The 3 weeks at 70 degrees, that we recommend is the minimum time it takes for average gravity beers to carbonate and condition. Higher grav beers take longer.
Stouts and porters have taken me between 6 and 8 weeks to carb up..I have a 1.090 Belgian strong that took three months to carb up.
And just because a beer is carbed doesn't mean it still doesn't taste like a$$ and need more time for the off flavors to condition out. You have green beer.
Temp and gravity are the two factors that contribute to the time it takes to carb beer. But if a beer's not ready yet, or seems low carbed, and you added the right amount of sugar to it, then it's not stalled, it's just not time yet.
Everything you need to know about carbing and conditioning, can be found here Of Patience and Bottle Conditioning. With emphasis on the word, "patience."
If a beer isn't carbed by "x number of weeks" you just have to give them more time. If you added your sugar, then the beer will carb up eventually, it's really a foolroof process. All beers will carb up eventually. A lot of new brewers think they have to "troubleshoot" a bottling issue, when there really is none, the beer knows how to carb itself. In fact if you run beersmiths carbing calculator, some lower grav beers don't even require additional sugar to reach their minimum level of carbonation. Just time.
I've carbed hundreds of gallons of beer, and never had a beer that wasn't carbed, or under carbed or anything of the sort (Except for a batch where I accidently mixed up lactose or Maltodextrine for priming sugar). Some took awhile, (as I said up to six months) but they ALL eventually carbed.
If your beer is cooler it would take longer for the beer to get to the correct level of carbonation, because sluggish yeast do things slower than more awake ones, and the cooler a beer is stored, the sluggish the yeast is.
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