Preliminary numbers for estimating and for checking a drawing. Use inside dimensions. The duct design, the equipment manufacturer and the local authority having jurisdiction come first.

Maintained by BuildSolver · Updated October 17, 2026

Calculator · HVAC ducts

Rectangular to round duct calculator

A 10x12 duct carries air like a round duct of 11.96 in.: at the same airflow both lose the same pressure per foot. Their areas differ, though. The rectangle has 120 sq in. of cross-section, and the 11.96 in. round has 112.4 sq in. This page converts a duct shape you already have, from a rectangle to its round equivalent or from a round size to a rectangle when one side is fixed, such as the depth of a joist bay. To size a duct from the CFM and a friction rate instead, use the duct sizing calculator.

Choose a rectangle to round conversion, or a round to rectangle conversion with one side fixed.
Type the inside width and height, or the round diameter and the side you cannot change. Add the airflow in CFM if you want velocity and friction.
The result shows the round diameter, or the whole-inch rectangle, with areas, sheet metal per foot and, with an airflow, velocity and friction.

Example result for the default inputs

10x12 in. rectangular duct, inside dimensions, 400 CFM.

Equivalent round diameter

12.0 in.

Next round size up

12 in.

Aspect ratio

1.2:1

Calculation details
Stock size	The equivalent is 11.96 in. before rounding, a hair under 12 in.
Cross-section area	Rectangle 120 sq in., its 12.0 in. equivalent round 112.4 sq in. (1.07 times). Equal friction and airflow define the equivalent, and the areas differ.
Sheet metal per foot of length	Rectangle 3.67 sq ft, round 3.13 sq ft (12.0 in. round).
Velocity at 400 CFM	Rectangle 480 FPM, its 12.0 in. equivalent round 512 FPM. The rectangle is slower because it has more area.
Friction at 400 CFM	0.0357 in. w.c. per 100 ft, galvanized sheet metal. The rectangle and its equivalent round lose the same.

Use inside dimensions. Liner or insulation inside the duct reduces the clear size, and the equivalent applies to the clear size.
Rectangular sheet metal only. Flex duct and fibrous glass duct board are not modeled here.

For estimation purposes only. Consult a licensed engineer for final designs.

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How the equivalent is worked

A rectangular duct and a round duct are equivalent when the same airflow gives the same friction loss per 100 ft in both. The equation behind that comparison is Huebscher's, and it is the one the ASHRAE circular equivalents table is built on. The reverse conversion searches whole inches for the smallest side that does not fall short.

Equivalent round diameter: D = 1.30 x (a x b)^0.625 / (a + b)^0.25a and b are the inside width and height in inches. A 10x12 duct gives 11.96 in., and 12x12 gives 13.1 in. The result is rounded only for display.
Round to rectangle: smallest whole-inch b such that D(a, b) is not below the round diameterWith one side held fixed, the equivalent grows with b, so the page tries b = 1, 2, 3 and so on until the equivalent reaches the round size. For a 10 in. round and an 8 in. side the answer is 8x11 in., which has an equivalent of 10.2 in. The next smaller whole inch, 8x10, gives 9.8 in. and falls short.
Area and velocity: V = CFM / (a x b / 144) (FPM), round: V = CFM / (pi x D^2 / 576)Equal friction and equal airflow define the equivalent, while the areas differ. A 120 sq in. rectangle is 1.07 times the area of its 12.0 in. round, so at 400 CFM the air moves at 480 FPM in the rectangle and 512 FPM in the round.
Friction rate: Darcy and Colebrook at D, galvanized, 0.0003 ft roughness, standard air 0.075 lb/ft3At the same airflow, a rectangle loses what its equivalent round loses. At 400 CFM the 10x12 duct is at 0.036 in. w.c. per 100 ft. Duct sizing from a friction rate is a different job, done on the duct sizing calculator.
Sheet metal per foot: rectangle 2 x (a + b) / 12, round pi x D / 12 (sq ft per ft of length)The perimeter of the cross-section, which is the surface of metal a foot of duct takes. A 12x36 duct and a 20x20 duct share a 21.9 in. equivalent, and the 12x36 takes 8.00 sq ft per ft against 6.67.

Eight conversions through the same function

Rows one to five convert a rectangle to a round. In the last three, a round duct with one side fixed gives the smallest whole-inch rectangle that does not fall short. Area ratio is the rectangle's cross-section over its equivalent round's, and it stays above 1 in every row.

Round equivalent, area ratio and aspect ratio for eight duct conversions
Case	Rectangle, in.	Equivalent round, in.	Area ratio	Aspect ratio
4x6 duct	4x6	5.3	1.08	1.5:1
8x12 duct	8x12	10.7	1.08	1.5:1
10x12 duct (the default)	10x12	12.0	1.07	1.2:1
12x12 duct	12x12	13.1	1.07	1.0:1
12x36 duct	12x36	21.9	1.14	3.0:1
10 in. round into an 8 in. deep bay	8x11	10.2	1.07	1.4:1
10 in. round into a 7.25 in. deep bay (2x8 joists)	7.25x12	10.1	1.08	1.7:1
14 in. round at a 10 in. height	10x17	14.1	1.08	1.7:1

A 12x36 and a 20x20 are both 21.9 in. round equivalents. Of the two, the 12x36 is the flatter duct and takes 8.00 sq ft of sheet metal per foot against 6.67. In the joist bay rows the equivalent lands a little above the round it replaces, 10.2 in. against 10 in. for the 8 in. bay, because the other side moves in whole inches.

Standards and data sources

ASHRAE Handbook, Fundamentals, Chapter 21, Duct Design - the table of circular equivalents of rectangular ducts for equal friction and capacity, and the Darcy and Colebrook friction loss with the roughness of galvanized sheet metal used for the friction rate.
Huebscher, ASHVE Transactions, 1948 - the equation for the equal friction and equal capacity equivalent of a rectangular duct, D = 1.30 (a b)^0.625 / (a + b)^0.25.
The Engineering ToolBox, circular equivalents of rectangular ducts - a published copy of the equivalents table. The page was checked against seven of its printed sizes, from 4x6 (5.33 in.) to 12x36 (21.9 in.).

Limitations of this calculator

The duct sizing calculator lists the closest whole-inch rectangle to its round result, which can sit a little under the round: for a 10 in. round it shows 12x7, whose equivalent is 9.93 in. This page gives the smallest rectangle that is not under the round, so with the 7 in. side fixed it answers 7x13. Both are whole-inch choices around the same round size.
This page converts a shape you have already chosen. It does not size a duct from an airflow and a friction rate. For that, use the duct sizing calculator, which also shows a closest rectangular alternative.
The equivalent holds for equal friction and equal airflow. It does not give equal area, equal velocity or equal noise. The rectangle moves the same air more slowly.
Inside dimensions only. Liner, wrap and duct board walls reduce the clear size, and a size taken from the outside of a duct overstates the equivalent.
Rectangular sheet metal against round galvanized sheet metal. Flex duct, fibrous glass duct board and ductwork with a different roughness are not modeled, and neither is oval duct.
Friction is worked for standard air at 0.075 lb/ft3 and a roughness of 0.0003 ft. Altitude, temperature and a rougher duct change the rate.
Fittings, transitions, takeoffs and dampers are outside the equivalent. It compares straight runs, and the loss of an elbow or a transition is not this number.
The other side in the round to rectangle mode is a whole inch. Real stock widths, field-fabricated sizes and duct board sizes may differ, so check what your supplier makes. The search stops at 100 in., and a side that comes out under 3 in. is refused.
The aspect ratio is shown as a fact. No limit on it, and no velocity limit, is applied on this page. Local codes, the equipment manufacturer and your Manual D design set those.
Stock round sizes come from a residential list that stops at 20 in., so a larger equivalent shows no stock size.
Preliminary numbers for estimating and for checking a drawing. A permit-grade duct design is a full Manual D calculation, and the installer and the local authority having jurisdiction have the final word.

Common mistakes converting duct sizes

Matching the area instead of the equivalent diameter. A 10 in. round has 78.5 sq in. of area. An 8 in. high rectangle with the same area is 9.8 in. wide, and its equivalent is only 9.7 in. At 400 CFM that duct runs at 0.100 in. w.c. per 100 ft, against 0.085 for the 10 in. round. A rectangle needs more area than the round it replaces.
Measuring the outside of the duct. The equivalent is worked on the clear inside size. Lined duct, wrapped duct and duct board lose an inch or more on each side, so take the dimension from the inside, or subtract the liner before you enter it.
Treating a rounded 12.0 as a pass. A 10x12 duct has an equivalent of 11.96 in., which prints as 12.0. For a strict 12 in. round it is a hair short, and the page returns 10x13 when you ask for it. Decide whether the job needs a strict 12 in. or a nominal 12 in. before you pick the size.
Making the duct flat to fit the joist bay and forgetting the metal. Two ducts can have the same equivalent and cost different amounts. A 12x36 and a 20x20 are both 21.9 in., and the 12x36 takes 8.00 sq ft of sheet metal per foot against 6.67.
Using the round velocity for the rectangle. At 400 CFM a 10x12 duct runs at 480 FPM, and the 12.0 in. round at 512 FPM. Velocity follows the real cross-section area, and so does noise.
Applying the equivalent to a fitting. The equivalent compares straight runs of equal friction. An elbow, a transition or a takeoff in rectangular duct has its own loss, which comes from fitting data and not from this conversion.

Common questions about rectangular and round duct

How do you convert a rectangular duct to a round duct?

Use the equal friction equivalent, D = 1.30 x (a x b)^0.625 / (a + b)^0.25, with a and b the inside width and height in inches. A 10x12 duct gives 11.96 in., about a 12 in. round. A 12x12 gives 13.1 in. The equation is Huebscher's, and the ASHRAE Handbook table of circular equivalents is built from it.

Is a rectangular duct with the same area as a round duct equivalent?

No. Equivalent here means the same friction loss at the same airflow, and the rectangle needs more area for that. A 10 in. round is 78.5 sq in. A rectangle 8 in. high with that area is 9.8 in. wide and has an equivalent of only 9.7 in., so it loses more pressure at the same CFM.

What round duct is equal to a 12x12 rectangular duct?

A 12x12 duct has a round equivalent of 13.1 in. for equal friction and airflow, so the next stock round size up is 14 in. A 10x10 gives 10.9 in., an 8x12 gives 10.7 in. and a 4x6 gives 5.33 in.

What rectangular duct replaces a 10 in. round duct in a joist bay?

It depends on the fixed side. In a bay 8 in. deep, the smallest whole-inch other side is 11 in., so 8x11 in., with an equivalent of 10.2 in. In a 2x8 joist bay, 7.25 in. deep, it is 12 in., so 7.25x12 in. The next smaller whole inch falls short in both cases. Enter inside dimensions, and allow for liner.

Does the equivalent diameter depend on the airflow?

No. The equivalent comes from the shape alone. What changes with airflow is the friction rate and the velocity. For the 10x12 duct at 400 CFM the friction is 0.036 in. w.c. per 100 ft, and the velocity in the rectangle is 480 FPM.

Why is the velocity lower in the rectangle than in the equivalent round?

The equivalent matches friction and airflow, not area, and a rectangle needs more area to match the friction of a round. The 10x12 duct has 120 sq in. against 112.4 sq in. for the 12.0 in. round, so at 400 CFM it runs at 480 FPM and the round at 512 FPM.

Is a 10x12 duct the same as a 12 in. round?

Very nearly. The 10x12 equivalent is 11.96 in., which prints as 12.0 but is a hair under a true 12 in. round. If you need at least 12 in. exactly, the smallest whole-inch other side next to a 10 in. side is 13 in., which gives 10x13.

Should I use inside or outside dimensions?

Inside. The equivalent is worked on the clear size of the air path. Duct liner, wrap and duct board walls take inches off each side, so subtract them from an outside measurement before you enter the size.

How is this different from the duct sizing calculator?

This page converts a duct shape you already have, in either direction, with an optional airflow to show velocity and friction. The duct sizing calculator starts from the CFM and a friction rate and picks the round size, with a closest rectangular alternative shown beside it.

Is there a maximum aspect ratio for a rectangular duct?

This page does not set one and does not treat any ratio as a rule. It shows the ratio, for example 3.0:1 for a 12x36, so that you can compare it with what your design standard, your supplier or your inspector says. A flat duct takes more sheet metal per foot for the same airflow, which the result shows.

Used on the same job

Size the run before you convert it

Give the assistant the design CFM, the available static pressure, the longest supply run and the duct material, and it runs the free simplified duct sizing. Bring the round size it returns back here to fit it into a joist bay. Or enter the same inputs on the duct sizing calculator page.

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