Alligation Calculator
The cross runs the other way from intuition — the strong stock's share is set by the weak one's distance.
The formula
parts of strong = target - weak ; parts of weak = strong - target
The cross, and why it runs backwards
The share of the stronger stock is set by the distance from the target to the weaker one, and vice versa. It looks wrong until you test it: a target sitting just above the weak stock plainly needs only a trace of the strong one, and the cross is what produces that. Getting the arms the wrong way round is the single most common error in the method.
The range check
Mixing can never reach outside the interval the two stocks span. If the target lies beyond either, no combination of them will do and the calculator says so rather than returning a negative volume.
Which denominator?
Most of the confusion in solution work is not arithmetic but bookkeeping. Molarity divides by the volume of the finished solution; molality divides by the mass of the solvent; percent by mass divides by the mass of the solution again. The three agree closely in dilute water and diverge sharply in concentrated acid, which is why a bottle labelled 98 % is also labelled 18.4 M without contradiction.