducts are equivalent when they lose the same pressure per foot while carrying the same airflow. That is not the same as having the same area: a rectangular duct needs more area than its round equivalent, because its corners and longer perimeter add friction.

So the rectangular or flat oval duct carries the air more slowly than its round equivalent. The calculator shows both velocities when you enter an airflow.

The formulas

  • Rectangular (Huebscher): De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25
  • Flat oval: De = 1.55 × A^0.625 ÷ P^0.25, where the area A = π × b² ÷ 4 + b × (a − b) and the perimeter P = π × b + 2 × (a − b), with a the wide and b the narrow dimension
  • Round to rectangular: the calculator solves the Huebscher equation for the width at the height you choose, then rounds up to a whole inch

Any consistent unit works: inches in, inches out.

Using the result

Size the duct as round first (for example with the duct size calculator), then convert to the rectangular or flat oval shape that fits the space. Very flat ducts need much more sheet metal and lose more at fittings, so keep the sides as close to square as the space allows.

Worked example

These are the example values the calculator opens with, and the result the engine calculates for them.

Inputs

Convert
Rectangular → round
Rectangular width
14 in
Rectangular height
8 in
Airflow (optional, for velocities)
600 CFM

Result

Equivalent round diameter
11.46 in
Aspect ratio (long side ÷ short side)
1.75
Next standard round size
12 in
Area of the equivalent round duct
103.1 in²
Area of the rectangular duct
112 in²

A 14 × 8 in rectangular duct is equivalent to a 11.46-inch round duct.

Assumptions

  • Rectangular: Huebscher equation De = 1.30·(a·b)^0.625 / (a + b)^0.25. Flat oval: De = 1.55·A^0.625 / P^0.25 with A = π·b²/4 + b·(a − b) and P = π·b + 2·(a − b), where a is the major and b the minor dimension.
  • Equivalent diameters give equal friction loss per unit length at equal airflow; any consistent unit can be used.
  • Rounded rectangular widths are rounded up to the next whole inch.

Limitations

  • Equivalence holds for friction in straight duct. Fittings, transitions and very flat sections behave differently.
  • The flat oval formula is for the stadium shape (two straight sides joined by semicircles), not a true ellipse.

Frequently asked questions

What round duct equals a 14 × 8 rectangular duct?

About 11.5 inches by the Huebscher equation. Rounding up gives a 12-inch round duct.

Why is the rectangular duct’s area bigger than the round one?

Because equivalence is about friction, not area. A rectangle has more wall per unit of area, so it needs extra area to lose the same pressure per foot.

Does this work for velocity sizing?

No. Equivalent ducts have equal friction, not equal velocity. If you are sizing to a velocity limit, divide airflow by velocity to get the area you need instead.

Sources

  1. Equivalent Diameter of rectangular and oval ducts — The Engineering ToolBox. Huebscher equation De = 1.30·(a·b)^0.625/(a + b)^0.25.
  2. Exhaust Duct Design (ASHRAE Distinguished Lecture; friction per ASHRAE 2021 Handbook p. 21.7) — P. J. Brooks, SMACNA, for ASHRAE (hosted by ETEK). Duct friction loss in the ASHRAE 2021 Handbook uses Darcy–Weisbach with the Colebrook friction factor; absolute roughness is determined experimentally.

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