The quickest way to add 5 ft 7 3/4 in and 2 ft 9 1/2 in without making a mistake is to drop the units and work in sixteenths of an inch, then convert back at the end. Add 1,084 and 536 to get 1,620 sixteenths, divide by 192 (the number of sixteenths in a foot), and you have 8 ft 5 1/4 in.
That is the entire trick: once each length is a whole number, every carry rule is the same as adding minutes to hours, and nothing can round away. The calculator does it in one click, but the method itself is simple enough to run in your head on a job site.
The direct answer
For any sum or difference of lengths written in feet, inches and fractions:
- Multiply the feet by 192 (12 inches × 16 sixteenths).
- Multiply the whole inches by 16.
- Add the numerator of the fraction over 16 (so 3/4 is 12).
- Add or subtract the two totals.
- Divide the total by 192 for the feet, take the remainder, divide that by 16 for the whole inches, and keep the last remainder as the fraction over 16.
Open the feet and inches calculator to run the example below with every step shown.
A worked example with numbers
Add 5 ft 7 3/4 in and 2 ft 9 1/2 in:
- 5 ft 7 3/4 in → 5 × 192 + 7 × 16 + 12 = 1,084 sixteenths
- 2 ft 9 1/2 in → 2 × 192 + 9 × 16 + 8 = 536 sixteenths
- Sum → 1,620 sixteenths
- 1,620 ÷ 192 = 8 feet remainder 84 sixteenths
- 84 ÷ 16 = 5 whole inches remainder 4 sixteenths = 1/4 in
Final answer: 8 ft 5 1/4 in. The same length is about 8.4375 ft, 101.25 in, or 257.18 cm, using the exact definition 1 in = 2.54 cm.
Subtracting works the same way: swap the plus for a minus in step 4. If the result is negative, keep the sign on the outside and work with the magnitude.
Why 1/16 of an inch
A standard framing tape measure has 1/16 in as its smallest tick. Measurements finer than that come up in cabinetwork and drafting, but on a tape measure, 1/32 and 1/64 marks are rare. Storing lengths as whole sixteenths matches what you can read off a tape without squinting, and it means every intermediate value in a long addition stays exact.
Common mistakes
- Adding fractions with different denominators. 3/4 is 12/16 and 1/2 is 8/16. Mix them without converting and the carry rules bite.
- Forgetting that 12 inches make a foot, not 10. 11 in + 3 in is 1 ft 2 in, not 14 in; a mental shortcut that writes 1.4 ft gets this wrong.
- Typing a mixed number into a decimal field. 5 ft 6 in is 5.5 ft, not 5.6 ft. Use separate fields for feet, whole inches and the fraction.
- Rounding part-way through. 1/16 looks like a rounding error waiting to happen, but on a long run of eight studs it is 1/2 in, and that is a visible gap.
When to use the calculator
Tallying stud spacings, laying out trim from several leftover pieces, deciding whether a 3 ft 4 1/2 in couch fits past a 3 ft 2 3/4 in doorway: any time three or more lengths with fractions get added or subtracted in your head is a good time to open the feet and inches calculator. For the floor itself, the square footage calculator handles the multiplication once you have the lengths.
The unit math behind all of this comes from NIST, which defines the inch as exactly 2.54 cm; those definitions do not change, which is why the calculator is deterministic to the last sixteenth.