Calculating ABV from SG readings after late additions of fermentables

I just kegged an Imperial Pale Ale that included a late addition of fermentables -- i.e., I "krausened" it after about two weeks in primary with a 1 gallon starter using a high-gravity tolerant yeast. I know that's not technically krausening. Whatever ... the point is I added fermentables midway through this beer's fermentation. The final product turned out excellent, but I'd like to confirm that my figuring is correct; somehow I think I'm missing something. Here's what I've got:

OG: 1.075
SG before "krausen": 1.017
SG after "krausen": 1.024
FG: 1.014

So I figure the ABV before krausen was 7.6125% ((1.075-1.017)*131.25). After krausen I gained 1.3125% ((1.024-1.014)*131.25). Add these percentages together and I get 8.925%.

However I doubted I can just add the percentages together and get an accurate ABV. So I tried another method, re-calculating OG by adding the difference between FG and post-krausen SG to the OG figure. In other words:

OG: 1.075
Post-krausen SG: 1.024
FG: 1.014
1.024 - 1.014 = 0.007 (post-krausen SG-FG)
1.075 + 0.007 = 1.082 (OG + (post-krausen SG-FG))
With 1.082 as the effective OG, my calculations show the same exact result as the other method: 8.925% ABV.

Am I correct in this simplistic approach to adding gravity, or is there another step that I'm missing?

Thanks,
-Hrangil

hrangil said:

1.024 - 1.014 = 0.007 (post-krausen SG-FG)

Click to expand...

You mean 1.024 - 1.017 = 0.007

Had me confused for a minute.

It looks right to me. If you really really want to know, they have machines that will test the actual alcohol content... but I don't think that they are cheap.