Duct Volume Calculator
The volume of a duct is the amount of air space inside it: the cross-sectional area multiplied by the length of the run. This calculator works it out in cubic feet for the two shapes that cover nearly all ductwork, rectangular and round, taking the length in feet and the width, height, or diameter in inches, the way ducts are actually measured and sold.
It is pre-filled with a rectangular run 10 feet long, 24 inches wide, and 12 inches high. That duct holds exactly 20 cubic feet, a clean check number: one click on Calculate should reproduce it.
This is the static air volume inside the duct, not an airflow rate. How much air moves through the duct per minute depends on velocity as well; the section on volume versus CFM below shows that extra step.
Quick Answer
Key takeaways
- Volume is always cross-sectional area times length. Rectangular area is width times height; round area is pi times the radius squared. Everything else is unit conversion.
- Length goes in as feet and the cross-section dimensions as inches, because that is how ductwork is measured and sold. The calculator converts the inches to feet before multiplying.
- The two classic errors are using the diameter as the radius (answer four times too big) and forgetting the inch conversion entirely (answer 144 times too big).
- Volume is not airflow. Airflow in CFM needs one more input, air velocity, and no volume figure on its own can size a fan.
- Quick Answer
- How to run a duct volume calculation
- The two formulas, and why the inches get divided by 12
- Worked examples: one rectangular run, one round run
- Common duct sizes: what a run actually holds
- Duct volume is not airflow: the CFM step needs velocity too
- Four mistakes that wreck a duct volume number
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to run a duct volume calculation
Four steps, and the only fiddly one is measuring in the right places.
Pick the shape. Rectangular covers sheet metal trunk and branch ducts. Circular covers round pipe and spiral duct. Flexible duct is measured as round, using its nominal diameter.
Measure the inside, not the outside. Volume is the air space, so width, height, and diameter are internal dimensions. On lined or insulated duct, measure the clear opening the air actually sees.
Enter the length in feet. For a run made of straight sections and elbows, add the straight lengths and measure each bend along its centerline. For the sheet metal surface of an elbow rather than the air inside it, the companion duct bend area calculator covers that separate question.
Read the volume, then use the area. The result box also reports the cross-sectional area and the volume per foot of length, so you can extend the answer to a longer or shorter run of the same duct without starting over.
The two formulas, and why the inches get divided by 12
Both formulas are the same idea, area times length, with the cross-section worked out in square feet so the answer lands in cubic feet.
Round duct: Volume = pi x ((Diameter in inches / 24) squared) x Length (ft). Dividing the diameter by 24 converts inches to feet and halves it to a radius in one step.
The geometry is the standard prism and cylinder volume taught in any reference: a rectangular duct is a cuboid, a round duct is a cylinder, and Wolfram MathWorld’s reference pages for the cuboid and the cylinder give the same area-times-length forms. The unit handling follows the SI conversion factors maintained by the National Institute of Standards and Technology in its SI units guidance: 12 inches to a foot, so a square foot is 144 square inches and a cubic foot is 1,728 cubic inches. That 144 is why skipping the conversion is so destructive, as the mistakes section below shows.
Professional duct design goes well past volume: the ASHRAE Handbook duct design method and SMACNA construction standards size ducts from required airflow, friction loss, and fitting losses. Volume is the first geometric fact those methods build on, and it is the only fact this calculator claims to give you.
Worked examples: one rectangular run, one round run
Both examples are pre-filled in the calculator, one under each shape, so you can reproduce every number here with two clicks.
| Shape | Inputs | Cross-section | Volume |
|---|---|---|---|
| Rectangular | 10 ft long, 24 in wide, 12 in high | 2.00 sq ft | 20.00 cubic feet |
| Circular | 8 ft long, 18 in diameter | 1.77 sq ft | 14.14 cubic feet |
By hand, rectangular first: 24 inches is 2 feet and 12 inches is 1 foot, so the cross-section is 2 x 1 = 2 square feet, and 2 x 10 feet of length gives 20 cubic feet. Round: an 18 inch diameter is a radius of 0.75 feet, pi x 0.75 squared is 1.77 square feet, and 1.77 x 8 feet gives 14.14 cubic feet (14.137 before rounding). The round duct is shorter and still holds less, which is the usual pattern: a round duct of a given width has about 79 percent of the cross-section of a square duct of the same width, because the corners are missing.
Common duct sizes: what a run actually holds
Residential and light commercial work uses a short list of sizes over and over. These volumes come straight from the formulas above, so any row can be checked in the calculator by entering that size and a 10 or 25 foot length.
| Duct size | Cross-section (sq ft) | Volume, 10 ft run | Volume, 25 ft run |
|---|---|---|---|
| 6 in round | 0.20 | 1.96 ft3 | 4.91 ft3 |
| 8 in round | 0.35 | 3.49 ft3 | 8.73 ft3 |
| 10 in round | 0.55 | 5.45 ft3 | 13.64 ft3 |
| 12 in round | 0.79 | 7.85 ft3 | 19.63 ft3 |
| 14 in round | 1.07 | 10.69 ft3 | 26.73 ft3 |
| 12 x 6 in rectangular | 0.50 | 5.00 ft3 | 12.50 ft3 |
| 16 x 8 in rectangular | 0.89 | 8.89 ft3 | 22.22 ft3 |
| 20 x 10 in rectangular | 1.39 | 13.89 ft3 | 34.72 ft3 |
| 24 x 12 in rectangular | 2.00 | 20.00 ft3 | 50.00 ft3 |
Read the table by cross-section, not by the headline size. A 14 inch round duct and a 20 x 10 rectangular duct are near neighbours in area (1.07 against 1.39 square feet is still a gap, but they sit in the same trunk-duct conversation), while a 12 x 6 branch holds about a quarter of what the 24 x 12 example holds. When a room gets too little air, this table is often where the problem shows up first: the branch serving it is simply small.
Duct volume is not airflow: the CFM step needs velocity too
Volume tells you how much air a duct holds standing still. Airflow tells you how much passes through per minute, and the two are linked by velocity: CFM = cross-sectional area (sq ft) x velocity (feet per minute).
Take the worked example. Its cross-section is 2.00 square feet, so at a typical residential trunk velocity of 700 feet per minute it would carry 2.00 x 700 = 1,400 CFM. The same duct at 500 FPM carries 1,000 CFM. Nothing about the duct changed, only the speed of the air in it, which is set by the blower and the resistance of the whole system. The Building America guide to sealed and insulated metal ducts, maintained for the US Department of Energy, makes the related practical point that poorly sealed ducts waste energy and deliver less air than the blower moves, whatever the duct volume is.
Volume still earns its place. It is the number you need for air-change thinking when it is set against the room it serves (the air volume calculator works out the room side of that comparison), it feeds the airflow side of operating cost through the cost per CFM calculator, and it is a sanity check behind system sizing, which starts from the load figures an AC tonnage calculator estimates. Treat volume as step one of that chain, not a substitute for the rest of it.
Four mistakes that wreck a duct volume number
Each of these shows up in real estimates, and each has a recognizable fingerprint in the answer.
Using the diameter as the radius. Area depends on the radius squared, so this error multiplies a round duct’s volume by exactly four. If a round result looks suspiciously generous, this is the first thing to check.
Skipping the inch conversion. Multiplying feet by raw inches mixes units across the 144 square inches in a square foot, and the answer comes out 144 times too large. A 10 foot bedroom branch does not hold hundreds of cubic feet.
Measuring the outside of lined duct. Internal lining can take half an inch or more off each side. A nominal 24 x 12 duct lined on all sides may present a clear opening closer to 23 x 11, which is about 12 percent less area and volume.
Trusting flexible duct at face value. Flex duct that is compressed, sagging, or sharply bent has a smaller effective cross-section than its nominal diameter, and its volume (and far more importantly its airflow resistance) suffers. Pulled taut and gently routed, the nominal diameter is a fair input; draped over joists, it is an optimistic one.
What competing calculators miss
The duct volume tools ranking for this term mostly use the same correct geometry. The gaps are in how honestly and usefully the result is presented.
Miss 1: the formula written two conflicting ways on one page. A prominent ranking page describes the rectangular method as entering everything in inches and dividing by 1,728, then describes the round method with the length in feet converted mid-calculation. Both routes reach the same answer, but a reader hand-checking the work has to untangle two unit systems. This page uses one method throughout, length in feet and cross-section converted once, and the worked examples reproduce it exactly.
Miss 2: a bare cubic-feet figure with nothing to build on. Most tools stop at the single volume number. The result here also gives the cross-sectional area and the volume per foot of run, and the size table above extends that to the standard sizes, so planning a 35 foot run of 10 inch round is a multiplication (0.545 cubic feet per foot x 35, about 19.09 cubic feet) rather than another trip through a form.
Miss 3: volume dressed up as airflow. At least one ranking page pads its example results with a vague speed label that is not a physical quantity, and several blurbs imply volume alone sizes fans. It cannot: airflow needs velocity, and this page states that limit in the calculator itself and shows the CFM step openly instead of implying it.
One honest limit in the other direction: full HVAC sizing tools that start from CFM and friction loss answer a broader design question than this page attempts. If you are designing a system from scratch, use one of those for sizing and this calculator for the volume figures inside that work.
Frequently Asked Questions
Multiply the cross-sectional area by the length of the run. For a rectangular duct the area is width times height; for a round duct it is pi times the radius squared. Keep the cross-section in square feet and the length in feet and the answer is in cubic feet. The calculator converts the width, height, and diameter from inches for you.
Length is entered in feet, and width, height, and diameter are entered in inches, matching how ductwork is measured and sold. The result is in cubic feet, and the result box also shows the same volume in cubic inches and cubic meters.
Halve the diameter to get the radius, convert it to feet, square it, and multiply by pi and by the length in feet. A 12 inch diameter duct 10 feet long has a radius of 0.5 feet, so its volume is pi x 0.25 x 10 = 7.85 cubic feet. That row is in the size table above and reproduces in the calculator.
No. Volume is the static amount of air space inside the duct, measured in cubic feet. Airflow in CFM is that cross-section in motion: CFM equals cross-sectional area in square feet times air velocity in feet per minute. A duct with a 2.00 square foot cross-section carries 1,400 CFM at 700 FPM and 1,000 CFM at 500 FPM.
Measure the inside dimensions the air actually occupies: width and height for rectangular duct, diameter for round duct, and the straight length of the run. On lined duct, measure the clear opening inside the lining. For runs with elbows, add the sections and measure bends along the centerline.
Flexible duct, yes: enter it as circular using its nominal diameter, and pull it taut when you measure, because sagging and compression shrink the effective size. Oval (flat oval) duct, not directly: its cross-section is a rectangle capped with two semicircles, so neither shape setting matches it exactly.
It is the starting figure for air-change and purge estimates, for comparing branch sizes when one room is starved of air, and for checking that a quoted run is the size it claims to be. It also feeds the velocity step: once you know the cross-section, any target CFM turns into a velocity you can judge as quiet or noisy.
Multiply cubic feet by 0.0283168 for cubic meters, or by 28.3168 for liters. The worked example’s 20.00 cubic feet is 0.57 cubic meters, about 566 liters. The result box shows the cubic meter figure automatically.
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References
- Bureau International des Poids et Mesures, “The International System of Units (SI Brochure)” – the defining document for the metre and the derived volume units this calculator converts between. BIPM: The International System of Units, SI Brochure. Accessed October 2026.
- National Institute of Standards and Technology, “SI Units” – NIST guidance on SI length and volume units and the inch to foot conversion used for duct dimensions. NIST: SI Units, Office of Weights and Measures. Accessed October 2026.
- Wolfram MathWorld, “Cylinder” – the reference entry for the volume of a cylinder, V = pi r squared h, used for round ducts. MathWorld: Cylinder. Accessed October 2026.
- Wolfram MathWorld, “Cuboid” – the reference entry for the volume of a rectangular box, length x width x height, used for rectangular ducts. MathWorld: Cuboid. Accessed October 2026.
- Pacific Northwest National Laboratory, Building America Solution Center, “Sealed and Insulated Metal Ducts” – US Department of Energy backed guidance on sealing and insulating metal ductwork and the losses poor sealing causes. Building America Solution Center: Sealed and Insulated Metal Ducts. Accessed October 2026.
- ENERGY STAR, “Duct Sealing” – homeowner and contractor guidance on sealing and insulating ductwork to cut air losses. ENERGY STAR: Duct Sealing. Accessed October 2026.