Scaling/adjusting recipes for efficiency by hand


I haven't seen the answer on the forum and don't have beersmith (hopville doesnt have this option either) but have been using this formula for the past few days with really good success to convert recipes i want to make to my efficiency and process.
Firstly, I found this formula for calculating specific gravity on BYO:
SG = (W * PE * EE)/ V
Specific gravity= weight x potential extract x extract efficiency / volume
However, this only applies to using 1 grain so is useless for multiplegrain bill unless you calculate each one then add them up.
I brew 1 gallon batches at 85% efficiency so will walk through the process of converting BYO's 5 gallon recipe of Stone Pale Ale, listed efficiency is 65%.
Stone Pale Ale clone (65% efficiency, 5 gallons)
10.25 lbs 2 row pale malt
1 lb crystal 60L
.5 lbs crystal 75 L
9.25 AAU Magnum hops (90 mins)
1 oz Ahtanum hops (15 mins)
White Labs WLP002
1. Since I brew 1 gallon batches, I first divide the 2 row amount listed by 5 to get the amount of 2 row needed for a gallon batch at 65% efficiency.
10.25/5=2.05 lbs 2 row
2. Then I use the formula for calculating the specific gravity contribution of 1 grain. Since the 65% efficiency batch and 85% efficiency batch needs to have the same starting gravity, I set 2 versions of the formula equal to each other (1 side with the known values of original batch, the other with an unknown weight but 85% efficiency). Since 2 row has 37 points potential extract I add this to the formula.
SG=2.05 lbs x 37 (potential extract of 2 row) x .65 (efficiency)
then replace SG side with what I'm looking for in 85% efficiency batch:
W (unknown weight I need) x 37 x .85=2.05 x 37 x .65
31.45 W= 49.3025
divide by 31.45 to isolate weight needed and:
W=1.57 lbs 2 row
3. You can use this process for all the grains, or do it much simpler:
Divide original amount in 65% efficiency batch by weight of 85% batch to get a ratio to scale all other ingredients.
2.05 lbs/1.57 lbs=1.305
4. So now i would divide the other malts by 5 to get to 1 gallon size at 65% efficiency, then divide those amount by 1.305 to get the weight of other grains.
1 lb crystal 60L/5= .2 lbs crystal 60L at 65%
.2 lbs/1.305=.153 lbs crystal 60L at 85% efficiency
I only use the formula to calculate the needed weight of 2 row at my efficiency so can always set 1 side of the formula equal to 31.45W. Then I scale all other ingredients accordingly. Was racking my brain on a solution to doing this so hope this post is at least useful to others.
