Duct Size Calculator: Round and Rectangular Ducts by the Velocity Method

What it calculates

Given the airflow a duct has to carry and the air velocity you want in it, the calculator gives:

• the round duct diameter, rounded up to the next size step, with the velocity in the rounded duct;
• the rectangular duct width and height at the aspect ratio you choose, both rounded up, with the velocity re-checked in the rounded duct;
• the equivalent round diameter of that rectangle, for comparing it with round duct;
• every size in millimetres and inches.

It is meant for the early questions: will a duct this size fit in the ceiling void, how deep does the bulkhead need to be, and does a duct shown on a drawing look about right for the air it carries.

Inputs

Airflow is the air the length of duct carries, entered in cfm, m³/h or L/s. For a main duct it is the whole supply of the air handler; for a branch, only the share that branch serves.

Design air velocity is the speed of the air in the duct, in metres per second. It is the main choice in the method: a lower velocity is quieter and loses less pressure but needs a bigger duct, and a higher one saves space at the cost of noise and fan energy.

Rectangular aspect ratio is the width divided by the height. A ratio of 2 gives a duct twice as wide as it is deep. Raise it when the ceiling void is shallow.

The assumptions panel holds the size step that results are rounded up to and the velocity above which the calculator flags a noise risk.

Method

1. Convert the airflow to m³/s (1 cfm = 0.000471947 m³/s).
2. Area: A = Q / v.
3. Round duct: D = √(4A / π), rounded up to the next size step.
4. Rectangular duct: H = √(A / AR) and W = AR × H, each rounded up to the next size step.
5. Velocity re-check: v = Q / (W × H) in the rounded rectangle, and Q / (πD² / 4) in the rounded round duct. Because the sizes only round up, the actual velocity is never higher than the design velocity.
6. Equivalent round diameter of the rounded rectangle by Huebscher's formula: De = 1.30 × (W × H)^0.625 / (W + H)^0.25, with W and H in millimetres.

This is the velocity method, the simplest of the duct design methods described in the ASHRAE Handbook — Fundamentals. Designers more often size low-pressure supply duct by equal friction, or by static regain on long runs, and use velocity as a check; the velocity method is still the quickest way to a first size.

Assumptions

The velocity is the assumption to question first. Low-velocity supply systems in offices commonly run their main ducts at moderate speeds and slow down towards the diffusers, with the slowest air nearest the quietest rooms. A duct above a boardroom or a recording studio needs a lower figure than one in a basement plant room. The designer sets each velocity from the noise criteria for the space and the pressure the fan can deliver.

Limitations

• It does not calculate pressure loss. Friction along the duct and losses at bends, branches, dampers and diffusers decide the fan pressure, and sometimes the duct size.
• It ignores insulation and lining. Sizes here are internal. External insulation adds to the space a duct takes, and internal acoustic lining reduces the free area.
• It does not check the construction. Sheet thickness, joints, seams, reinforcement and supports come from the construction standard the project specifies, such as IS 655 or the SMACNA HVAC Duct Construction Standards.
• It does not lay out the system. Branch takeoffs, balancing and diffuser selection are separate design steps.
• It handles one section at a time. Every change in airflow along a run needs its own size.

Worked example

A main supply duct carrying 2,000 cfm at a design velocity of 5 m/s, with a 2 : 1 aspect ratio and sizes rounded up to the next 50 mm:

The result is a 500 mm round duct (19.7 in), in which the air moves at 4.81 m/s, or a 650 × 350 mm rectangular duct (25.6 × 13.8 in), in which it moves at 4.15 m/s (817 fpm). The rectangle's equivalent round diameter is 515 mm (20.3 in): rounding both sides up has given it slightly less friction than the 500 mm round duct.

If the ceiling void is too shallow for a 350 mm duct plus insulation and supports, a 4 : 1 aspect ratio gives 900 × 250 mm, at 4.20 m/s, for the same airflow. If the duct runs over a quiet room and the velocity is cut to 4 m/s, the sizes grow to 550 mm round or 700 × 350 mm.

How engineers use it

An HVAC engineer starts from the airflows set by the heat-load and ventilation calculations, lays out the duct routes against the structure, the ceiling and the other services, and then sizes each section. Low-pressure supply duct is usually sized for a constant friction loss per metre, with velocities checked against limits for noise; long runs may be sized by static regain so pressure stays even along the run. The sizes then go into coordination with sprinklers, cable trays and lighting, and the pressure loss of the worst run sets the fan.

A velocity-method size is still useful to the engineer at concept stage, to check whether a ceiling void or a shaft is deep enough before the layout is drawn.

When a professional design must replace it

Use the calculator to test ceiling depths, check a duct on a drawing against its airflow, and compare round and rectangular options. Replace it with a duct design by an HVAC engineer before ductwork is fabricated or ordered, wherever noise matters, wherever the fan pressure is tight, and for any duct that is part of a smoke control or pressurisation system, which has its own design requirements.