Inches to Fraction Calculator

Anywhere the tools, stock, or callouts on the drawing are graduated in fractions instead of decimals. Carpentry and framing are the obvious cases: a tape measure reads in sixteenths of an inch, and stud spacings, plate widths, and rough openings are quoted as 1 1/2 in, 3 1/2 in, 5 1/2 in, never as 1.5 in or 3.5 in. Plumbing follows the same convention for pipe diameters (1/2 in copper, 3/4 in PEX, 1 1/4 in DWV). Machining drops into 1/32 and 1/64 territory for drill bits, taps, reamers, and dowel pins, where catalog sizes are listed as fractions rather than thousandths. If you get a CAD readout in decimals (0.4375 in) and need to pick a real off-the-shelf size, you have to convert; 0.4375 = 7/16, which matches an actual drill bit in the index. The same goes in reverse: a tape-measure reading of 2 7/8 in often arrives in software as 2.875 in. This calculator converts both directions at the precision your trade uses.

Because 64 is the highest power of two that still gives you a sub-millimeter step (1/64 in = 0.015625 in = 0.397 mm), and a fractional inch system needs power-of-two denominators to stay closed under halving. Folding a measurement in half is the most basic ruler operation, and 1/64 lets you halve five times in a row before you bottom out (1/2 to 1/4 to 1/8 to 1/16 to 1/32 to 1/64). Below 1/64, the imperial world switches conventions entirely: machinists work in thousandths of an inch (thou or mil), not in 1/128 or 1/256, because the named fractions get unwieldy and tape measures stop graduating that finely. So 1/64 is the practical floor of the fractional system. Standard fractional drill-bit indexes ship in 1/64 increments from 1/16 in to 1/2 in for the same reason: it is the densest spacing where a labeled fraction still matches a real, manufacturable tool size.

Lowest terms means the numerator and denominator share no common factor greater than 1. After rounding 1.625 in at 1/64 precision you get 104/64, which is technically correct but useless on a tape measure; nobody reads sixty-fourths of an inch by counting tick marks past 64. Dividing both numbers by their greatest common divisor (here, 8) collapses 104/64 to 13/8 = 1 5/8 in, which matches the labeled mark on the rule. Reducing also normalizes the answer: 8/16, 4/8, and 2/4 all mean exactly 1/2 in, but only 1/2 is the canonical form a carpenter or machinist would speak out loud. This calculator always returns the reduced form, so the fractionString field gives you the answer in the same language the tool catalog and the cut list use.

Because the GCD is exactly the number you need to divide both top and bottom by in one step to land at lowest terms. The Euclidean algorithm computes it efficiently: gcd(a, b) = gcd(b, a mod b), repeated until the remainder is zero. For 104 and 64 the steps are gcd(104, 64) = gcd(64, 40) = gcd(40, 24) = gcd(24, 16) = gcd(16, 8) = gcd(8, 0) = 8, and 104/8 over 64/8 is 13/8. The alternative (factoring both numbers into primes and canceling shared factors) gives the same answer but takes far more work for large denominators. Doing it any other way (trial-dividing by 2, then 3, then 5, etc.) risks missing a common factor or stopping early; the GCD method always finds the unique largest one in a handful of subtractions. That is why every fraction calculator on the site, including the regular fraction calculator and the decimal-to-fraction converter, uses the same Euclidean GCD helper under the hood.

It uses the exact 1959 international yard agreement: 1 inch equals 25.4 mm, by definition, no rounding. That makes 1 inch equal exactly 2.54 cm. So the calculator just multiplies: mm = decimal inches x 25.4, and cm = decimal inches x 2.54. For example, 2.875 in = 2.875 x 25.4 = 73.025 mm = 7.3025 cm exactly. The same constant is what NIST, ISO, and every modern CAD package use, so the metric values you see here will match a CNC controller, a digital caliper, or a printed engineering drawing without drift. The decimal output is rounded to four places to stay readable; the exact value is preserved in the underlying multiplication, so 5/16 in always shows as 7.9375 mm rather than 7.94 or 7.93.