Why the kerf matters more than it looks
A kerf is not charged once to a log. It is charged once to every cut. A 16 inch log sawn at an inch and an eighth with a tenth of an inch of kerf gives twelve boards and takes thirteen cuts, so 1.3 inches of the diameter leaves as sawdust before you count a single slab. Put a quarter inch kerf through the same log and it gives eleven boards in twelve cuts, three inches of diameter gone, and the yield falls from 108 board feet to 95.3. The extra 0.15 inches of blade sounds trivial and it is not, because it is multiplied by the cut count, and the cut count rises as the boards get thinner.
That is also why the effect is worse on thin stock. Sawing 4/4 at a quarter inch kerf, the blade takes one inch of wood for every four you keep. Sawing 8/4 with the same blade it takes one for every eight. Mills differ in what they cut and the only figure worth using is the one you measure in your own wood, on your own blade, at the state of sharpness it is actually in.
Through and through against a cant
Sawing straight down the log gives you every width the log has to offer, from a full-diameter board through the middle down to narrow pieces near the outside. Squaring to a cant first throws away the outside before you start and then gives you a stack of identical boards at one width. The cant loses board feet on paper and gains uniform stock, and which of those matters depends entirely on what the lumber is for. This page shows both so the trade is a number rather than an opinion.
Note what happens to the tall dimension of a cant as the cant gets wider: the taller the cant, the narrower it has to be, because both are chords of the same circle. An 8 inch cant out of a 16 inch log is a shade under 14 inches tall. A 12 inch cant out of the same log is only 10.6 inches tall. The board count and the width move in opposite directions.
What this does not account for
The widths come from a perfect circle at the small end. Logs sweep, they go oval, they have a butt flare and they taper along their length, so a board that is 13 inches wide at one end may be 9 at the other. Taper and edging are handled on their own page, the edging and width yield calculator, because they are a second operation with a second set of losses. Log scale figures under the Doyle, Scribner and International rules come from the tree and log volume calculator.
Everything sawn here is green and oversize on purpose. How much oversize depends on how far the wood has to dry and how much it moves, which is the drying water weight and shrinkage calculator. Once the boards are off the mill they need stacking, and that is the stacking and sticker calculator. If you want the running cost behind each of these board feet, the cost per board foot calculator takes the cut count from here.
Questions people ask
How do I measure my kerf?
Cut a piece of scrap and measure the gap, or cut a board off a wide piece and measure what the piece lost: the original width minus the board minus the remainder is the kerf. Do it with the blade in the state you actually saw with rather than straight off a sharpening, because set wears down and a blade near the end of its run does not cut the same width it did at the start. Two blades that look identical can differ enough to change the board count on a big log.
Why are the outside boards so narrow when the log is big?
Because a board is a rectangle cut out of a circle, and its width is the chord at whichever of its two faces is further from the pith. The middle board gets nearly the full diameter. Move out one board thickness and the chord has already shortened; by the time you are near the edge the chord is dropping fast, which is why the last two or three positions often fall below any sensible cutoff and end up as slabs. Doubling the diameter does not double the number of usable boards, it more than doubles it, and that is the same geometry running the other way.
Should I be sawing thicker to lose less to the kerf?
Thicker stock does lose a smaller share of the log to sawdust, and that is arithmetic rather than advice. What it costs you is flexibility, drying time and the ability to get thin stock without resawing later, all of which are decisions about what the lumber is for. Run the page at both thicknesses and look at the board feet and the sawdust line side by side, then decide on the basis of the job. There is no thickness this page can recommend.
The sawn board feet came out over the log scale. Is the scale wrong?
Not necessarily, and neither is the mill. Log rules were built to predict output on particular assumptions about kerf, thickness and how logs were sawn at the time, and those assumptions do not match every mill. Some rules under-predict small logs badly and others are closer. A difference between scale and sawn output is a normal and well-known thing rather than an error in either figure, and its direction and size change with diameter. Use both numbers for what they are: one is an estimate agreed for trade, the other is what came off the bed.
Does this tell me what my lumber is worth or what grade it is?
No, and it deliberately does not try. Grade depends on defects, on the rule being applied and on who is applying it, none of which a diameter and a thickness can tell you. This page counts geometry: how many rectangles of a given thickness fit a circle of a given diameter, how wide each one can be, and how much wood the cuts removed. What the boards turn out to be worth is a separate question that belongs to whoever is buying them.