Why Round Duct Is the Reference Point for Sizing
Duct sizing calculations, including the friction-rate and velocity relationships covered elsewhere in this cluster, are most cleanly derived and expressed for round duct — a round cross-section has the most efficient ratio of flow area to duct wall surface area (perimeter) for a given size, meaning round duct produces the lowest friction loss for a given airflow and cross-sectional area compared to any other shape. This is why duct sizing methodology typically calculates an ideal round diameter first, even when the actual installed duct will be rectangular (a common practical necessity in tight ceiling cavities or wall spaces where round duct's circular cross-section doesn't fit efficiently).
Why You Can't Just Match Cross-Sectional Area
It's tempting to think converting round duct to rectangular is simply a matter of matching cross-sectional area — calculate the round duct's area, then find rectangular dimensions with the same area. This doesn't actually work, because friction loss depends not just on cross-sectional area but on the ratio of that area to the duct's wetted perimeter (the total interior surface area in contact with the moving air, which is what generates friction). A rectangular duct with the same cross-sectional area as a round duct, but with different perimeter (because rectangular shapes with the same area can have very different perimeters depending on their aspect ratio), will have a genuinely different friction loss — matching area alone doesn't preserve friction performance.
The Equivalent Diameter Formula
The standard formula for equivalent round diameter of a rectangular duct is De = 1.30 × (a × b)^0.625 / (a + b)^0.25, where a and b are the rectangular duct's two side dimensions. This formula is specifically derived to find the round-duct diameter that produces the same friction loss (not just the same cross-sectional area) as the given rectangular dimensions — a rectangular duct built to satisfy this equivalent diameter relationship, for a target round diameter, will perform equivalently to that round duct in terms of friction loss, even though its actual cross-sectional area typically ends up somewhat larger than the round duct's own area.
Why Extreme Aspect Ratios Perform Worse
A rectangular duct with dimensions close to square (a low aspect ratio, where a and b are similar) has a more efficient area-to-perimeter ratio, closer to round duct's efficiency, than a rectangular duct with an extreme aspect ratio (a very wide, flat shape) carrying the same equivalent diameter. This is why duct design guidance generally recommends avoiding extreme rectangular aspect ratios where space permits — a very flat, wide duct needs meaningfully more material and cross-sectional area to match the same equivalent round diameter's friction performance compared to a more square-shaped rectangular duct, even though both would satisfy the same equivalent diameter formula.
Why Rectangular Duct Is Still Often Necessary Despite Being Less Efficient
Despite round duct's inherent efficiency advantage, rectangular duct remains extremely common in real installations because it fits more practically into the physical constraints buildings actually present — shallow ceiling cavities, wall chases, and other confined spaces often can't accommodate a round duct's circular cross-section as efficiently as a flatter rectangular shape can. The equivalent diameter formula exists specifically to let designers make this practical shape compromise while still calculating and specifying rectangular dimensions that deliver the airflow performance the original friction-rate-based round duct sizing calculation intended.
Why This Site's Calculator Provides Both Round and Rectangular Output
This site's Duct Sizing Calculator's rectangular equivalent output applies this same underlying logic — starting from the friction-rate-derived ideal round diameter, it computes a rectangular equivalent sized to preserve that same friction performance, rather than simply reporting a rectangular shape with matching cross-sectional area (which, as covered above, would not actually preserve the intended friction-loss design target).