# 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 😃