Introduction
Behind every duct size on a plan sit three calculations and one design method. The calculations convert airflow into area, area into diameter, and pressure budget into a friction rate; the method, equal friction, ties them together so every duct is designed to the same pressure drop per foot. This guide derives each step with numbers you can check by hand, in imperial and metric. To skip the arithmetic, use the Ductwork Calculator — then come back here to understand what it did.
The Three Formulas
Formula 1 — Duct area from airflow and velocity
A (ft²) = CFM ÷ V (FPM)
Airflow divided by velocity gives the cross-sectional area the air must pass through. This is the continuity equation: the same CFM through a smaller area must move faster. Pick the velocity from noise guidelines — 900 FPM (4.57 m/s) maximum for residential branch runs — and the area follows. Example: 200 CFM ÷ 900 FPM = 0.2222 ft², which is 32 in² (0.2222 × 144).
In metric: A (m²) = Q (m³/s) ÷ V (m/s). 200 CFM = 94.4 L/s = 0.0944 m³/s; 0.0944 ÷ 4.57 = 0.02066 m² = 206.6 cm². Same duct, either system.
Formula 2 — Round diameter from area
D = 2 × √(A ÷ π), with A in square inches giving D in inches.
Continuing the example: A = 32 in²; 32 ÷ π = 10.186; √10.186 = 3.192; × 2 = 6.38 in → 8-in round (152 mm → 203 mm), rounding up to the next standard size. Standard round ducts step in 2-inch increments, so calculated diameters almost never land exactly on a stocked size — always round up, never down.
Metric check: A = 0.02066 m²; 0.02066 ÷ π = 0.006577; √ = 0.0811; × 2 = 0.162 m = 162 mm → 175 or 200 mm standard (European) or 8 in (203 mm) in North American stock.
Formula 3 — Design friction rate
FR = (ASP ÷ TEL) × 100
Where ASP is the available static pressure for the ductwork (inches of water column) and TEL is the total equivalent length in feet of the longest run — straight duct plus every fitting converted to equivalent feet. The result is inches of water column per 100 ft.
Example: the air handler is rated for 0.50 in w.g. total external static pressure. Component losses — filter, evaporator coil, supply and return grilles — consume about 0.25 in w.g., leaving ASP = 0.25 in w.g. for ducts. The longest run: 60 ft of trunk + 25 ft of branch = 85 ft of straight duct, plus fittings totaling 165 ft equivalent (takeoffs, elbows, boots, transitions) → TEL = 250 ft. FR = (0.25 ÷ 250) × 100 = 0.10 in w.g./100 ft — the top of the standard 0.08–0.10 residential band (≈ 0.82 Pa/m).
The Equal-Friction Method, Step by Step
Equal friction (ACCA Manual D’s core method) sizes every duct section so each experiences the same friction rate. The procedure:
- Determine room-by-room CFM from the load calculation. Sum to get total system CFM.
- Sketch the layout — trunk route, branch takeoffs, register locations — and measure straight lengths.
- Convert fittings to equivalent length using a standard table (see below) and add to straight lengths → TEL for the longest supply run and longest return run.
- Compute the design friction rate from available static pressure ÷ TEL.
- Size each section: area = section CFM ÷ target velocity, or read diameter directly from a ductulator (friction-rate chart) at the design FR.
- Verify the critical path: the run with the highest TEL must fit within the pressure budget; if FR lands above 0.10, the layout needs shorter runs, fewer fittings, or larger ducts.
A ductulator is just these formulas printed as a slide rule: set CFM against the friction rate and read the diameter. The calculator performs the same lookup digitally. For the reasoning behind each input choice, the complete guide covers terminology and the worked bedroom example.
Equivalent Length Reference
These are typical planning values for residential fittings; manufacturer data and Manual D tables govern final design:
| Fitting | Equivalent length (ft) | Equivalent length (m) |
|---|---|---|
| 90° smooth-radius elbow, round | 10 | 3.0 |
| 90° pleated / adjustable elbow | 15 | 4.6 |
| 90° rectangular elbow without turning vanes | 20–30 | 6.1–9.1 |
| 90° rectangular elbow with turning vanes | 10 | 3.0 |
| 45° elbow | 5 | 1.5 |
| Supply takeoff with damper | 35 | 10.7 |
| Return takeoff | 25 | 7.6 |
| Register / diffuser boot | 15 | 4.6 |
| Gradual transition | 10 | 3.0 |
| Abrupt transition | 20 | 6.1 |
A single supply takeoff (35 ft) outweighs 35 feet of straight duct — fittings dominate residential TEL. Fitting mistakes are catalogued in the common mistakes guide.
Round-to-Rectangular Conversion
Rectangular ducts are sized by equal friction to carry the same CFM at the same pressure drop as a round duct. Common equivalents (round → rectangular at equal friction):
| Round diameter | Area | Typical rectangular equivalents |
|---|---|---|
| 6 in (152 mm) | 28.3 in² | 8×4, 6×6 in |
| 8 in (203 mm) | 50.3 in² | 10×6, 8×8 in |
| 10 in (254 mm) | 78.5 in² | 12×8, 10×10 in |
| 12 in (305 mm) | 113.1 in² | 14×10, 12×12 in |
| 14 in (356 mm) | 153.9 in² | 16×12, 14×14 in |
Keep the aspect ratio (width ÷ height) at 4:1 or less — flat, wide ducts have more surface friction per unit of area and need upsizing. A 20×6 in duct looks like it should match a 14-in round by area, but its friction is substantially higher.
Worked Example: Sizing a Trunk Segment
A trunk segment carries 600 CFM (283 L/s) to four downstream branches. Design friction rate: 0.09 in w.g./100 ft.
Step 1 — Velocity target. Supply trunk: 800 FPM (4.06 m/s).
Step 2 — Area. 600 ÷ 800 = 0.75 ft² = 108 in².
Step 3 — Round diameter. 2 × √(108 ÷ π) = 2 × 5.864 = 11.73 in → 12-in round (305 mm).
Step 4 — Rectangular option. From the table, 12-in round ≈ 14×10 in (356×254 mm) — which fits nicely in a 16-in joist bay.
Step 5 — Actual velocity. 12-in round = 113.1 in² = 0.785 ft²; 600 ÷ 0.785 = 764 FPM (3.88 m/s) — within the 700–900 trunk band.
After the first branch peels off 150 CFM, the next segment carries 450 CFM and resizes to 10-in round (254 mm) — the stepped trunk. Trunk stepping logic and layout strategy are explored in the case study walkthrough.
Where the Formulas Stop
The math sizes ducts; it doesn’t place them. These formulas assume straight, sealed, properly supported ducts — always verify against the equipment’s blower performance table and local code, as the code compliance guide details.
Related Guides
- Complete Guide — terminology, worked bedroom example, and sizing overview.
- Pro Tips — layout and installation practices that keep the math valid.
- Estimating Guide — turning a sized layout into a material list.
- Material Guide — how duct material changes friction behavior.
- Installation Checklist — verifying the installed system matches the design.
Frequently Asked Questions
What is the formula for duct size?
Area = CFM ÷ velocity (FPM); then diameter = 2 × √(area ÷ π) for round duct, rounding up to the next standard size. The design friction rate = (available static pressure ÷ total equivalent length) × 100.
What is equal friction method?
A Manual D duct-sizing method where every duct section is designed to the same pressure drop per unit length — typically 0.08–0.10 in w.g. per 100 ft (0.65–0.82 Pa/m) residential. It balances duct size, cost, and blower load across the whole system.
How do you calculate equivalent duct length?
Add the straight duct length to the equivalent length of every fitting (e.g., 35 ft for a supply takeoff with damper, 10 ft for a smooth 90° elbow). The total (TEL) is what the friction rate divides into.
How do you convert round duct to rectangular?
Use equal-friction equivalents: a 10-in round ≈ 12×8 in rectangular. Keep aspect ratio ≤ 4:1, since wide flat ducts have higher friction per unit area than the round equivalent.
What friction rate should I design to?
Compute it from your system: (available static pressure ÷ longest-run TEL) × 100. Residential designs typically land at 0.08–0.10 in w.g./100 ft. If your calculation gives 0.15+, the layout needs fewer fittings, shorter runs, or a lower-loss design.
Get Your Number
Three formulas and one method: area from CFM and velocity, diameter from area, friction rate from pressure budget and equivalent length — all tied together by equal friction. Run your own numbers through the Ductwork Calculator, then spot-check one run by hand using the steps above. If the hand calc and the calculator agree, you understand the system; if they don’t, you’ve found the input worth double-checking.
Disclaimer: These formulas are planning tools based on standard Manual D methods. Actual system performance depends on installation quality, equipment static pressure ratings, and local code requirements. Verify designs with a licensed HVAC professional and your local building authority.
