Abstract
Equations for converting between relative density and percent by mass extract based upon physically meaningful values (rather than fitted parameters) are derived from physical principles. An exact equation and two approximate formulas using one and two physically meaningful parameters respectively are given based on the partial specific volumes of sucrose and water in solution, which are calculated for sucrose concentrations varying between 0 and 20% by mass fraction. The predictions of these equations are compared to the American Society of Brewing Chemists (ASBC) tables and the accuracy of the predicted values is analyzed. The root mean squared error over the entire range of the ASBC tables of the approximate formula with two parameters is less than 0.016°P and that of the formula using only one parameter is less than 0.023°P. The approximate formula with one parameter provides a simple and easily remembered, but nevertheless highly exact means for any brewer to calculate extract without specialized analytical devices.
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