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Round duct diameter, from CFM and velocity.
Enter the airflow for a duct run and the air velocity you want to design for. The tool gives the calculated diameter and the next whole-inch size.
Short answer
Round duct diameter = square root of (4 x CFM / (pi x velocity)). At 400 CFM and 700 ft/min the calculated diameter is 10.24 in, so use 11 in round duct, which runs at 606 ft/min.
Duct run
Result
Worked example
A run must carry 400 CFM at 700 ft/min. The cross-section is 400 / 700 = 0.571 sq ft. Diameter = square root of (4 x 0.571 / pi) = 0.853 ft = 10.24 in. Rounded up that is 11 in, where the same 400 CFM moves at 606 ft/min.
Formula, assumptions and sources
CaptiveAire's duct calculator gives the relationship as diameter = square root of (4 x CFM / (pi x velocity)), derived from Q = V x A with A = pi x D squared / 4, and notes that round duct comes in standard sizes (typically 1-inch steps for small sizes, 2-inch steps for larger) so the calculated diameter is rounded up. This tool rounds up to the next whole inch only; check the sizes your supplier stocks. It sizes by velocity, not by friction rate: pressure loss from length, elbows, fittings and flex duct is not modelled, and the tool does not suggest a velocity. For a whole-house system, ductwork is normally designed by a qualified HVAC contractor.
Source: CaptiveAire, HVAC Calculator Toolbox: Round Duct Sizing (opened 2026-10-08)
The formula, one variable at a time
Airflow equals velocity times cross-sectional area (Q = V × A). In HVAC units, Q is airflow in cubic feet per minute (CFM), V is air velocity in feet per minute (ft/min), and A is the duct's cross-section in square feet. A round duct's area is π × D² ÷ 4, where D is the diameter in feet. Solve for diameter and you get D = √(4 × CFM ÷ (π × V)) feet, and multiplying by 12 converts to inches. CaptiveAire's duct toolbox gives this same relationship and notes that round duct is made in standard sizes, typically in 1-inch steps for small sizes and 2-inch steps for larger sizes, so the calculated diameter is rounded up.
Worked examples
The default. 400 CFM at 700 ft/min needs 400 ÷ 700 = 0.571 sq ft, a calculated diameter of 10.24 in. Rounding up to 11 in lowers the actual velocity to about 606 ft/min.
A branch run. 200 CFM at 600 ft/min needs 0.333 sq ft, which is 7.82 in, so choose 8 in, where velocity falls to about 573 ft/min.
A tighter velocity. 400 CFM at 900 ft/min needs 0.444 sq ft, which is 9.03 in. It just exceeds 9 in, so the tool rounds up to 10 in (733 ft/min). A calculated diameter a hair over a whole inch always jumps a full size.
What can a given round duct carry?
People often ask the reverse question, such as how many CFM an 8-inch round duct carries. The answer depends on the velocity you design for. Multiplying each diameter's area by common velocities gives:
| Diameter | Area (sq ft) | CFM at 500 ft/min | CFM at 600 ft/min | CFM at 700 ft/min | CFM at 800 ft/min |
|---|---|---|---|---|---|
| 4 in | 0.087 | 44 | 52 | 61 | 70 |
| 5 in | 0.136 | 68 | 82 | 95 | 109 |
| 6 in | 0.196 | 98 | 118 | 137 | 157 |
| 7 in | 0.267 | 134 | 160 | 187 | 214 |
| 8 in | 0.349 | 175 | 209 | 244 | 279 |
| 9 in | 0.442 | 221 | 265 | 309 | 353 |
| 10 in | 0.545 | 273 | 327 | 382 | 436 |
| 11 in | 0.660 | 330 | 396 | 462 | 528 |
| 12 in | 0.785 | 393 | 471 | 550 | 628 |
For example, an 8 in duct carries about 209 CFM at 600 ft/min, and about 279 CFM at 800 ft/min. Published charts for the same duct may show different numbers, because many size by a friction rate (pressure loss per 100 ft) instead of a velocity, and flex duct and sheet-metal duct have different friction. The CaptiveAire page itself now offers a calculator keyed to a target friction rate, and the duct friction rate calculator and ductulator on this site work from friction rate as well.
Choosing a velocity
This tool does not pick a velocity for you. CaptiveAire describes duct sizing as balancing noise levels, pressure drop and material cost: a higher velocity allows a smaller duct but increases noise and pressure loss, and a lower velocity does the reverse. Take the figure from the equipment manufacturer, your design standard or your HVAC contractor. For a whole-house system, residential duct design is normally done by a contractor using an accepted method such as ACCA Manual D.
Finding velocity for a duct you already have
Rearrange the same relationship: velocity = CFM ÷ area. A 6 in duct has an area of 0.196 sq ft, so 150 CFM moves at about 764 ft/min. The tool also reports the actual velocity after rounding up, which is the number to check against your limit.
Common mistakes
- Using the diameter in inches in the area formula without converting to feet (divide by 12).
- Rounding down to the nearest size, which raises velocity above what you designed for.
- Applying a round-duct answer to a rectangular duct. Rectangular sizes need an equivalent-diameter conversion; use the round to rectangular duct calculator.
- Ignoring the rest of the system. Long runs, elbows, dampers and flexible duct add pressure loss that a velocity-only size does not capture.
Sources
Retrieved
Every link below was opened and read in October 2026. The note after each link says which statement on this page it supports.
- CaptiveAire, HVAC Calculator Toolbox: Round Duct Sizing (retrieved 2026-10): diameter = square root of (4 x CFM / (pi x velocity)); Q = V x A; standard sizes and rounding up; sizing balances noise, pressure drop and cost; friction-rate method
- ACCA, Manual D: Residential Duct Systems (retrieved 2026-10): the residential duct design standard referred to for whole-house systems
Safety and limits
This is a planning aid, not professional advice. Electrical and HVAC work can cause fire, shock and carbon monoxide hazards; have a licensed professional size, install and inspect equipment.
FAQ
How do I size a round duct for a given CFM?
Divide CFM by velocity to get the area in square feet, then diameter = square root of (4 x area / pi). 150 CFM at 600 ft/min needs 6.77 in, so 7 in round duct.
What velocity should I use?
This tool leaves that to you. Duct velocity is a design choice that trades noise, pressure drop and duct size; a contractor or the equipment manufacturer's guidance sets it.
Why does the tool round up?
Round duct is sold in standard sizes, so the next size up is used; a bigger duct lowers the velocity below your target.
How many CFM can an 8 inch round duct carry?
It depends on the velocity you design for. An 8 in round duct has an area of 0.349 sq ft, so it moves about 175 CFM at 500 ft/min, 209 CFM at 600 ft/min and 279 CFM at 800 ft/min. Charts based on friction rate give different numbers.
Why does my chart give a different CFM for the same duct size?
Charts are built on different assumptions: some fix a friction rate per 100 feet, some fix a velocity, and flex duct has more friction than sheet metal. This calculator uses velocity only, so use a friction-rate tool if your design standard works that way.
What happens if the air velocity in the duct is too high?
CaptiveAire notes that proper sizing balances noise, pressure drop and cost, so a velocity set too high tends to mean more noise and more pressure loss. Check your equipment's limits.
How do I size a rectangular duct for the same airflow?
Convert between round and rectangular with an equivalent-diameter method, which keeps friction the same, not area. This tool is round only, so use the round to rectangular duct calculator.