Updated September 2026
You have a CFM number — from a Manual J load calculation, an equipment nameplate, or a rule-of-thumb estimate — and need a duct size. This page walks through exactly how that conversion happens, with the arithmetic shown at every step, so the calculator's answer isn't a black box.
Duct size isn't a direct function of CFM alone — it also depends on how much friction (static pressure loss) you're willing to accept per 100 feet of duct. More CFM through the same size duct means more friction and higher velocity; the same CFM through a bigger duct means less of both. The equal-friction method fixes a target friction rate and solves for the diameter that hits it at your specific CFM.
Say a bedroom branch needs to deliver 400 CFM, sized to the standard residential friction rate of 0.1 in.wg per 100 ft.
d = (0.109136 × Q1.9 / FR)1/5.02. Plugging in Q = 400 and FR = 0.1 gives an exact diameter of 9.83 inches.V = 183.3 × 400 / 10² = 733 fpm. Actual friction at 10": 0.092 in.wg/100 ft — just under the 0.1 target, because the rounded-up size is very slightly larger than the exact theoretical one.733 fpm falls in the "typical for supply branches" range (roughly 600–900 fpm) — a reasonable result for a bedroom branch. If it had come out above roughly 1,200–1,500 fpm — the point this calculator flags as audibly loud — the practical fix is to loosen the friction-rate target (accept more static pressure loss for a smaller duct) or size up a step manually and accept extra material cost for a quieter run.
Because the friction rate is a free variable, the same 400 CFM sizes to different ducts depending what target you pick: at a looser 0.15 in.wg/100 ft it would round to a 9" duct at higher velocity; at a tighter 0.06 it would round to a full 12" at noticeably lower velocity. A single static "CFM → duct size" table (like the duct sizing chart on this site) has to pick one friction rate and hold it fixed — which is exactly why the calculator, not a table, is the accurate tool when your target friction rate differs from the standard default.
If noise matters more than static pressure in a specific run — say a duct passing directly over a bedroom — switch the calculator to "target velocity" mode. It solves a different, simpler formula directly: d = 13.541 × √(Q / V). For the same 400 CFM targeting 700 fpm: d = 13.541 × √(400/700) = 13.541 × 0.756 ≈ 10.2", rounding up to 12" — noticeably larger than the friction-based result, because a strict velocity ceiling is a more conservative constraint here than the standard friction rate alone.
Everything above assumes the CFM input is already correct — the calculator can't validate that part. CFM should come from an actual Manual J heat-loss/heat-gain calculation split across rooms, or from the rated blower airflow of the installed equipment divided across branches by load. A rough field estimate some techs use for a quick trunk check is about 400 CFM per ton of cooling capacity — useful for a sanity check, not a substitute for a real load calculation on a specific job.
Does a bigger duct always mean better performance? Not necessarily — oversizing wastes sheet metal and space and can lead to poor mixing at very low velocities. The equal-friction method is designed to land in a reasonable middle range, not the biggest duct that fits.
What if my CFM doesn't match any standard duct size cleanly? That's normal — almost no exact CFM lands precisely on a stocked size. The rounding-up step handles it automatically and always favors the safe (lower friction, lower velocity) direction.
Is the formula different for return ducts? The underlying friction and velocity equations are the same; what differs is the target — returns are conventionally sized to a lower velocity (often 500–600 fpm) for comfort, rather than the standard friction rate used for supply branches.