How this calculator works
Both lengths are first converted to inches, so every operation works on one number. Addition and subtraction carry or borrow in twelfths of a foot, then the result is rounded to the chosen fraction of an inch and reduced to lowest terms. Multiplication of two lengths produces an area, so the result is shown in square feet and square inches. Division produces a plain ratio with no unit.
Formula
total inches = feet x 12 + inches. For addition, subtraction, multiplication and division use the total inches values. The displayed feet are the whole part of total inches / 12, and the remaining inches are rounded to 1/2, 1/4, 1/8, 1/16, 1/32 or 1/64 inch.
Worked example
5 ft 8 in plus 2 ft 4 in is 68 in plus 28 in, or 96 in, which is exactly 8 ft. 5 ft 8 in minus 2 ft 4 in is 40 in, or 3 ft 4 in. Multiplication gives 68 x 28 = 1,904 square inches, or 13.2222 square feet.
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Frequently asked questions
Why does the result sometimes lose the inches field?
When the remaining inches round to exactly zero, the answer is written as whole feet, such as 8 ft rather than 8 ft 0 in. Both mean the same length.
What happens when subtraction gives a negative length?
The result keeps a minus sign, such as -1 ft 6 in. A negative length is useful in a difference or offset calculation even though a physical board cannot have one.
Why are inches limited to less than 12?
The two fields split one measurement into whole feet and the leftover inches. Allowing 15 inches would be ambiguous, so put the extra foot in the feet field instead.