A duct size calculator gives the round duct diameter (and a rectangular equivalent) needed to carry a given airflow at a sensible air velocity. Get it wrong and the system is either noisy and starved or oversized and sluggish.
Enter the CFM the run carries and pick a target velocity, and it sizes the duct. Lower velocities are quieter but need bigger ducts — the calculator shows the trade-off so you can round to the next standard size.
Duct cross-sectional area = CFM ÷ velocity (in feet per minute). Diameter = √(4 × area ÷ π). Residential supply runs are typically sized around 700-900 fpm (lower for returns) to balance noise and friction. This velocity method is a quick guide; a full design uses Manual D with total friction loss.
400 CFM at 800 fpm needs about 72 in² of duct — roughly a 10 in round duct (or about 12 × 6 in rectangular).