Board feet, nominal sizes and the gap between them
A board foot is a volume, not a length: one foot square and one inch thick. That is why the formula mixes units. Thickness and width go in inches and length in feet, then the result is divided by twelve to cancel the mismatch. Lumber is sold this way because it lets a yard price a 2×6 and a 1×12 off the same rate, and it is the only measure that survives contact with a mixed cut list.
The number that decides whether your total is right is not on the tape at all. Softwood is named at its rough-sawn size and sold at its dressed size, so a 2×4 measures about one and a half by three and a half. Board feet are conventionally priced on the nominal number, which means the yard is charging you for wood that was planed off before it left the mill. That is not a trick but the convention, and it means a quote worked out on measured dimensions comes in roughly a third light against the invoice.
So pick a basis and stay on it. Nominal if you are pricing, actual if you are working out what will really fit in a wall cavity or what a load weighs. This tool takes whichever numbers you type and never converts between them, because dressed sizes vary by mill and by species and a lookup table would be overwriting a measurement you took yourself.
The mistake that costs money is a cut allowance of nothing. Trim ends, checked boards and the offcut that fits nowhere are all real, and they never show up in the arithmetic. Zeus keeps the lumber receipt against the job it was bought for, so next season the allowance you use is one your own jobs earned.