In your home heating/air conditioning system, you have ductwork to push air through your home. Round ducting is often found -- it pushes air more efficiently because there is less surface area to resist air flow and alter temperatures. In some circumstances, however, space availability may require you to use rectangular ducting. Adaptors are commercially available to change from round to rectangular ducting, but before buying one, be sure to measure the cross-sectional area of both types of duct.
Measure the diameter of your round duct. The diameter is the largest distance from one side of a circle to the other. For example, 20 cm (8 inches).
Divide the diameter by 2 to get the radius of the circular duct cross-section. In the example in Step 1, 20/2 = 10 cm (4 inches).
Multiply this number by itself -- for example, 10 x 10 = 100 (4 x 4 = 16).
Multiply this number by 3.14 (pi) to get the area of the round duct in square inches -- for example, 100 x 3.14 = 314 square cm (16 x 3.14 = 50.24 square inches).
Select a size of square duct that has the same area. This can be found by multiplying the two adjacent sides of the rectangular duct. For example, if you found a duct that measured 25 cm by 12.5 cm (10 inches by 5 inches), its area would be 312.5 square cm (50 square inches).
Select an adaptor that will convert between the round and the square duct sizes from your local building supply centre; for example, our original 20 cm (8 inch) round duct should be mated to the 25 cm by 12.5 cm (10 inch by 5 inch) rectangular duct because they have the same cross-sectional area.
Duct sizing can get very technical when taking friction losses, flow rates, velocities, surface tension, material composition and hydraulic diameters into consideration. As a rule of thumb, size rectangular ducts slightly larger than circular ducts in terms of cross-sectional areas, due to increased surface areas in rectangular ducts.