## Gravity from OG and degrees Brix

This calculator can be used to find the specific gravity of your wort based on a refractometer measurement and a measurement of its original gravity (from a hydrometer). This gives you a way of tracking the fermentation of your wort without having to waste 6 ounces of every time in order to do another measurement with a hydrometer.

## How it works

The formulae are as follows:

Measure: og (using a hydrometer) B=reading from the refractometer, in degrees Brix Constants: Z=.372 k=261 p=.5815 q=3.96 r=5.3 Calculate d=Z[1/(1-B/k)-1], which is an approximation to the difference between the index of refraction of the wort and the index of refraction of water g=1.002-p(og-1)+qd+rd^2To see how this is implemented in the actual program, you can do View > Page Source (or the equivalent in a browser other than Firefox), and look at the JavaScript source code. For references, see these two posts on HBD by Louis Bonham: 1, 2. My method is that I first convert degrees Brix to index of refraction, using a formula that approximates a table in the CRC Handbook. Since the refractometer physically measures index of refraction, this really does give the index of refraction of your sample; it's essentially just undoing the calibration built into your refractometer. Then I approximate the ABW as 102(og-g). (This is based on a rough approximation from the table on p. 98 of Palmer's How to Brew, along with the approximation that ABW=(4/5)ABV.) Finally I take Bonham's equation relating ABW, g, and index of refraction, and solve it for g. Preliminary results seem to show that this method works to a precision of about ±.005. Some of this is random error (because in order to check whether the result is right, I need to do two hydrometer measurements and one refractometer measurement, each of which has random errors) and some is systematic error (because of all the approximations being made, e.g., ignoring the effect on the index of refraction from all the other stuff in the wort). After I worked out these formulae and implemented them in this calculator, I came across a formula by Bonham, quoted here; the two formulae seemed to give identical results when I tried them on the same data.