Sorted first, weighed second
This tool assumes the lot has already been sorted into piles by karat before anything touches the scale — which is the only version of a mixed lot that has an honest melt value at all. Melting a jumble of 9K and 22K pieces together first and then weighing the puddle throws away the one piece of information the arithmetic needs: how much of the mass was which purity. A blend melted before it is measured is not "somewhere in between" in any calculable sense, and no calculator, this one included, can back that information out afterward.
Sorting by karat is also usually the easy part, because the stamp does most of the work: 375/9K, 585/14K, 750/18K and 916/22K are visually distinct enough, once you know to look, that a magnifying loupe and a few minutes with a box of scrap is normally enough to make four or five piles. Unmarked pieces are the exception — those need testing before they can go in any pile with confidence, and guessing a karat from colour alone is unreliable enough to be worth avoiding entirely.
Why the total is not just a sum of individual items
Grouping by karat before pricing, rather than listing every single item, mirrors how a buyer actually processes a lot: they weigh each purity once, not piece by piece, because the melt value only depends on the total weight at each purity, not on how many individual objects contributed to it. Ten 14K rings weighing 30 grams together are worth exactly the same as one 14K bangle weighing 30 grams — the melt calculation cannot see, or price, individual pieces.
That said, individual pieces are exactly what a buyer who is not melting can see, and it is worth pausing before any lot goes to scrap. A recognisable maker's mark, a signed piece, genuine antique or period jewellery, or anything with a stone of real size can be worth several times its metal content intact — and once a lot is melted there is no getting that back. Sorting by karat for a melt-value estimate is a good way to know what you are holding; it is not, by itself, a reason to melt any of it.