Why the narrow end sets the width
A square-edged board has parallel edges, so the widest one you can rip out of a tapered flitch is a rectangle that fits inside it, and a rectangle inside a wedge is limited by the narrow end. Everything the wide end had over the narrow end becomes two triangular edgings. On a flitch running 12 inches down to 7 over 8 feet, that is a pair of triangles totalling close to 1.9 board feet on an inch and an eighth of thickness, off a piece that only yielded 5.25 board feet square-edged.
Crosscutting attacks that directly. Cut the flitch in half and the wide piece no longer has to obey the narrow end, only its own narrow end at the cut. On that same example, cutting at 4 feet gives a 9 inch board 4 feet long and a 7 inch board 4 feet long, which is 6 board feet against 5.25. The recovery is real and it costs you the long piece, which may be worth more than the extra width for what you are doing.
Where the taper came from
Taper is a property of the tree, and it runs about the same down every board out of the same log because they are all slices of the same cone. Butt logs flare and taper hardest, upper logs run straighter. If you are getting boards with more than about three quarters of an inch of taper per foot, you are usually looking at a butt log, and those are the ones where crosscutting pays.
There is a second way to lose the taper before it becomes an edging, which is to saw the log around rather than straight through, turning it so each face is opened in turn. That is a cut plan decision made before the flitch exists, and it is on the log cut plan and yield calculator rather than here.
The numbers this page will not give you
Whether a board with wane on it is acceptable, what grade any of this is, and what a buyer will pay are all outside what geometry can answer. Wane is entered here as your own tolerance rather than as a rule, because the rules differ by species, product and the grading agency involved, and they change. If a specification governs your lumber, that specification decides, not this page.
Board feet as a unit, including the difference between nominal and rough measure, is covered on the board foot calculator. Once these boards are edged they go on sticks, which is the stacking and sticker calculator, and they will get narrower as they dry, which is the drying water weight and shrinkage calculator. For the fitting of rectangles into sheet goods rather than logs, the same kind of arithmetic is on the sheet nesting calculator.
Questions people ask
Why does the page round the width down instead of up?
Because you cannot edge a board to a width the wood does not have. If the narrow end allows 7.4 inches and you edge to whole inches, the board is 7, and the 0.4 goes into the edging. Rounding up would produce a board that has a strip of nothing along one edge for part of its length. If you would rather keep that width, set the increment to a quarter or an eighth of an inch and the page will keep it, at the cost of ending up with widths that are awkward to work with later.
Is it always worth crosscutting a tapered flitch?
No, and the page will tell you when it is not. The gain comes from the wide piece being allowed a bigger width, and it is only worth having if the extra board feet matter more than the length you destroyed. A long clear board is often worth more per board foot than two short ones, and once you cut it the length is gone. Short flitches and gentle tapers usually show no gain at all, because the minimum piece length you set does not leave room for the cut to fall anywhere useful.
What is the usable face width, exactly?
It is how wide the clean, square-edgeable face is at that end, as you read it. That means not counting bark, not counting the rounded wane at the edges if you do not want wane, and not counting a split or a section you have already decided to cut off. Two people can read the same flitch differently and both be reasonable. The wane field exists so you can put some of that rounded edge back in deliberately if your use tolerates it.
Do the edgings have any value?
That depends on what you can do with them and on nothing this page knows. They are triangular in plan, often with wane on one side, and they come in the widths that the taper happens to produce. Some shops resaw them into narrow stock, some sell them, some burn them. The page reports the board feet that end up in them so the number is visible rather than invisible, which is the main thing: an edging pile is easy to stop noticing.
Should I edge before drying or after?
Both are done and each has consequences the page does not weigh. Edging green means handling less wood through the dryer and stacking uniform widths. Edging after drying means you can put the edge where the board ended up rather than where it started, since drying moves boards. The trade involves your stacking, your drying method and what the lumber is for, and it is a shop decision rather than a calculation.