Calculator
Duct Size Calculator
A duct sized to the exact diameter the math produces is a duct nobody stocks. Sheet metal and flex duct come in fixed steps — 6, 7, 8, 9, 10 inches and up — so the real question is never 'what diameter,' it is 'what velocity do I actually get once I round up to the size on the shelf.' Round up too little in your head and you order a size that runs slower than you planned; skip the check entirely and you can end up with a branch that whistles at the register or a trunk that starves the far end of the run.
This calculator works the airflow forward from a room's actual heat delivery and the temperature rise the equipment runs at, converts that CFM to a duct area at a target velocity, rounds up to a stock round size, and then reports the velocity you actually get in that size — which is always a little lower than the target, because rounding up the diameter always rounds up the area with it. A flat 'one inch of duct per 1,000 BTU' guess skips every one of those steps and cannot tell you which way the rounding pushed you.
Calculate your quantity
BTU/hr
deg F between return and supply
Airflow
203 CFM
Round duct
8 in diameter
- Required duct area
- 41.56 sq in
- Exact diameter
- 7.27 in
- Velocity in the chosen size
- 579 fpm
- Rectangular equivalent
- 5.2 in wide x 8 in
- Register free area
- 58.2 sq in
- 203 CFM through a 8 in duct runs at 579 fpm. Branch runs above about 900 fpm start to be audible in a quiet bedroom.
Shopping summary
- • 8 in round branch duct (or 5 x 8 in rectangular)
This is an estimate — confirm structural work with a professional.
How this calculation works
Airflow starts from heat, not from duct size: CFM equals BTU/hr divided by 1.08 times the temperature rise between the air leaving the coil or furnace and the air already in the room. That 1.08 is air's own physical properties (density times specific heat times minutes per hour) folded into one constant, so a 12,000 BTU/hr load at a 55 degree rise needs about 203 CFM — and the same load at a 90 degree rise needs barely more than half that, because each cubic foot of air is carrying more heat.
Once CFM is known, duct area follows from a target velocity: CFM divided by velocity, times 144 to convert square feet to square inches, gives the cross-section the air needs. Rearranging a circle's area formula turns that into an exact diameter — and because that exact diameter almost never lands on a stock size, the calculator rounds up to the next one sold and re-runs the velocity at the size you will actually buy, rather than stopping at a number nobody can order.
- Target velocity is a choice, not a constant — quiet bedroom branches run slower (600-700 fpm) than a main trunk (up to 1,200 fpm), because velocity noise is what a person sitting near a register actually hears.
- Rounding up to a stock size always lowers the resulting velocity below your target, never raises it — the area only ever goes up when you round the diameter up.
- The rectangular equivalent assumes a height you choose and solves for width at the same cross-sectional area; it is not automatically a shape that fits the joist bay or wall cavity you have.
- Register free area is not duct area. A grille's blades and frame reduce the actual open area below its face size, which is why the register figure here is computed at a slower 500 fpm rather than the duct's own target velocity.
The formula
cfm = btu / (1.08 x tempRise); requiredArea = (cfm / velocity) x 144; diameter = sqrt(4 x requiredArea / pi)
- btu
- Heat the duct has to deliver to the room, BTU/hr — the same figure the room's share of a heat-loss or equipment-output calculation would produce.
- 1.08
- 0.075 lb/cu ft air density times 0.24 BTU/lb-deg F specific heat times 60 minutes per hour, folded into one constant used throughout residential airflow calculations.
- tempRise
- The temperature difference, in deg F, between supply air leaving the equipment and room air. A higher rise moves the same BTU/hr with less airflow, which is why it shrinks the duct.
- velocity
- The target speed of air moving through the duct, in feet per minute — the input that trades off noise (lower) against duct size and material cost (higher).
- 144
- Square inches per square foot, converting the CFM/velocity ratio (in square feet) into the square-inch cross-section a duct's dimensions are actually specified in.
- diameter
- A round duct's diameter for a given cross-sectional area, from A = pi r^2 rearranged — the exact figure before it gets rounded up to whatever size is actually stocked.
Where these numbers come from
- 1.08 (CFM-to-BTU/hr conversion constant)
- Physics-derived: air's density and specific heat combined with minutes per hour. It is the standard multiplier used throughout residential airflow and duct-sizing calculations, not specific to any one manufacturer's product.
- 600-700 fpm branch, up to 1,200 fpm trunk velocity targets
- Trade convention drawn from residential duct-design practice: slower velocities in the runs nearest a register, where a person can hear it, and higher velocities tolerated in trunks that are further from any occupied space.
- 4 through 20 in stock round duct sizes
- Manufacturer-published: the diameters sheet-metal and flex duct are actually sold in. Sizes between these steps exist as custom fabrication only and cost more than ordering the next stock size up.
- 500 fpm register face velocity
- Trade convention for sizing the free area of a supply or return grille, deliberately slower than duct velocity because a grille's opening is the point closest to an occupied room.
Worked examples
A 12,000 BTU/hr bedroom branch at standard rise
| Heat delivered to the room | 12000 |
|---|---|
| Supply temperature rise | 55 |
| Target velocity | 700 fpm (residential branch) |
| Rectangular duct height | 8 in |
| Airflow | 203 CFM |
|---|---|
| Round duct | 8 in diameter |
| Required duct area | 41.56 sq in |
| Exact diameter | 7.27 in |
| Velocity in the chosen size | 579 fpm |
| Rectangular equivalent | 5.2 in wide x 8 in |
| Register free area | 58.2 sq in |
203 CFM at a 700 fpm target calls for a 7.27 inch duct — no such thing is sold, so the calculator rounds to 8 inches, the next size up. That larger area drops the real velocity to 579 fpm, well below the 700 fpm target and comfortably quiet, but it also means the theoretical 700 fpm branch you planned for on paper never actually exists in the wall.
The 5.2 by 8 inch rectangular equivalent is worth checking against the stud bay before ordering flex duct instead of rigid: a shallower rectangular height than 8 inches would need a wider board to hold the same area, which can matter more than the round size in a tight wall cavity.
A 40,000 BTU/hr trunk feeding several rooms
| Heat delivered to the room | 40000 |
|---|---|
| Supply temperature rise | 55 |
| Target velocity | 1,200 fpm (main trunk) |
| Rectangular duct height | 8 in |
| Airflow | 674 CFM |
|---|---|
| Round duct | 12 in diameter |
| Required duct area | 80.81 sq in |
| Exact diameter | 10.14 in |
| Velocity in the chosen size | 858 fpm |
| Rectangular equivalent | 10.1 in wide x 8 in |
| Register free area | 193.9 sq in |
674 CFM at the higher 1,200 fpm trunk target still rounds up from a 10.14 inch exact diameter to 12 inches, the next stock step, landing the real velocity at 858 fpm — again below target, and by a wider margin than the branch example, because the jump from 10 to 12 inches is a bigger area increase than 7.27 to 8 was.
This is the number to size the trunk on, not the sum of every branch it feeds run individually — a trunk moves air toward several registers at once, and its own velocity target is chosen for that role rather than for sitting quietly next to a bed.
Common mistakes
- Ordering the exact theoretical diameter instead of the next stock size, then paying a sheet-metal shop to custom-fabricate a size that is sold off the shelf one step up.
- Leaving the temperature rise at a generic default when the actual equipment's rise is printed on its data plate or set by its control board — a furnace running a 40 degree rise needs meaningfully more CFM, and duct, than one running 90.
- Picking a single high velocity target for every run in the house because it produces smaller numbers, then wondering why a bedroom branch is audible at night.
- Treating the register free-area figure as interchangeable with duct cross-section — a grille rated at the duct's own area will restrict flow more than the number on the page suggests, because grille blades take up real space.
- Sizing one trunk CFM as a simple sum of rooms without checking that the rooms are ever calling for heat simultaneously at their full individual loads — trunks are sized on the load they actually carry together, not a worst-case addition of every branch's peak.
- Assuming a bigger duct is always the safer choice. Oversizing a branch drops velocity so far that air stratifies and barely moves out of the register in a long run, which reads as a supply problem exactly like an undersized duct does.
Shopping summary
Buy round duct or flex to the stock size this page lands on, in the length the actual run needs plus fittings for every elbow and transition — each elbow behaves like the airflow devices on the bathroom fan CFM calculator do, adding equivalent length that a straight-run measurement alone will not show.
Get the BTU/hr figure this page needs from the heat loss calculator for a heating design, split across however many rooms the trunk serves, rather than guessing a whole-house number and dividing it evenly — rooms rarely share heat loss in equal shares.
If the run terminates at an attic or crawlspace vent rather than a room register, check it against the attic ventilation calculator instead — that page sizes net free area for passive ventilation, a different job from moving conditioned air to an occupied room.
FAQ
Why does the velocity I actually get never match the target I entered?
Because stock duct sizes are discrete steps and the calculator always rounds the diameter up to the next one sold, never down. A bigger diameter means a bigger cross-section, and the same CFM through a bigger cross-section runs slower — so the real velocity in any stock size is always at or below your target, never above it.
What target velocity should I actually use for a bedroom versus a trunk?
600 to 700 fpm keeps a branch feeding an occupied room quiet enough not to notice; a shared trunk running through a mechanical closet or unconditioned space can run 900 to 1,200 fpm because nobody is sitting next to it. Picking a trunk-speed target for a bedroom branch is the single most common way this calculation produces an audible register.
Does duct shape — round versus rectangular — change how much air it can move?
Not meaningfully at the same cross-sectional area, which is exactly what the rectangular equivalent figure gives you: the same area as the round duct, reshaped to fit a joist bay or wall cavity a round pipe would not fit into. What does change airflow capacity is friction loss, which rises faster in a flatter, more elongated rectangle than in a near-square one at the same area.
Why did raising the temperature rise shrink my duct size?
Because CFM is BTU/hr divided by 1.08 times the rise — a higher rise means each cubic foot of supply air is carrying more heat, so fewer cubic feet per minute are needed to deliver the same BTU/hr. A variable-speed furnace or heat pump running a higher rise than a standard 55 degrees genuinely needs a smaller duct for the identical heat delivery.
Is a bigger duct always the safer, quieter choice?
No. Oversizing drops velocity so low that air barely moves through a long run, especially past the first branch takeoff, which shows up as weak airflow at the far register — a different-looking version of the same complaint an undersized duct produces. There is a right-sized answer, not a bigger-is-safer one.
How does this relate to the heat loss calculator on this site?
That page produces the whole-building or per-room BTU/hr figure this one needs as its starting input. Heat loss answers how much heat a space needs; this page answers how big a duct has to be to deliver it at a velocity that is livable — they are sequential steps in the same design, not the same calculation twice.
Where to go next
The projects this number is a step of, the guides that explain the method behind it, and the rest of its trade group.