4.375
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4.375
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4.375
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4.375
in
The Fraction Calculator for Construction solves the arithmetic that trips up even experienced builders: adding, subtracting, multiplying, and dividing fractions and mixed numbers as they appear on tape measures, cut lists, and material specifications. In the workshop and on the job site, measurements are always expressed in fractions of an inch — ¼, ⅛, 1/16, 3/32 — and combining these measurements requires fraction arithmetic that most people haven't practiced since middle school.
Consider a common scenario: you need to cut three pieces from a board. The first piece measures 2-¾ inches, the second is 1-⅜ inches, and the third is 3-5/16 inches. How long a board do you need, including saw kerf? Adding these mixed numbers — 2 3/4 + 1 3/8 + 3 5/16 — requires finding a common denominator (16 in this case), converting all fractions, adding numerators, and simplifying the result. This calculator does all of that in a single step, returning both the simplified fraction form and the decimal equivalent for cross-checking.
Tape measures used in the US use a binary subdivision system: each inch is divided into halves (½), then quarters (¼), eighths (⅛), sixteenths (1/16), and for precision work, thirty-seconds (1/32) and sixty-fourths (1/64). All marks on a standard tape correspond to these fractions. Working in this system means fractions are unavoidable — the only question is whether you do the math by hand (error-prone), with a construction calculator (expensive and single-purpose), or with this free tool (instant and precise).
The calculator supports mixed numbers (whole number + fraction), which is how measurements appear on cut lists: 5-7/8, 12-3/16, 27-5/32. Enter the whole number, numerator, and denominator for each operand. If your number has no whole part (pure fraction), enter 0 for the whole number. If your number has no fractional part (whole number only), enter 0 for the numerator.
Beyond addition and subtraction for combining or differentiating measurements, this calculator handles multiplication (scaling up a cut list by a factor, calculating area from fractional dimensions) and division (finding how many times a fractional piece fits into a given length, calculating unit costs from fractional quantities). All results are automatically simplified to their lowest terms and converted to decimal for easy verification on a digital caliper or calculator.
The inches-decimal output assumes your fractions represent inches and gives you the decimal inch equivalent — useful for setting digital calipers, programming CNC machines, or checking measurements on a digital readout (DRO) on a lathe or mill.
Each mixed number is converted to an improper fraction: whole × denominator + numerator / denominator. The operation is then applied: Add: (a/b) + (c/d) = (a×d + c×b) / (b×d). Subtract: (a×d − c×b) / (b×d). Multiply: (a×c) / (b×d). Divide: (a×d) / (b×c). The result is simplified by dividing both numerator and denominator by their GCD (greatest common divisor, computed via the Euclidean algorithm). The whole number part is extracted as Math.floor(numerator / denominator).
A simplified fraction where the denominator is a power of 2 (2, 4, 8, 16, 32, 64) corresponds to a mark on a standard tape measure. If the result denominator is not a power of 2 (e.g., denominator = 3 or 5), the measurement cannot be read directly from a standard tape and must be converted to decimal inches for use with digital calipers or a calculator.
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Results
5-¾ + 3-⅝ = 9-⅜ inches (9.375 in decimal). A board cut from this combined length needs to be at least 9-⅜ inches long.
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3-½ minus 3/16 equals 3-5/16 inches (3.3125 in). Used when setting a door stop reveal back from a face.
US tape measures mark each inch with progressively finer lines. The longest mid-inch mark is ½. The next set of marks (reaching halfway between ½ marks) are ¼ and ¾. The next set are eighths (⅛, ⅜, ⅝, ⅞). The shortest marks on most tapes are sixteenths. Count the number of small divisions from the last whole inch to read the fractional part, then identify which fraction that represents using the length of the mark as a guide.
US construction uses fractions because traditional tape measures are divided into binary fractions (halves, quarters, eighths, sixteenths), which are easy to bisect physically. Metric countries use decimal millimeters instead. The imperial fraction system is deeply embedded in US building codes, lumber sizing, and trade practice, making it unlikely to change in the near term.
To add or subtract fractions, both must express parts of the same-sized whole — that is, they need the same denominator. For example, ¾ and ⅝ cannot be added directly because they use different-sized parts. Converting both to sixteenths: 12/16 + 10/16 = 22/16 = 1-6/16 = 1-⅜. The calculator finds this common denominator automatically.
Board feet = (thickness in inches × width in inches × length in feet) ÷ 12. If your dimensions are in fractions, convert each to a decimal using this calculator, then perform the board feet formula. For example, a board that is 1-¾ in thick, 5-½ in wide, and 8 ft long = 1.75 × 5.5 × 8 ÷ 12 = 6.42 board feet.
Large denominators (like 64 or 128) can result from multiplying or dividing fractions with different denominators. The calculator simplifies results by dividing by the GCD, so if the simplified denominator is 32 or 64, that is the actual precision of the result. Check whether your work requires this level of precision or whether rounding to the nearest 16th is acceptable.
Yes — metric measurements use decimal fractions (millimeters), but if you encounter fractional metric dimensions (e.g., 2.5 mm expressed as 5/2 mm), the calculator handles them correctly. However, metric shop work typically stays in decimals, so fraction calculation is less common in metric workshops.
Add the two measurements using the Add mode to get their sum, then divide by 2 using the Divide mode (divide sum by 2/1). The result is the exact fractional midpoint. This is useful for finding the center of a board, spacing evenly divided shelf pins, or centering hardware on a door.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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