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

> Duct sizing by the velocity method divides the airflow by a chosen air velocity to get the duct's cross-sectional area, then turns that area into a round diameter or a rectangular width and height. A lower velocity gives a larger, quieter duct; a higher one gives a smaller duct with more noise and more pressure loss.

## 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

| Assumption | Default | Basis |
| --- | --- | --- |
| Design velocity | 5 m/s | A moderate figure for a main duct in an office ceiling void |
| Aspect ratio | 2 : 1 | Easy to fabricate and fits most ceiling voids |
| Size step | 50 mm | Sizes rounded up to the next 50 mm |
| Velocity flagged for noise | 8 m/s | A screening threshold only; the designer's noise criteria govern |

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:

| Step | Calculation | Result |
| --- | --- | --- |
| Airflow | 2,000 × 0.000471947 | 0.944 m³/s (944 L/s, 3,398 m³/h) |
| Area | 0.944 / 5 | 0.1888 m² |
| Round diameter | √(4 × 0.1888 / π) | 490 mm, rounded up to 500 mm |
| Rectangular height | √(0.1888 / 2) | 307 mm, rounded up to 350 mm |
| Rectangular width | 2 × 307 | 614 mm, rounded up to 650 mm |
| Velocity in 650 × 350 mm | 0.944 / (0.65 × 0.35) | 4.15 m/s |
| Equivalent round diameter | 1.30 × (650 × 350)^0.625 / (650 + 350)^0.25 | 515 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.

## Frequently asked questions

### How do I convert cfm to a duct size?

Convert the airflow to m³/s, divide by the air velocity you want in the duct to get the area, then find a round diameter or a width and height that give that area. At 5 m/s, 2,000 cfm needs about 0.19 m², which is a 500 mm round duct or a 650 × 350 mm rectangular duct once the sizes are rounded up.

### What air velocity should a duct be designed for?

It depends on where the duct runs and how quiet the space must be. Main ducts in plant rooms and shafts can run faster than branches above occupied rooms, and the last runs to diffusers are slowest of all. The designer sets velocities from the noise criteria for each space and the pressure the fan can deliver; the calculator flags anything above 8 m/s as worth checking.

### What is the equivalent diameter of a rectangular duct?

It is the diameter of a round duct that carries the same airflow with the same friction loss. Huebscher's formula, De = 1.30 × (W × H)^0.625 / (W + H)^0.25, is the one commonly used. It is not the round duct of equal area: a rectangle has more wall for its area, so its equivalent diameter is smaller than an equal-area circle.

### Why does the aspect ratio matter?

A flat, wide duct fits a shallow ceiling void, but for the same airflow it uses more sheet metal, has more surface for friction and is harder to stiffen than a squarer one. Ratios up to about 2 or 3 to 1 are easy to live with; above 4 to 1 the penalty grows, so it is usually kept for places where the ceiling depth leaves no choice.

### Can I use these sizes for fabrication?

No. They are first sizes for checking ceiling space and coordination. The final sizes come from a duct design that checks pressure loss through the whole system, fittings and dampers included, and the sheet thickness, joints and reinforcement come from the construction standard the project specifies.

## Sources

- [ASHRAE Handbook — Fundamentals](https://www.ashrae.org/technical-resources/standards-and-guidelines) — Duct design
- [SMACNA HVAC Duct Construction Standards](https://www.smacna.org/) — Metal and flexible duct construction
- [IS 655](https://standards.bis.gov.in/website/published-standards/department-wise) — Metal air ducts — specification

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Source: https://hagerstone.com/calculators/duct-size-calculator