Duct Size Calculator

Duct Sizing: Equations, Variables, Methods, and Worked Examples

Duct sizing converts an airflow requirement into practical duct dimensions that deliver air quietly, efficiently, and within available static pressure. The calculator above gives you instant results; the guide below explains the underlying equations, variables, and assumptions so you can verify results, tune designs, and answer common questions clients and inspectors ask. We cover continuity, velocity targets, friction loss, \(D_\mathrm{eq}\) for rectangular ducts, and the most used design strategies: equal friction, constant velocity, and static regain.

\( \displaystyle \textbf{Continuity:}\quad Q = V A \qquad \textbf{Friction (Darcy–Weisbach):}\quad \Delta P_f = f\,\frac{L}{D_h}\,\frac{\rho V^2}{2} \)

Here \(Q\) is volumetric flow, \(V\) is average duct velocity, \(A\) is cross-sectional area, \(f\) is the Darcy friction factor, \(L\) is duct length, \(D_h\) is hydraulic (or equivalent) diameter, \(\rho\) is air density, and \(\Delta P_f\) is pressure drop to be balanced by the fan’s available static pressure together with dynamic losses from fittings.

Core Duct Sizing Equations

\( \displaystyle A = \frac{Q}{V} \quad\Rightarrow\quad D_\mathrm{round} = \sqrt{\frac{4A}{\pi}} \)

\( \displaystyle D_\mathrm{eq,rect} = 1.30\,\frac{(ab)^{0.625}}{(a+b)^{0.25}} \quad \text{(approx. for rectangular a×b giving same loss as a round)} \)

\( \displaystyle \Delta P_f = f\,\frac{L}{D_h}\,\frac{\rho V^2}{2} \ ,\qquad \Delta P_\mathrm{tot} = \Delta P_f + \sum K_i\,\frac{\rho V^2}{2} \)

\( \displaystyle \textbf{Reynolds number:}\quad \mathrm{Re} = \frac{\rho V D_h}{\mu} \ ,\qquad f=f(\mathrm{Re},\,\varepsilon/D_h) \)

Symbols & Units (commonly used):

\(Q\) — Airflow (CFM or m³/s)
\(V\) — Velocity (fpm or m/s)
\(A\) — Duct area (ft² or m²)
\(D_h\) — Hydraulic or equivalent diameter (in or mm)
\(\rho\) — Air density (≈ 0.075 lbm/ft³ at 70°F; 1.2 kg/m³ at 20°C)
\(\mu\) — Dynamic viscosity (≈ 1.81×10⁻⁵ Pa·s at 20°C)
\(\varepsilon\) — Roughness height (material dependent)
\(K_i\) — Loss coefficients for fittings (elbows, tees, transitions)

Recommended Velocity Ranges (Rule-of-Thumb)

Application	Typical Velocity	Notes
Main supply trunks	900–1,500 fpm (4.5–7.5 m/s)	Balance noise vs. size; higher in commercial cores
Branch runs	600–900 fpm (3–4.5 m/s)	Lower to reduce noise near occupied spaces
Terminal/room diffusers	400–700 fpm (2–3.5 m/s)	Comfort & acoustic driven
Return air	700–1,200 fpm (3.5–6 m/s)	Often slightly higher is acceptable

Design Methods: Equal Friction, Constant Velocity, Static Regain

1) Equal Friction

Set a target friction rate (e.g., 0.08–0.10 in w.g. per 100 ft) and size each segment so the friction loss per length is constant. This keeps pressure drops comparable along the path and is widely used for quick, practical layouts.

2) Constant Velocity

Hold velocity nearly constant along the run (e.g., 1,000 fpm in a supply trunk) and adjust size as flow changes. Simpler fan estimates and good for noise control when velocity is chosen carefully.

3) Static Regain

Gradually reduce duct area in the direction of flow so velocity decreases after takeoffs. The regained static pressure offsets downstream losses, helping maintain roughly uniform pressure to terminals in large systems.

Material Roughness and Its Impact

Rougher ducts increase friction factor \(f\) at high Reynolds numbers. Flexible duct has additional loss from inner core corrugations and bends. Keep flex straight and stretched; use smooth metal for long trunks when static pressure is limited.

Duct Type	Qualitative Roughness	Design Note
Galvanized steel (spiral/rect.)	Low	Good for mains; predictable fittings
Fiberglass duct board	Moderate	Slightly higher loss; good acoustics
Flexible duct	High (effective)	Keep short & straight to limit losses

Step-by-Step Duct Sizing Workflow

Determine design airflow \(Q\). From room loads and ventilation (CFM per space or device).
Select target velocity \(V\). Use ranges above considering acoustics and space constraints.
Compute area & preliminary size. \(A=Q/V\), then pick round \(D\) or rectangular \(a\times b\) meeting space and construction limits.
Estimate friction rate. Use equal friction target (e.g., 0.08 in w.g./100 ft) or compute via \(f\)–Re–roughness relations.
Add fitting losses. Sum \(\sum K_i \rho V^2/2\) for elbows, branches, transitions.
Check fan/static budget. Ensure \(\Delta P_\mathrm{tot}\) ≤ available fan static at design flow.
Refine. Adjust size or layout to reduce noise, minimize height, or meet architectural constraints.

Worked Examples

Example 1 — Size a Supply Branch by Velocity

A branch must deliver \(Q=300\ \text{CFM}\). Choose a quiet branch velocity \(V=800\ \text{fpm}\).

\( \displaystyle A = \frac{Q}{V} = \frac{300}{800} = 0.375\ \text{ft}^2 \ ,\qquad D_\mathrm{round} = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4\times 0.375}{\pi}} \approx 0.69\ \text{ft} = 8.3\ \text{in}. \)

Choose a standard 8 in round (slightly higher velocity) or 9 in for lower noise. If space requires rectangular, solve for \(a\times b\) with the same area and check \(D_\mathrm{eq,rect}\) for comparable losses.

Example 2 — Rectangular Equivalent Diameter

You must fit a flat rectangular branch of \(a=6\ \text{in}\) by \(b=14\ \text{in}\). What round size yields similar friction?

\( \displaystyle D_\mathrm{eq,rect} \approx 1.30\,\frac{(ab)^{0.625}}{(a+b)^{0.25}} = 1.30\,\frac{(6\cdot 14)^{0.625}}{(6+14)^{0.25}} \approx 1.30\,\frac{(84)^{0.625}}{(20)^{0.25}}\approx 9.4\ \text{in}. \)

A 9–10 in round has similar friction loss to 6×14 rectangular at the same flow rate.

Example 3 — Friction Drop Check (SI)

A 12 m spiral round duct (smooth steel) carries \(Q=0.65\ \text{m}^3\!\!/\text{s}\). Assume \(D=0.35\ \text{m}\). Compute velocity and estimate friction drop with \(f=0.022\) (representative turbulent, smooth).

\( \displaystyle A = \frac{\pi D^2}{4} = 0.0962\ \text{m}^2,\quad V = \frac{Q}{A}=\frac{0.65}{0.0962}=6.76\ \text{m/s}. \)

\( \displaystyle \Delta P_f = f\,\frac{L}{D}\,\frac{\rho V^2}{2} = 0.022\,\frac{12}{0.35}\,\frac{(1.2)(6.76^2)}{2} \approx 0.022\times 34.29\times 27.4 \approx 20.7\ \text{Pa}. \)

Add fittings: if elbows/tees sum to \(\sum K_i=2.0\), dynamic loss \(= 2.0\cdot \rho V^2/2 \approx 2.0\cdot 27.4=54.8\ \text{Pa}\). Total \(\approx 75.5\ \text{Pa}\). Verify against the fan’s available static.

Noise, Velocity Pressure, and Comfort

High velocity increases velocity pressure, \(p_v=\rho V^2/2\), which drives both noise and dynamic losses in fittings. To keep rooms quiet:

Reduce velocity approaching terminals (branch & diffuser necks).
Use gradual transitions (length ≥ 3–5 × hydraulic diameter).
Limit sharp elbows; use radius elbows or turning vanes.
Consider lined duct or terminal attenuators where needed.

Assumptions and Limitations

Standard air: Many quick calcs assume 70°F and sea-level density. Correct for altitude/temperature when necessary.
Balanced distribution: Real systems require balancing (dampers, diffuser selection). Sizing alone doesn’t guarantee exact room flows.
Roughness & fittings data: Use manufacturer/standards data for \(K\) and roughness; generic values are approximations.
Flex duct practice: Performance degrades with sag and tight bends; sizing by rigid rules but installing flex loosely leads to under-delivery.
Space constraints: Architectural limits may force rectangular shapes; check \(D_\mathrm{eq}\) and adjust for higher friction.

Duct Sizing: Frequently Asked Questions

How do I choose a target velocity?

Start with the ranges in the table: higher in mains, lower near occupants. If noise is critical, choose the lower end; if space is tight, you may need higher velocity (smaller ducts) and accept more noise/pressure drop.

Round vs. rectangular ducts—what’s better?

Round is typically more efficient (lower surface area and friction for the same flow). Rectangular is used where height/width constraints apply. Convert to an \(D_\mathrm{eq,rect}\) to compare apples to apples.

What friction rate should I use for equal friction?

Residential designers often start at 0.08–0.10 in w.g./100 ft (≈ 0.66–0.83 Pa/m). Commercial mains may target 0.08–0.2 depending on fan capacity and noise goals. Always verify total static vs. the fan curve.

Do altitude and temperature matter?

Yes. Lower density air (high altitude/higher temperature) reduces pressure drops but may require higher volumetric flow for the same mass flow/heat transport. Adjust density \(\rho\) accordingly.

Can I upsize ducts to reduce noise?

Yes—lower velocity reduces noise and dynamic loss. But upsizing increases material cost and space. Find a balance with diffuser noise ratings and architectural constraints.

How do I account for fittings?

Add each fitting’s loss coefficient \(K_i\) multiplied by \( \rho V^2/2 \). Common elbows, tees, and transitions have published \(K\) values. Your total system pressure drop equals straight-run friction plus fittings losses.

Key Takeaways

Start with airflow. Use loads/ventilation to get \(Q\), then pick velocity to compute area and preliminary size.
Check losses. Combine friction and fittings: \( \Delta P_\mathrm{tot}=\Delta P_f+\sum K_i\rho V^2/2 \).
Mind acoustics. Lower velocities near occupied zones; choose smooth paths and gentle transitions.
Use the right method. Equal friction for speed and balance, constant velocity for acoustics, static regain for large networks.
Validate with the fan curve. The sized network must operate at the fan’s available static at design \(Q\).

The equations above match what your calculator uses: continuity to set size, loss models to guard against excessive static, and velocity guidance for comfort. Pair these principles with good field practice—short straight flex runs, sealed joints, smooth fittings—and your duct design will deliver the specified airflow quietly and efficiently.