Rule of Thumb for Sizing Subwoofers

The addition and integration of subwoofers into a stereo system is one of the most misunderstood things in audio. To make life easier, i have developed a rule-of-thumb to help simplify things a bit.

Begin by calculating the surface area of the woofers in your speakers. For those of you who are a bit rusty with middle school math, A = π r². 

For example, if we have a 6" woofer in each of the front (L/R) speakers, then A = 2 * 3.14 * 3 * 3 = 56.5 sq/in. If we have a pair of 8" woofers in each front speaker, then A = 4 * 3.14 * 4 * 4 = 200.9 sq/in. 

The rough range for the ideal size of a subwoofer is between 1x and 2x the area of the front woofers. 

Sticking with the example of 6" woofers, we would be looking for a subwoofer (or subwoofers) with an area of between 56.5 and 113 sq/in.

We can convert area to diameter with the following formula: D=2 (sqrt(A/Pi)), which in this case works out to 8.5" to 12"

Now that we have a rough range, let's try to narrow things down a bit. To do so, we start by looking at the in room frequency response curve of our front speakers to get a sense of where we need to crossover... Don't worry if you don't have the tools to do this yourself, audio reviews will often include information that is "good enough" for this step. 

For this example, we can pretend our 6" speakers are pretty flat down to about 500hz, and fall off a cliff by 300hz. 

The goal is to find the largest subwoofer within the rough range calculated earlier that allows the subwoofer to "disappear" in the room, put another way, we want the subwoofer to have little directivity at the frequencies it will be used for. 

We can approximate this frequency for any given subwoofer with the following formula: 13500 / driver-diameter / 2. For an 8.5" subwoofer this works out to be 794hz, and for a 12" subwoofer it is 562hz. 

Given that the 6" example speakers dont need any help below 500hz, a 12" subwoofer with its ability to disappear below 562hz is a pretty good place to start. 

Somewhat counterintuitively, if the example 6" speaker rolled off the low frequencies at around 1khz rather than 500hz, we would be better off opting for the 8.5" subwoofer with its ability to "disappear" at frequencies up to about 800hz. Alternatively, we could go for a pair of 8.5-12 inch subwoofers, with one located close to each of the front speakers - since with this arrangement some directivity is acceptable.  

With all that said, modern digital signal processing (DSP) such as DIRAC or the DSP built into some of the nicer subwoofers make it much easier to integrate a subwoofer by using digital "tricks."

I personally prefer to get the fundamentals as close to "right" as i can, and just use digital "tricks" for fine tuning. 

To be clear, rules of thumb never tell the whole story, they are specifically designed to simplify an otherwise complex issue… But they are still good tools for narrowing down the field.

This particular “rule” provides a starting point for the selection of a subwoofer, not an end point.