Inch Fraction Calculator

About this calculator

Fractional inches are the working unit on most North American jobsites. A 2×4 stud is 1½″ × 3½″ actual; a 4×8 sheet is 96″ on the long edge; a half-inch drywall sheet is 0.500″ thick. When a cut list calls for nine equal pieces from a 96″ rail, the answer is not a round number — it is 10⅔″ each, and the calculator on your phone returns 10.666666667, which is useless for marking a board.

This tool keeps every calculation in integer arithmetic, so adding 1/2 + 3/8 returns 7/8 exactly — not a decimal approximation. It accepts mixed numbers (1 1/2), proper or improper fractions (3/8 or 11/8), and decimal inches (0.625), and gives you back the simplified fraction, the mixed-number form, the decimal equivalent, and the millimetres reading for cross-checking with a metric tape.

How to use it

Type a value into Value A. Pick the operation: plus, minus, times, or divided by. Type Value B. The result updates as you type.

The inputs are forgiving: a space between whole and fraction (1 1/2), or no space (1½ is not accepted; type 1 1/2). Negative numbers are allowed for subtraction edge cases. Decimal input gets rounded to the nearest 1/64″ and then simplified — close enough for any carpentry application.

The math behind it

Every input is parsed into an integer numerator and denominator. Addition and subtraction use the cross-product over a common denominator: a/b + c/d = (a·d + b·c) / (b·d). Multiplication is a·c / b·d. Division is a·d / b·c, with a guard for divide-by-zero.

The result is then simplified by dividing the numerator and denominator by their greatest common divisor (computed with the Euclidean algorithm). A result with numerator larger than denominator is also displayed as a mixed number (e.g. 11/8 → 1 3/8). The millimetres reading multiplies the decimal value by 25.4 — the exact conversion factor defined by the National Institute of Standards and Technology.

Tips for carpenters and framers

Carpenters routinely subtract for joint thickness. A 96″ rail cut into three pieces with two 1/8″ saw kerfs leaves (96 − 2/8) ÷ 3 = 31 15/16″ per piece, not 32″. Use the divide operation, not estimation.

For batten spacing on siding or shelving, divide the wall length minus all gaps by the panel count. The fractional remainder tells you where to favour the trim joint. For framing layouts on 16″ centres, multiply the spacing by stud count to confirm the layout lands square at the corner — a 1/16″ drift over twelve studs becomes 3/4″, which shows in the drywall.

Common gotchas: the 8d common nail is 2½″ long, not 2 5/8″ — the size code does not correspond to the length. The 2× lumber sizes have nominal vs actual dimensions (2×4 = 1½″ × 3½″); the fractional difference matters every time you stack them. And when reading a tape, the longest mark is the inch, the next-longest is the half, then quarter, eighth, sixteenth — count the marks, do not eyeball.