Add, subtract, multiply, and divide feet-and-inches measurements like a pro. Free with steps.
Carpenters, builders, and DIYers constantly do arithmetic that calculators choke on: what is 5 ft 8 in plus 3 ft 4 in? How many 16-inch stud bays fit in a 12-foot wall? Our free Feet and Inches Calculator adds, subtracts, multiplies, and divides imperial measurements and answers in feet-and-inches, decimal feet, and total inches — with the conversion steps shown.
The imperial system’s mixed radix is the whole problem: 12 inches to the foot, but decimal everywhere else. Doing 7 ft 9 in − 2 ft 11 in by hand means borrowing a foot as 12 inches, a maneuver that produces endless jobsite errors. The calculator converts everything to total inches, does the math once, and converts back — the same method old-timers use on a scrap of lumber, without the arithmetic risk.
Fractions are rounded to the nearest sixteenth of an inch, the standard resolution of a tape measure. If you need finer precision for machining, use the decimal-feet readout instead.
The foot is a mixed-radix unit: twelve inches make a foot, but feet themselves count in tens. That collision is what makes 5′8″ + 3′4″ harder than 5.8 + 3.4. Adding the inches gives 12, which is not “12” in the answer but one more foot and zero inches — a carry at 12 instead of 10, which decimal-trained brains constantly fumble.
Subtraction is worse because of borrowing across the radix. In 7′9″ − 2′11″, the inches column needs 9 − 11, so you borrow one foot — but it arrives as 12 inches, not 10. The inches become 21 − 11 = 10, and the feet become 6 − 2 = 4: answer 4′10″. Every carpenter has a story about a miscut board born from borrowing 10 instead of 12.
The professional fix is the total-inches method: convert each measurement to inches (feet × 12 + inches), do ordinary decimal arithmetic, then divide by 12 to recover feet and inches. It replaces mixed-radix gymnastics with one multiplication and one division, and it is exactly what this calculator does internally before formatting the pretty answer.
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For addition and subtraction, convert both values to total inches, compute, then convert back. Multiplication of two lengths yields square inches (an area); division yields a unitless ratio.
A shelf needs a 5 ft 8 in board joined to a 3 ft 4 in board. What is the total length?
Total: 9 ft 0 in. The inches summed to 12 and carried cleanly into a whole foot — the case beginners get right and the messy remainders they get wrong.
A 7 ft 9 in stud must be cut down to fit a 2 ft 11 in opening header. How much is removed?
Answer: 4 ft 10 in. Doing this by hand requires borrowing a foot as 12 inches — the calculator sidesteps the trap entirely.
Dana is framing a 12-foot wall with studs 16 inches on center. How many bays, and what is the leftover? Twelve feet is 144 inches; 144 ÷ 16 = 9 exactly, so nine 16-inch bays fill the wall with zero waste — which is precisely why 16-inch spacing and 12-foot multiples dominate US framing. The last stud lands exactly at the 12-foot mark. If the wall were 12 ft 6 in (150 in), the division gives 9.375 bays: nine full bays plus a 6-inch rip bay at the end, and Dana knows before cutting a single stud.
The same arithmetic runs the other direction for trim. Crown molding comes in 12-foot sticks; a room with two 14 ft 3 in walls and two 11 ft 7 in walls needs 2 × 171 in + 2 × 139 in = 620 in = 51 ft 8 in of molding. Four 12-foot sticks give 48 feet — short. Five sticks give 60 feet with 8 ft 4 in of waste, some of which becomes the scarf-joint overlaps. The feet-and-inches addition, done once correctly, is the difference between one trip to the lumberyard and two.
A second scenario: hanging a gallery wall. Three frames — 18 in, 24 in, and 12 in wide — must center on a 9 ft (108 in) wall with equal gaps. Frames total 54 in; remaining 54 in splits into four gaps (two ends + two middles) of 13.5 in each. Working in total inches keeps the halves exact; working in feet-and-inches invites a rounding error that shows up as a visibly crooked row.
The foot-inch system survives in US construction because it divides beautifully. Twelve splits evenly by 2, 3, 4, and 6, so a foot halves, thirds, and quarters without repeating decimals — 4 inches is exactly a third of a foot, while a third of a meter is 0.333… endlessly. Carpenters halve and quarter measurements all day, and base-12 makes those operations exact where base-10 makes them approximate.
Tape measures encode this divisibility physically. The standard 16-inch stud marks, the red 19.2-inch truss marks (for five trusses per 8 feet), and the black diamonds at 16 inches are all fractions of standard sheet sizes: a 4×8 sheet breaks at 16, 32, and 48 inches. The entire dimensional lumber system — 2×4s, 4×8 sheets, 16-inch centers — is one coherent base-12 machine, and fluency in feet-and-inches arithmetic is fluency in that machine.
Surveyors and engineers, tellingly, abandoned feet-and-inches for decimal feet a century ago. A surveyor writes 123.45 ft, never 123 ft 5.4 in, because decimal feet do ordinary arithmetic and interface cleanly with trigonometry and GPS. The conversion is trivial — divide total inches by 12 — but the cultural split persists: builders think in feet-and-inches, engineers in decimal feet, and every handoff between them is a translation this calculator performs instantly.
The metric world watches this with amusement, but metric has its own mixed radix: time. Hours, minutes, and seconds are base-60/base-12, and nobody proposes decimalizing the clock for carpenters. The lesson is general — whenever a trade’s units predate decimalization, the winning move is not to fight the radix but to convert to the smallest unit, compute, and convert back. Total inches is to carpentry what total minutes is to scheduling.
Feet-and-inches arithmetic: convert each value to total inches (ft×12+in), compute, convert back (in÷12 = feet + remainder inches). Add/subtract give lengths; multiply gives square inches; divide gives a unitless ratio. Decimal feet = total inches/12. Carry/borrow at 12, not 10. Source: Sigma Calculator, Feet and Inches Calculator, https://sigmacalculator.net/math-calculators/feet-and-inches-calculator/
Cite this page as: Feet and Inches Calculator, Sigma Calculator, https://sigmacalculator.net/math-calculators/feet-and-inches-calculator/
Last updated: October 12, 2026