How This Calculator Works

Every number this calculator shows comes directly from two published engineering formulas — not a lookup table, not a rule of thumb, and not a guess. This page walks through exactly what the calculator does with your inputs, in the same order the code runs it, so you can see why the duct size you get matches what a duct-sizing worksheet or ductulator would give you.

Step 1 — The equal-friction method

The default sizing mode is equal friction: you pick a friction rate — how much static pressure the air loses per 100 feet of straight duct — and every run in the system is sized to lose pressure at that same rate. It's the method taught in ACCA Manual D and used by most residential and light-commercial duct designers because it's simple to apply consistently across a whole system and tends to produce reasonably quiet, reasonably efficient ducts without a lot of iteration.

The calculator solves the standard round-duct friction equation for galvanized sheet metal:

FR = 0.109136 × Q^1.9 / d^5.02

where FR is friction rate in inches of water gauge per 100 feet, Q is airflow in CFM, and d is duct diameter in inches. This is the Darcy-Weisbach-derived friction equation for smooth round galvanized duct that underlies the friction charts (ductulators) HVAC techs have carried for decades — the calculator just solves it directly instead of reading it off a paper wheel.

Step 2 — Solving for diameter, then rounding up

Given your CFM and target friction rate, the equation is inverted algebraically to solve for the exact diameter that would produce exactly that friction rate. That exact value is almost never a size a sheet-metal shop stocks — 9.8", 13.4", 17.4" — so the calculator rounds up to the next size in the standard round-duct series (4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 40, 42, 48 inches). Rounding up rather than down is deliberate: a slightly larger duct runs at a slightly lower actual friction rate and velocity than requested, which is the safe direction — undersizing would push both above target.

Step 3 — Velocity, computed from the rounded size

Once the standard size is picked, velocity is recalculated for that actual size (not the exact theoretical one) using:

V = 183.3 × Q / d²

giving feet per minute. This is the number that determines whether a duct will be noticeably noisy — quiet is generally under 600 fpm, 600–1,200 fpm is typical for branches and trunks, and above roughly 1,500 fpm usually reads as audibly loud. The actual friction rate for the rounded-up size is also recomputed and shown, so you can see it's at or slightly below your target, never above it.

Step 4 — The velocity-target mode

Switching the "size by" dropdown to target velocity instead skips the friction equation and solves directly for the diameter that produces a chosen fpm:

d = 13.541 × √(Q / V)

This is useful when noise is the binding constraint rather than static pressure — for example sizing a duct run near a bedroom where you want to guarantee a velocity ceiling regardless of what friction rate that implies.

Step 5 — The rectangular equivalent

Round duct is the most material- and friction-efficient shape, so it's sized first; the rectangular options shown underneath are then generated by solving ASHRAE's round-to-rectangular equivalent-diameter equation for a matching width at each of several standard heights (8, 10, 12, 14, 16, 18 inches):

De = 1.30 × (a·b)^0.625 / (a+b)^0.25

The calculator holds the height fixed and numerically searches for the width that makes a rectangle's equivalent diameter match the round duct's — this is solved by bisection rather than a closed-form formula, since the equation can't be rearranged cleanly for width. Full worked examples of this conversion are on the round-to-rectangular page.

Assumptions baked into the math

• Galvanized sheet metal is the friction basis — it's the standard reference material for the friction equation. Flex duct has meaningfully higher friction per foot — commonly cited at 3–8× a smooth metal duct's friction depending on how taut and well-supported it is — so a flex run should generally be sized up one increment from the metal-duct result shown here.
• Straight duct only. The friction rate calculated is for straight pipe — it doesn't add pressure-drop equivalents for elbows, transitions, dampers, or boots. A full Manual D system design accounts for total effective length including fittings; this calculator sizes an individual run's straight section.
• No distinction between supply and return in the math itself — the same formulas apply to both. Return ducts are conventionally sized to a lower velocity target for comfort reasons (often 500–600 fpm for a return trunk, versus 700–900 fpm for supply branches).

What this tool is not

This is a single-run sizing calculator, not a full Manual D/Manual J system design tool. It doesn't calculate room-by-room heat loss/gain, total effective length with fitting equivalents, or blower static-pressure budgets across a whole duct system. For a complete design, run full Manual D calculations (or have an HVAC contractor do so) and use this calculator to spot-check individual run sizes against the same equal-friction logic the industry standard is built on.

Where to verify this independently

The friction and equivalent-diameter equations above are standard, published HVAC engineering formulas — the same ones behind paper and slide-rule "ductulators" — not something invented for this site. If you want to cross-check a result, any ACCA Manual D-compliant duct calculator or friction chart using galvanized round duct as the basis should return the same standard size for the same CFM and friction rate.

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