Calculating Finishing Gravity with a Refractometer is Nuts
Santa kindly gave me a Refractometer for Christmas this year, which rocked because it was on my list of gifts for your favorite homebrewer. And just a couple of weeks ago I brewed up a doppelbock and got to try my new toy out. It was everything I dreamed it would be. Geeky. Easy to read. Rather badass looking. I was happy. Then I went to take a reading after fermentation had slowed down and got a sky-high reading. Wait? Did I under-pitch? Was the yeast bad? It looked like a clean steady fermentation and the sample didn’t tast under-attenuated. What was wrong? Well I failed to research exactly how refractometers work. Well, look at me, Mr. Half-Assed researcher.
Here’s the deal. Refractometers are excellent at giving an easily read brix/specific gravity for unfermented wort. They also auto-correct for temperature which make it easy to check specific gravity during the boil or mash. Totally rad. But once alcohol gets into the mix the light refraction gets all jacked up and this is why I had such a high reading on my doppelbock. This lead me to the question, how do refractometers work in the first place?
Okay, this is complicated. A refractometer measures the angle of refraction. Wait, so what’s refraction? When you step into the pool and you look down and notice that your leg looks slightly bent to the side, that’s refraction. The angle of that refraction changes depending on the content of the water. Let’s say instead of a pool you stepped into a fresh batch of home brewed wort and looked down then you would notice that your leg looked bent even further than it had in the water. That difference is how we get this not too crazy equation:
Refraction Index = sin(I)/sin(r)
Luckily, you don’t even need to think about that equation. The refractometer is already designed to do all that work for you. Cool. Easy. Now we get to the problem. Just as sugar content impacts the angle in which your leg bends so too does alcohol. Damn. What a pain. But there’s good news! Some people, who are much smarter than me, figured out how to get over this little inconvenience and still make the refractometer useful for working out the finishing gravity of a beer. And here it is:
SG = 1.001843 - 0.002318474*OB - 0.000007775*OB*OB - 0.000000034*OB*OB*OB + 0.00574*FB + 0.00003344*FB*FB + 0.000000086*FB*FB*FB
Where: SG is estimated specific gravity of the sample; OB is Original Brix; and FB is Final Brix
WTF? Seriously? Those number look totally arbitrary. I mean 0.000007755? Who figures this stuff out? Well it works. I tested a sample and compared the refractometer reading with a hydrometer reading and after running the formula above I landed on the same number give or take a point. Which is plenty good for my little home brewery. The best part is you actually don’t have to sit there with a calculator and crunch all those numbers because we have the fancy internets to do that work for us. Two calculators I’ve found to make this easier are at:
And a cool Excel sheet at MoreBeer: http://morebeer.com/public/beer/refractbeer.xls
Several recipe programs also have this calculator built into them as well.
What have we learned? Refractometers are cool. They have an outstanding geek factor that I love. They also make it easy to test specific gravity at any point during the brew day. We also learned that they’re not the best solution for figuring out finishing gravity, but there’s some crazy math out there that will make it doable. In the end I think a refractometer is fine for checking-in on a fermenting beer, but once you want to calculate your final gravity it’s time to bring out the old hydrometer.
Two great sources I used in writing this:
Brew Your Own's guide to Refractometers: http://www.byo.com/stories/article/indices/29-equipment/1343-refractometers
[Image via Flickr - Maggie Hoffman]