Inch Fraction Converter (Decimal and mm to 1/16, 1/32, 1/64)

Decimal inches or millimetres to the nearest fraction on a tape measure, with the residual printed in thousandths of an inch and in millimetres so you can decide whether it matters. Whole inches, numerator and denominator come out as separate numbers, reduced to lowest terms — and feet and inches go in as well as out.

Multiply, round, then halve until it stops

Every sixty-fourth, reduced, in decimal inches and millimetres

Round metric sizes and the nearest fraction at three denominations

The divisions themselves, for reference

A fraction is a nearest value, and the residual is the answer

Converting a decimal to a fraction is not a conversion, it is a rounding. 3.937 in is not 3 15/16 in; it is 3 15/16 in minus half a thousandth. Most of the time that does not matter and occasionally it matters enormously, and the only way to know is to be shown the difference. So this page prints the residual three ways — in thousandths of an inch, in millimetres, and as a share of the measurement — and puts the worst possible residual for your chosen denominator next to it. Half a sixteenth is 31.25 thou, which is 0.79 mm; half a sixty-fourth is 7.81 thou, which is 0.198 mm. Those are the bounds, and nothing you round can ever be further out than that.

The arithmetic is short. Multiply the fractional part by the denominator, round to the nearest whole number, and that is your numerator. Then reduce: because every denominator on a rule is a power of two, reducing is nothing more than halving both numbers while the numerator is even. 14/16 halves to 7/8 and stops because 7 is odd. 48/64 halves to 24/32, then 12/16, then 6/8, then 3/4, and stops. Six halvings covers every case up to sixty-fourths, which is why this needs no loop and no greatest-common-divisor algorithm.

Why the numerator and denominator are separate numbers here. This page’s calculator computes numbers; it has no way to assemble the text “3 15/16”. Rather than print something that looks like a fraction and is not, it gives the whole-inch part, the reduced numerator and the reduced denominator as three rows, plus the unreduced numerator over the denominator you asked for. That is more honest and, for anybody actually working, more useful: the unreduced numerator is the number of tape divisions to count, and the reduced pair is what you say out loud.

Metric to fractions is where the trouble is. Almost nothing round in millimetres is round in inches, because a millimetre is 0.03937 in — about two and a half sixty-fourths, and no rule is marked in those. The exceptions are the sizes that were inches to begin with: 25.4 mm is exactly 1 in, 12.7 mm exactly 1/2, 6.35 mm exactly 1/4, 3.175 mm exactly 1/8. Everything else carries a residual, and the residual does not shrink smoothly as the numbers get bigger — it is a sawtooth, which the chart above shows over a hundred millimetres. 100 mm lands within half a thousandth of 3 15/16 in, which is luck; 15 mm is twenty-eight thousandths off its nearest sixteenth, which is luck in the other direction.

Feet and inches. A US framing dimension is written as feet, whole inches and a fraction — 5 ft 7 3/8 in — and that is three numbers, not one. This page takes them as three inputs and gives them back as three outputs, with the decimal inch (67.375) and the millimetre figure (1711.325, exactly) alongside. For the trade scales that live on the same fractions, see the drill bit size converter, where a 1/4 in drill, an E drill and a 6.35 mm drill are one bit with three names, and the wire gauge converter for the gauge numbers that sit between the fractions. The figures behind this conversion come from a published table, not a definition, so a different source may give slightly different numbers. The reference below is the one used here.

Frequently asked questions

Related calculators

References

1. National Institute of Standards and Technology, Refinement of Values for the Yard and the Pound, Federal Register notice of 1 July 1959, which fixed the international inch at exactly 25.4 mm and the avoirdupois pound at exactly 0.45359237 kg. Both exact values are used throughout this batch; every inch-to-millimetre figure here is therefore exact, not approximate.
2. ISO 3:1973, Preferred numbers — Series of preferred numbers, which defines the R5, R10, R20 and R40 series. Copyrighted; cited by number. The R10 series used here — 1, 1.25, 1.6, 2, 2.5, 3.15, 4, 5, 6.3, 8 — is the rounded decimal geometric series with ten steps per decade and is recomputed on this page from 10^(n/10) rather than copied.