How duct size is worked out
A duct has to have enough open area for the air to pass through at a reasonable speed.
Airflow divided by speed gives the area needed. So 400 CFM at 700 feet per minute needs about 0.57 square feet of open duct, which is a round duct about 10 inches across.
That is the whole calculation. Everything difficult about ducts is in choosing the speed and in fitting the result into a real ceiling.
Round ducts are more efficient than rectangular ones of the same area, because air has less surface to rub against. But round ducts are deep, and ceiling voids are shallow, so most homes end up with flat rectangular ducts or with flexible round duct squashed into a space it does not fit.
