HVAC Duct Size Calculator
Duct sizing balances airflow against air velocity: too small and the duct is noisy and high-resistance, too large and it wastes space and material. This calculator applies the continuity relation, airflow equals velocity times cross-sectional area, to find the area a duct needs for a target velocity, then gives the equivalent round duct diameter. It also checks a rectangular duct you specify, reporting the velocity that duct would carry at your airflow. The formulas are exact physics and geometry with no estimated constants.
Duct sizing formula
Required area (sq ft) = airflow / velocity
Required area (sq in) = required area (sq ft) * 144
Round diameter (in) = sqrt(4 * area sq in / pi)
Rectangular area (sq in) = width * height
Rectangular velocity (ft/min) = airflow / (rectangular area / 144)
The continuity relation flow equals velocity times area gives the required cross-section. The factor 144 converts square feet to square inches. The diameter follows from the area of a circle.
Duct sizing context
- Airflow equals velocity times cross-sectional area; this is the continuity relation.
- Higher velocities reduce duct size but increase noise and friction losses.
- Round ducts use less material than rectangular ducts for the same area.
- Design velocities depend on the application and acceptable noise level.
- Check the rectangular duct velocity against your design limit before selecting it.
HVAC duct size: frequently asked questions
How do I size a duct from airflow and velocity?
Air volume flow equals velocity times cross-sectional area, so area equals airflow divided by velocity. With airflow in cubic feet per minute and velocity in feet per minute, area comes out in square feet. The round duct diameter follows from the area of a circle.
What air velocity should I use?
Design velocity depends on the application and noise limits; supply trunks often use higher velocities than branch runs. Velocity is an input here so you can match the design value for your system from ductwork design references.
How is the round duct diameter found?
From the area of a circle, area equals pi times radius squared. Rearranged, diameter equals the square root of four times the area divided by pi. The calculator converts the result to inches for practical duct selection.
Can I check a rectangular duct?
Yes. Enter a rectangular duct width and height and the calculator reports the air velocity that duct would produce at your airflow, so you can confirm it stays within your design limit. Velocity equals airflow divided by the rectangular cross-section area.
Are these formulas exact?
Yes. They are the continuity relation (flow equals velocity times area) and the geometry of a circle and rectangle, with exact unit conversions. There are no empirical constants, so the results are exact for the values you enter.
Official sources
- U.S. Department of Energy: Heating, cooling, and ductwork guidance.
- National Institute of Standards and Technology: Unit definitions (cubic foot, foot).
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.