Boil size and OG

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Wiesty

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Hey everyone!
Another noobish question from me. I'm putting together a recipe for a Tripel I am making and am trying to figure out the OG.
Here is the base recipe....

5.25 gallons
12 lbs Pilsen LME
Estimated OG 1.082

I've modified it a bit as such
11 lbs Pilsen LME
1 lbs Belgian Candi
Calculators I've used still put this at around 1.082. Still 12 lbs of fermentables right?

HOWEVER, When I put these into BeerSmith, and I include that I am making 5.25 gallon batch with a preboil of around 4 gallons, it shoots out a noticeably lower OG. Beersmith says I should use 12 lbs of LME and 1 lbs of Candi to reach the desired OG.

So my question is....does boil volume have anything to do with gravity? I will obviously top off the water in the end so it shouldn't (or at least I thought) make a difference. Why the discrepancy between Beersmith and other calculators/the original recipe?
 
It could be an issue with your equipment profile settings, did you set the top up water? Under fermenter/bottling volumes, when I set the batch volume to 5.25 and the top up water to (5.25 - 4 + boiloff volume) I get an OG of 1.082.

Edit:

To answer your question, yes and no depending on how you look at it. Gravity is indirectly a measure of the sugar content relative to the water, given a constant amount of sugar your gravity will be higher with less water and your gravity lower with more water. When you boil wort your concentrating the sugars in the water and increasing the gravity. BUT you can only get as much sugar out of it as you put in it, if you know how much sugar you've added in total, and how much volume you will end with, you should be able to calculate your OG regardless of starting water volumes. That make sense?

Edit Edit:
So toping off the water in the end DOES make a difference in OG:
Step 1) Added fermentables to 4 gal water = increase in gravity
Step 2) Boiled wort, lost water volume = increase in gravity
Step 3) Top up water to 5.25 gal which dilutes the sugar solution = decrease in gravity
 
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