# Lever Rule - Calculations - Binary Phase Diagrams

Binary Phase Diagrams

Before any calculations can be made a tie line is drawn on the phase diagram to determine the percent weight of each element; on the phase diagram to the right it is line segment LS. This tie line is drawn horizontally at the composition's temperature from one phase to another (here the liquid to the solids). The percent weight of element B at the liquidus is given by wl and the percent weight of element B at the solidus is given by ws. The percent weight of solid and liquid can then be calculated using the following lever rule equations:

where wo is the percent weight of element B for the given composition.

The numerator of each equation is the original composition we are interested in +/- the Opposite lever arm. That is if you want the percent weight of solid then take the difference between the liquid composition and the original composition. And then the denominator is the overall length of the arm so the difference between the solid and liquid compositions.