Inch Fraction Calculator

What is an inch fraction calculator?

An inch fraction calculator converts a measurement written as a decimal number of inches into the nearest fractional inch — the form used on a tape measure or ruler — and, at the same time, into millimeters. Imperial rulers are divided into halves, quarters, eighths, sixteenths, and finer marks, so a decimal reading such as $0.3125$ in is far easier to use once it is expressed as $5/16$ in.

The calculator takes two inputs: the decimal inch value and the precision (the largest denominator you want, such as $1/8$, $1/16$, $1/32$, or $1/64$). It rounds to the closest mark at that precision, reduces the fraction to lowest terms, separates any whole-inch part, and shows the equivalent length in millimeters.

How does the calculator work?

First the decimal value is rounded to the nearest multiple of the chosen fractional step. With a denominator $d$ (for example $d = 16$) and a decimal value $x$, the total number of fractional units is

$n = \operatorname{round}(x \cdot d)$

The whole-inch part and the remaining numerator are then

$w = \left\lfloor \frac{n}{d} \right\rfloor, \qquad p = n - w \cdot d$

so the value is $w \tfrac{p}{d}$ inches. The fraction $\tfrac{p}{d}$ is reduced by dividing numerator and denominator by their greatest common divisor $g = \gcd(p, d)$:

$\frac{p}{d} = \frac{p / g}{d / g}$

The millimeter equivalent comes from the exact definition of the inch:

$\text{mm} = x \cdot 25.4$

Worked examples

• $0.5$ in at $1/16$ precision: $n = \operatorname{round}(0.5 \cdot 16) = 8$, giving $8/16 = 1/2$ in, and $0.5 \cdot 25.4 = 12.7$ mm.
• $0.0625$ in at $1/16$ precision: $n = 1$, giving $1/16$ in exactly.
• $0.3125$ in at $1/16$ precision: $n = 5$, giving $5/16$ in.
• $1.25$ in at $1/16$ precision: $n = 20$, so $w = 1$ and $p/d = 4/16 = 1/4$, giving $1 \tfrac{1}{4}$ in and $1.25 \cdot 25.4 = 31.75$ mm.

Practical notes

• Choosing a finer precision (a larger denominator) gives a closer fraction but a less convenient one to read on a ruler. A coarser precision such as $1/8$ rounds more aggressively, so the displayed fraction may differ slightly from the exact decimal.
• Because $25.4$ mm per inch is an exact definition, the millimeter output is exact for the decimal you enter, independent of the fraction precision you pick.
• When the rounded fraction reduces to a whole number (for example $2.0$ in), the calculator shows only the whole-inch part and no fraction.