Degree of Saturation (Se = wGs)

$Se = wG_s$ is the phase diagram's one indispensable identity, and it drops straight out of the definitions: water content is the mass of water over the mass of solids, and multiplying by $G_s$ converts that mass ratio into the volume ratio that saturation needs. With w = 18%, $G_s$ = 2.70 and e = 0.65, the voids are S = 18 × 2.70 ÷ 0.65 = 74.8% full of water and the rest is air. Solve it the other way for a saturated sample, S = 100%, and you have the standard laboratory route to void ratio from nothing but an oven and a balance.

The trap is units: this identity only balances if w and S are both fractions or both percentages, and mixing them is the classic factor-of-100 blunder. The solver keeps both in percent and lets you enter either as a fraction if you prefer. The second trap is $G_s$ itself: quartz sands sit at 2.65, most clays at 2.68–2.75, but organic soils drop to 2.3 and iron-rich laterites climb past 3.0, so assuming 2.65 on a peaty site will quietly corrupt every void ratio you report. And if your arithmetic returns S above 100%, the sample was not what you thought: check the oven temperature and check whether the "solids" included gypsum, which gives up its water of crystallisation at 105 °C.