Calculating ABV with sugar addition to secondary

I recently effed up my pumpkin beer by forgetting to add the sugar addition to the boil. I didn't realize this until racking to the secondary. So I decided to boil the sugar addition, cool it and add it to the secondary to try to rectify my mistake as best I could.

My question is, am I able to determine a proper ABV if I have the following gravity readings:

OG
SG from secondary before sugar addition
SG from secondary after sugar addition
FG

I've seen similar questions pertaining to fruit additions in the secondary where people say that the effects are negligible due to the high water content of most fruit. Since this was brown sugar sterilized in a bit of boiling water, the sugar to water ratio is very high and I suspect it should impact the ABV.

I'm not overly concerned on the ABV (as long as the beer tastes good) but it would be nice to know if someone has a formula!

Easy...it's all about the differential. You'll need to add in absolute terms instead of percentage terms. Multiply percents by volumes to get ounces of alcohol, add together, then divide by total volume.

OG to SG before sugar gives you %ABV...so say 5 gallons x 5% = .25 gallons alcohol
plus
SG before sugar to SG after sugar gives you another %ABV...so say 5.25 gallons x .5% = .026 gallons alcohol

.25 + .026 = .276 gallons alcohol / 5.25 total gallons = 5.25% combined ABV

Note: It's more accurate to calculate by weight, but this gets you close and is easier.

Thanks Ty!

That makes sense. I'll run through the math tonight.