There's a reason pros go to school and serve apprenticeships before sizing ductwork for residential HVAC systems. This complicated process involves such variables as the output of the system, the airflow needs of the conditioned space as well as the furnace or air conditioner, the friction generated by air flowing through the ducts and the thermal characteristics of the building. The calculations are beyond the scope of the average homeowner, although it doesn't hurt to have a general idea of what's involved.
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If you have to replace a section of ductwork because it's leaking or contaminated by mold or rodent debris, you don't have to make all these calculations. All you have to do is measure the existing ductwork and buy an identical replacement. In some cases, it's advantageous to switch from rectangular or circular ducts to oval or oblong ones because they fit better in tight spaces, and for that, it's best to use an online conversion tool to avoid having to make complicated calculations.
How Pros Size Ductwork
Ductwork sizing starts with measuring in square feet the floor area of the entire space to be conditioned. Once you have the measurements of each room and the living space in total, it's time to calculate the necessary cubic feet per minute (CFM) for each room and the house overall and factor in the output of the HVAC system, which you do by dividing 400 (the average HVAC output in CFM/ton) by the square footage to provide a multiplier. The airflow required in each room is then [(HVAC system tonnage x 400) / area of entire building]. This will give you the multiplier for all the rooms in CFM. For example, for a 2,000 square-foot home: (4 tons x 400)/2,000= 0.8 multiplier. With this, a 120 square-foot room x 0.8 multiplier = 150 CFM.
Once you have calculated the CFM for each room, you need to evaluate the friction loss rate of your system. This is impacted by a variety of factors, including the length of each duct, how many vents or branches come off it, whether it's the main duct or how far from the HVAC unit a particular branch is located along the main duct. Most pros use an online calculator, such as the one at FreeCalc.com.
Having determined the required airflow and the friction loss, an HVAC technician can now calculate the correct duct size. This is still a complex calculation, and most pros resort to a slide-rule-like device known as an air duct calculator, or "ductulator." It isn't impossible for homeowners to do their own duct sizing using these tools and resources, but because even a small miscalculation can result in poor air quality or impaired performance of the system, it's best to leave it to pros.
Measuring for Replacement Ductwork
If you are trying to measure ductwork solely for the purpose of removing and replacing a broken piece or insulating existing ductwork, you don't need to worry about airflow and CFM. If you have round ducts, you simply measure the diameter (D) of the duct (the cross-section). This will tell you what size duct to purchase to replace it. If you have rectangular or square ducts, measure the width (W) and height (H) of the duct and use these figures when buying new parts.
If you need to change from circular to rectangular ducts, you have to make sure the ducts have the same cross-sectional areas. The area of a circle is π D2 /4, and the area of a rectangle is W x H, so set up the equation (π D2)/ 4= W x H, plug in the values you know and solve for the ones you don't know. Note that there is more than one possibility when switching from circular to rectangular ductwork. For example, if the cross-sectional area is 6 inches, both 4 x 7-inch and 5 x 6-inch ductwork would provide enough cross-sectional area. This conversion can be helpful when extending ductwork or replacing parts.
Switching to Oval Ducts
Converting from round to rectangular ducts is fairly straightforward, but the math involved in switching to oval ductwork is a little more complicated. For this, it's easier to use an online conversion tool, such as the one provided at the Engineering ToolBox. You can also use this tool to convert to oblong ducts with straight sides and rounded ends, and if you're math challenged, you can use it to convert from round to rectangular and vice versa.