This is an article I wrote for SoundGirls. Here’s the original.

Do you usually choose speakers by guessing? I want to show you one simple tool to find the exact right speaker for any space.

It is called Forward Aspect Ratio (FAR) and it is simply the shape a speaker makes, defined by depth and width. Here’s how you can reverse engineer it to master the universe.

- Measure the depth of your space at mid-width.
- Measure the width of your space at mid-depth.
- FAR = depth ÷ width.
- Cov. Angle = 2 × arcsin(1 ÷ FAR).

Let’s walk through it together.

## 1. Measure the depth of your space at mid-width.

## 2. Measure the width of your space at mid-depth.

## 3. FAR = depth ÷ width

50 ÷ 40 = 1.25

FAR = 1.25

## 4. Cov. Angle = 2 × arcsin(1 / FAR)

2 × arcsin(1 ÷ 1.25) = 106º

We need a 106º speaker.

## Yikes! How do I type this into the google calculator?

Easy. Search google.com for calculator. Make sure you are in degrees. Click inside the calculator input window and type 2 [shift + 8] [shift + s] 1 / 1.25 [enter]. On a mobile device, turn to landscape mode and use the Inv button to show sin-1.

## What if I don’t have the right speaker?

Don’t worry. As long as you have no more than a 3 dB error on each side, you’ll be fine.

Drop this into Google: ABS((20 × log(FAR A))-(20 × log(FAR B))) where FAR A is the speaker you need and FAR B is the speaker you have. As long as the result is less than 3, you’re good.

## What if the result is more than 3?

If your speaker is too wide, just know you’re going to get some extra wall reflections.

If your speaker is too narrow, consider subdividing the space. Take your FAR, cut it in half, and redo your calculations.

## Further questions?

Click here to download *105 Questions about Sound System Tuning*. It’s everything you wanted to know about live sound system setup but were afraid to ask.

cq Robinson says

Shouldn’t it be 2 * arctan(1/FAR) ?

Nathan Lively says

Hey cq, thanks for checking out the article. I could be wrong, but I think ArcTan would give you the effective coverage angle of the Lateral Aspect Ratio. Check it out.

cq Robinson says

Ah, I see. Thanks. I was not clear on the concept of FAR vs coverage angle.

FAR = (length of coverage area) / (width at half length),

but coverage angle is the angle such that

(level on axis at distance L) = (level on edge of coverage at distance L/2)

cq Robinson says

To put it another way, I was confusing coverage angle and effective angle.

sen says

“(level on axis at distance L) = (level on edge of coverage at distance L/2)”Where does the formula come from?

sen says

How to calculate FARA and FARB in the same space? Aren’t the FARA and FARB results the same in the same room? How to calculate the FAR difference between the have speaker and the need speaker?

Nathan Lively says

hmmm, I guess I don’t know what you mean by FARA and FARB. Maybe you could provide an example?

sen says

How to calculate FAR A and FAR B in the same space? Aren’t the FAR A and FAR B results the same in the same room? How to calculate the FAR difference between the have speaker and the need speaker?

sen says

my mean is: In the text“…….. ABS((20 × log(FAR A))-(20 × log(FAR B))) where FAR A is the speaker you need and FAR B is the speaker you have. ……”How to calculate this FAR B？

sen says

Is the angle a vertical coverage angle or a horizontal coverage angle?

Nathan Lively says

Either will work.

Nathan Lively says

Hey Sen, this is what it says in the article:

Does that answer your question?

sen says

In the text“Don’t worry. As long as you have no more than a 3 dB error on each side, you’ll be fine.” How to define “each side”?

“ABS((20 × log(FAR A))-(20 × log(FAR B))) ”Is the calculated result an error on each side? How to calculate the error on each side? Divide this calculation by 2, 4, or 6,or other?

Nathan Lively says

Hey Sen, I see what you mean now. Thanks!

FAR = 1 / sin(x / 2)

But, you need x in radians, so the final formula might be 1 / sin((90 * pi / 180) / 2) for a 90º speaker.

sen says

Must I convert to radians to calculate? Can I calculate by angle? Like this: The need speaker angle FAR A is 90, and the owned speaker FAR B angle is 60，ABS((20 × log(90))-(20 × log(60)))，Can calculate it this way?

Nathan Lively says

I’m sure you could figure out how to make it work. For that specific formula you need FAR. I have a little spreadsheet that I built to help with this that might be helpful for you. If you email me I’ll send it to you: nathan@sounddesignlive.com

sen says

I have sent you an email.

Nathan Lively says

Hey sen, I see an email from you back in March, that I replied to. I don’t see another one, yet.

Nathan Lively says

The formula gives you the total difference in FAR so the maximum deviation you’d want is 6dB.

sen says

{{I’m sure you could figure out how to make it work. For that specific formula you need FAR. I have a little spreadsheet that I built to help with this that might be helpful for you. If you email me I’ll send it to you: nathan@sounddesignlive.com}}

I have sent you an email for it.