Duct Size Calculator

The friction-rate method

Duct sizing is not about squeezing air through the smallest pipe that will take it. It is about picking how much pressure you are willing to spend per hundred feet of duct, and then sizing every section to spend it at the same rate.

That number is the friction rate, in inches of water gauge per 100 feet. The residential convention is 0.1 in.w.g. per 100 ft, and it exists because it produces velocities that are quiet and duct sizes that fit in a house. Size everything at the same friction rate and the system self-balances: air divides itself between branches roughly in proportion to their capacity, because each path costs the same per foot.

The underlying relationship, for galvanised round duct, is:

Δp = 0.109136 × Q^1.9 ÷ D^5.02

where Δp is inches w.g. per 100 ft, Q is CFM and D is diameter in inches. Rearranged for what you actually want:

D = (0.109136 × Q^1.9 ÷ Δp)^(1/5.02)

Note that exponent of 5.02 on the diameter. Duct resistance is extraordinarily sensitive to size — a small increase in diameter buys a large reduction in pressure loss. Going from 6 in to 7 in, a 17% increase, cuts the friction loss by more than half.

A worked example

A branch run carrying 400 CFM — one ton of cooling at the standard 400 CFM per ton — in galvanised round duct at 0.1 in.w.g. per 100 ft.

• Q^1.9 = 400^1.9 = 88,000
• 0.109136 × 88,000 = 9,604
• 9,604 ÷ 0.1 = 96,040
• D = 96,040^(1/5.02) = 9.83 inches

Round up to the stock 10 in. Check the velocity:

• Area = π × 5² ÷ 144 = 0.545 sq ft
• Velocity = 400 ÷ 0.545 = 733 fpm

That is right at the top of the comfortable range for a branch feeding a bedroom register, and a fraction over the 700 fpm most designers hold to. Squeeze the same 400 CFM into 8 in round and the calculation says you are running at 0.19 in.w.g. per 100 ft and 1,146 fpm — nearly twice the friction and audible in a quiet room. That is the trade-off in one example: friction rate sets size, size sets velocity, and velocity sets noise.

Velocity is a noise specification

Air makes noise moving through duct, and the noise rises sharply with velocity. The working limits:

• Branch runs to bedrooms and living spaces: 500–700 fpm. Above about 750 you hear it, and above 900 people complain.
• Supply trunks and mains: 700–900 fpm. They are usually in an attic, crawl or basement, so a little more noise is tolerable, and the runs are short.
• Returns: 500–700 fpm. Return grilles are often in a hallway at head height, so they are the most audible part of the system and the most commonly undersized.
• Mechanical rooms and commercial mains: 1,000–1,500 fpm is normal, because nobody is trying to sleep next to it.

Velocity too low is also a fault, though a rarer one. Below about 400 fpm supply air fails to throw across the room from the register and dumps straight down the wall, which people experience as a cold draught in one spot and a stuffy room everywhere else.

Equivalent round diameter for rectangular duct

Rectangular duct is not sized by matching cross-sectional area — that gets it wrong, because a flat duct has far more wall surface per unit of air and therefore more friction. The correct conversion is the equivalent round diameter:

De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25

where a and b are the rectangular dimensions in inches. A rectangular duct has the same pressure loss as the round duct whose diameter equals its De.

The practical consequence: aspect ratio costs you. A 8 × 8 square duct has a De of 8.7 in. Flatten it to 4 × 16 — same 64 square inches — and the De drops to 8.3 in, so it carries less air for the same pressure. Push it to 3 × 22 and it falls further still. Keep the aspect ratio under about 4:1 where you can, and treat every extra bit of flattening as a real loss you are paying for in blower power, not a free way to fit duct into a joist bay.

What this does not cover

This sizes duct sections. It does not size a system. A real design — Manual D — starts by measuring the available static pressure at the blower, subtracts the filter, coil, registers and grilles, divides what is left by the total effective length of the longest run including every fitting's equivalent length, and only then arrives at the friction rate to size with. An elbow can be worth 25 feet of straight duct, a boot more. On a badly laid out system the fittings dominate.

Two more things worth stating plainly: flexible duct only performs near these numbers when it is pulled taut and fully supported, and a compressed or sagging flex run can lose several times its rated pressure per foot. And any duct outside the conditioned envelope should be sealed with mastic and insulated — leaky attic duct routinely throws away twenty to thirty percent of the system's capacity before the air reaches a room.