Adjusting pre-boil gravity up
Let's say you are brewing a 5 gallon batch of beer. You have completed your mash and sparge and have collected the predetermined amount of wort (6.9 gallons). The only problem is you take a gravity reading and find that you have missed your target pre-boil gravity (1.040) by 5 points. Use this formula to calculate the amount of fermentable sugar to add to your wort.
X = (Volume of Wort * (Target Gravity Points - Actual Gravity Points)) / Potential Points of Addition
Of course, the variable here is the Potential Points of Addition. Each fermentable item has potential points. Check out this chart for the fermentable you are using. In this example, we are using DME which has a potential of 45.
X = (6.9 * (40 - 35)) / 45
X = (6.9 * 5) / 45
X = 34.5 / 45
X = .767
In this case we will need just over 3/4lb of DME added to our wort in order to bump up our gravity the needed 5 points.
Adjusting pre-boil gravity down
Let's say you are brewing a 5 gallon batch of beer. You have completed your mash and sparge. Your target pre-boil gravity is 1.040 and your target pre-boil volume is 6.9 gallons. You take a gravity reading of the full 6.9 gallons and find that your gravity is 1.042. Use this formula to calculate the amount of water to add to your wort.
X = (Volume before dilution * (Actual gravity points – Target gravity points)) / Target gravity points
X = (6.9 * (42 - 40) / 40
X = (6.9 * 2) / 40
X = 13.8 / 40
X = .345
In this case we will need .345 gallons (approximatly 44oz) of water added to our wort to reduce the gravity to 1.040.
Alcohol by Volume ABV
The basic formula most home brewers use for calculating the ABV of your beer is straightforward. The formula is as follows:
ABV = (OG - FG) * 131.25
It should be noted that the formula is less accurate as ABV increases. A more accurate formula requires knowing the alcohol by weight (ABW). The formula is as follows assuming you already know the ABW.
ABV = (ABW * (FG / .794))