Reversing the ABV Calculation to Solve for OG or FG

This isn’t revolutionary but when I was searching around trying to figure out how to reverse the Alcohol by Volume (ABV) formula to solve for FG, I had a really hard time finding a good resource to explain the calculation. So, if anyone else is in need, this is all the information that I was hoping to find, but figured out myself. Using these formulas you can calculate Alcohol By Volume, Final Gravity, and Original Gravity as long as you have a number for two of the three. Happy math-ing! 

Here are the three formulas written out solving for Alcohol By Volume, Final Gravity, and Original Gravity. 

ABV = (OG – FG) * 0.13125

-FG = (ABV / .13125) – OG 

OG = (ABV * .13125) + FG

Example: 

I’ll use the Baladin beer that started this search as an example. I knew it was 8.5% ABV and had an OG of 1.079. 

This is the formula to find FG. 

(ABV / 0.13125) – OG = -FG

In order to plug the numbers into the formula numbers. Enter ABV as a whole number and the OG or FG removing the “1” so for this plugging the numbers in looks like this. 

(8.5 / 0.13125) – 79 = -FG

64 – 79 = -FG

-15 = -FG

15 =FG 

So the Baladin beer finished around 1.015 specific gravity. Ahhh algebra. 

Then we can reverse the formula to check it! 

ABV = (OG – FG) * 0.13125

8.5 = (OG – 15) * 0.13125

8.5 * 0.13125 = OG – 15

64 + 15 = OG 

79 = OG

Hurrah! 

Worth noting: I know there are many much more precise calculations out there that will render more precise numbers. I was just interested in a general FG in this case so this simpler formula works well for me. Please don’t use it if you are calculating ABV for a precise need (especially any government regulations.) 

Ok, math class dismissed! You earned a beer 😃