Can I derive Final Gravity from Original Gravity and ABV?

Question

I think the answer is yes. Since we use OG and FG to determine ABV ... I would assume we could do the same with ABV and OG to determine FG, right?

Answer 1

You can calculate ABV using the below equation:

ABV = (OG - FG) * 131

So, with the use of some Algebra, you can calculate FG using the below equation:

FG = -1*(ABV/131 - OG)

Answer 2

Yes, it's a simple calculation:

ABV = (OG - FG) * 131

For example:

ABV = (1.055 - 1.012) * 131

ABV = (0.043) * 131 = 5.633%

So to reverse it,

FG = (131 * OG - ABV) / 131

For example:

FG = (131*1.055 - 5.633) / 131

FG = (138.205 - 5.633) / 131 = 1.012

I have seen 129 used as the scaling factor as well, which would drop the ABV to 5.547%, but for homebrewing purposes either seem ok, or split the difference and use 130...