HVAC ducts must be sized accurately to deliver the airflow needed for effective heating and cooling. Ducts with a cross-sectional area that is too small won't provide enough air, while those with an area that is too large will cause your HVAC equipment to overwork and wear out more quickly.
Duct size is determined by the velocity of airflow needed to supply the part of the building the duct is servicing. Airflow is measured in cubic feet per minute (CFM), but duct dimensions are typically measured in inches, which calls for a conversion factor to convert a cross-sectional area from square inches to square feet. Even though most pros and homeowners routinely refer to charts rather than doing the calculations themselves, it's good to know this conversion factor and how to use it.
How to Convert to Square Feet
Area is always measured in square units because it's calculated by multiplying one dimension by another. This is most obvious when calculating the area of a rectangle, which you do by multiplying the length of the rectangle by the width. If the length is L inches and the width is W inches, the area is L x W square inches. To calculate the area of a circle, you multiply the radius by itself (in other words, you square the radius) and multiply by π (pi = 3.14), which expressed mathematically is πr2. If you're using oval-shaped ducts with a long radius r1 and a radius of r2, the area is (π x r1 x r2).
The problem for ductwork installers is that dimensions are usually measured in inches, but you need square footage for airflow calculations. To convert from square inches to square feet, all you need to remember is that there are 12 inches in a foot. Therefore, 1 square foot is 12 x 12 = 144 square inches and 1 square inch = 1/144 = 0.0069 square feet.
Transitions and Sample Calculations
Ductwork installations often call for transitioning from rectangular to round or oval ductwork or vice versa because of space limitations. When changing shapes, it's important to maintain the same cross-sectional area. To see how this is done, consider transitioning from a square 6 x 6 duct to a circular one.
The cross-sectional area of the square duct is 8 x 8 = 64 square inches. To find a round duct with the same area, consider that πr2 = 64 and solve for r: r2 = 64/3.14 = 20.4 square inches, so r = √20.4 = 4.5 inches. Since radius is half the diameter of a circle and you always measure round duct by diameter, you need 9-inch round duct to make the transition.
To calculate the cubic feet in a sample 1-foot length of this duct, convert the cross-sectional area to square feet using the conversion factor: 36 square inches x 0.0069 square feet per square inch = 0.25 square feet. Multiply that by 1 to find that each sample section has a volume of 0.25 cubic feet. Using this figure, you can calculate airflow in cubic feet per minute.
Most Pros Use Charts
In reality, airflow through a duct system depends on other factors besides cross-sectional area, the main ones being shape and friction loss due to the duct material. Flexible ducting has corrugated sides that impede airflow, and air passes more smoothly through round ducts than rectangular ones. Calculations of the required airflow in CFM using the cross-sectional area of the ductwork and the conversion factor don't take frictional losses into account, so pros usually use duct sizing charts rather than trying to handle all the complex calculations themselves.
Chris Deziel is a contractor, builder and general fix-it pro who has been active in the construction trades for 40 years. He has degrees in science and humanities and years of teaching experience. An avid craftsman and musician, Deziel began writing on home improvement topics in 2010. He worked as an expert consultant with eHow Now and Pro Referral -- a Home Depot site. A DIYer by nature, Deziel regularly shares tips and tricks for a better home and garden at Hunker.com.