A 500 × 250 mm duct is not a 400 mm round duct. Here is the right conversion.

Quick answer: To swap a round duct for a rectangular one that carries the same airflow with the same friction loss per meter, use the equivalent diameter formula (Huebscher, 1948): De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25, where a and b are the two sides in the same units. A 500 × 250 mm rectangular duct has an equivalent diameter of 381 mm, not 400 mm. The 400 mm figure you see on many charts is the diameter with the same cross section area, and a rectangle with that area loses about 25 percent more pressure per meter than the matching round duct. Convert by friction, not by area.

This is the conversion every duct sizing job runs into. The airflow and the friction rate give you a round diameter. Then the ceiling turns out to be 250 mm deep, and you need a rectangle. How you do that step decides whether the fan sees the pressure drop you planned for.

The formula, in both unit systems

The equivalent diameter is the round duct that, at the same airflow, has the same friction loss per unit length as the rectangular one:

De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25

• It works in any consistent unit. Put millimeters in, get millimeters out. Put inches in, get inches out.
• The constant 1.30 and the exponents come from Huebscher’s 1948 work and are the version published in the ASHRAE Fundamentals duct design chapter. Because the formula is an empirical fit, it is meant for ordinary rectangular ducts, not for extreme shapes.
• It converts friction, and only friction. It does not say the two ducts have the same velocity, because the rectangle’s actual area is larger than the round duct’s. After you pick a rectangle, check its real velocity using its real area (airflow divided by a × b).

Worked example, metric. A 500 × 250 mm duct:

1. a × b = 125,000, and 125,000 raised to the 0.625 power is about 1,517
2. a + b = 750, and 750 raised to the 0.25 power is about 5.23
3. De = 1.30 × 1,517 ÷ 5.23 = about 381 mm

Worked example, imperial. A 20 × 10 inch duct:

1. a × b = 200, and 200 raised to the 0.625 power is about 27.4
2. a + b = 30, and 30 raised to the 0.25 power is about 2.34
3. De = 1.30 × 27.4 ÷ 2.34 = about 15.2 inches

Equivalent diameter table (rectangular to round)

Calculated from the formula above. Use it to sanity check any calculator or chart.

Rectangular (mm)	Aspect ratio	Equivalent round, friction (mm)	Round with the same area (mm)
300 × 300	1 : 1	328	339
400 × 200	2 : 1	305	319
500 × 250	2 : 1	381	399
600 × 200	3 : 1	365	391
600 × 300	2 : 1	457	479
800 × 200	4 : 1	414	451
1000 × 200	5 : 1	454	505

Rectangular (in)	Equivalent round, friction (in)
8 × 8	8.7
10 × 8	9.8
12 × 8	10.7
12 × 12	13.1
14 × 6	9.8
16 × 8	12.2
20 × 10	15.2
24 × 8	14.6
30 × 10	18.3
24 × 24	26.2

Read the metric table left to right and you can see the gap open up. For a square duct the friction diameter is only about 3 percent below the same area diameter. At 5 : 1 it is about 10 percent below. The flatter the duct, the more the area method flatters it.

Why equal area gives the wrong answer

Air drags against the duct wall. The wall is the perimeter, and the air is the area. A round duct has the least perimeter for its area of any shape, so it has the least drag per unit of airflow. A rectangle with the same area has a longer perimeter, and the more it is stretched the longer that perimeter gets. Corners also hold slow, swirling air that adds loss without carrying flow.

So two ducts with identical cross section area do not lose identical pressure. The one with more wall loses more. Equal friction is the fair comparison, and that is what the Huebscher equation encodes.

There is a second tempting shortcut that is also wrong for this job: hydraulic diameter, 4 × area ÷ perimeter, which for a rectangle is 2ab ÷ (a + b). It is a valid quantity in fluid mechanics, and it is used for Reynolds number. But for a 500 × 250 mm duct it gives 333 mm, which is well below the 381 mm friction equivalent, and designers do not use it for round to rectangular conversion. Use De.

What the penalty looks like in pascals

To see the size of the effect, take a flow of 0.25 m³/s (about 530 cfm) and compare ducts that all have the same cross section area as a 400 mm round duct, which is about 0.126 m². These are our own calculations using the Darcy-Weisbach equation with the Colebrook friction factor, air at 1.2 kg/m³, and a roughness of 0.09 mm for galvanized steel, applying the rectangular duct through its equivalent diameter. Treat them as a way to compare shapes. They will differ from a handbook chart by a few percent depending on the assumed roughness and air properties.

Same area as 400 mm round	Size (mm)	Friction vs the round duct
Round	400 diameter	baseline, about 0.13 Pa/m
Square, 1 : 1	354 × 354	about 17 % higher
2 : 1	500 × 250	about 25 % higher
3 : 1	612 × 204	about 39 % higher
4 : 1	707 × 177	about 53 % higher
5 : 1	791 × 158	about 67 % higher

If you replaced a 400 mm round run with the same area 500 × 250, the friction rate would sit about a quarter above what you designed. Over a long run that adds up in the total pressure the fan must overcome. Going the other way, the 381 mm round duct that is friction equivalent to the 500 × 250 has less area than the rectangle, so it also runs at a higher velocity (about 2.2 m/s against 2.0 m/s in the rectangle at this flow). That is the other thing the conversion hides: friction matches, velocity does not.

Aspect ratio: how flat is too flat

Guidance varies. Sources you will meet put the practical limit at 2 : 1 where possible, with 3 : 1 accepted in tight ceilings, while others say keep it below 4 : 1, and some calculators go to 5 : 1. None of these is a law. The table above shows the reason for the advice: friction, material, and fitting losses climb steadily as the duct flattens, and a very flat duct is also more likely to flex and drum. Treat 2 : 1 as the comfortable target, accept more only when the space forces it, and always check the local code and the project specification, which may set a hard limit.

The equal friction method, step by step

Most residential and light commercial supply ducts are sized by the equal friction method: pick one friction rate and size every section to it.

1. Pick the friction rate. Common design values for low velocity comfort systems sit around 0.8 to 1.0 Pa/m (roughly 0.08 to 0.10 inches of water per 100 feet). Your fan curve, available static pressure and noise limits set the real number.
2. Find the airflow in each section, from room loads and outlet counts.
3. Size the round duct for each airflow at that friction rate.
4. Convert to rectangular only where space demands it. Use the equivalent diameter to find a rectangle with the same friction, or fix one side to the ceiling depth and solve for the other.
5. Round to a standard size. Standard rectangular sizes come in fixed steps, so the real friction will land slightly above or below the target.
6. Recheck velocity and friction on the size you actually chose, using its real area.
7. Total the run. Add the straight duct loss to every fitting, then find the critical path, the longest or highest resistance route from the fan to an outlet, because that path sets the fan pressure.

Doing this on your phone

HVAC Duct Design, one of our apps, does the steps above on an iPhone or iPad. Enter an airflow and choose friction rate or velocity, and it shows the round size, then the matching standard rectangular sizes with a height or width you can lock and an aspect limit you set. Duct runs add fittings, pressure drop per section, a running total and the critical path, and jobs stay on your device. It is a one time purchase, not a subscription. See HVAC Duct Design.

Use any tool, ours included, as an estimate. The formulas above are fits to test data, real fittings and duct materials vary, and a design that matters should be checked against the ASHRAE Fundamentals handbook, ACCA Manual D or your local code, and signed off by the person responsible for it.

Frequently asked questions

What is the equivalent round duct for a rectangular duct? The round duct that gives the same friction loss per meter at the same airflow. Calculate it with De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25.

Is a rectangular duct with the same area as a round duct equivalent? No. The rectangle has more wall, so it loses more pressure. At 2 : 1 the difference is about a quarter more friction in our calculation.

What is the equivalent round size of a 20 × 10 inch duct? About 15.2 inches.

Does equivalent diameter give the same velocity too? No. It matches friction only. Divide the airflow by the rectangle’s real area to get its velocity.

What aspect ratio should I design for? Stay near 2 : 1 when you can. Accept 3 : 1 in tight spaces, and treat anything flatter as a last resort, subject to your code and specification.

Why does my chart say 400 mm for a 500 × 250 duct? Some charts and calculators show the same area diameter, which is 399 mm for that duct. The friction equivalent is 381 mm.

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Sources and further reading

• Engineering ToolBox: Equivalent Diameter, Rectangular vs. Circular HVAC Ducts for the definition and sizing tables.
• Data Driven AEC duct sizing calculator, which lists the Huebscher equation and the workflow of sizing round first, then converting and rechecking.
• CCC Engineering: round vs rectangular ductwork guide for the aspect ratio discussion. Its 500 × 250 mm to 400 mm example is the area equivalent, which is why this post separates the two.
• Goodwin: equal friction method duct sizing for the equal friction workflow.
• ASHRAE Handbook, Fundamentals, duct design chapter, the primary reference for the equation and friction data. Confirm constants and design values there before relying on them.
• The pressure drop comparison table is our own calculation, with the assumptions stated above, and is not taken from any of these sources.