Fractional Inch Converter

There is no single nearest fraction

Ask what 10 mm is in inches and the honest answer is another question: to what denominator?

Three different fractions, and the error swings from under a tenth of a millimetre to nearly half. The 32nds answer is larger than 10 mm and the 16ths answer is smaller, so they bracket it from opposite sides.

Notice also that 1/16 and 1/8 give the same fraction. 10 mm falls close enough to 3/8 that allowing sixteenths buys nothing — which is its own useful signal, and one a single-answer converter cannot show you.

The rule underneath is simple: rounding to 1/d can never be more than half a division out, so the error is bounded by 1/(2d). At eighths that bound is 1.59 mm; at 64ths it is 0.20 mm. Which denominator is appropriate is a question about the job, not about the arithmetic — a carpenter marking a stud wall and a machinist boring a bearing seat need different rows of that table, and the calculator gives all of them rather than choosing.

Only 25.4 mm is exactly an inch

Since the international yard and pound agreement of 1959, an inch is exactly 25.4 millimetres. Not approximately — exactly, by definition, which is unusual and worth appreciating: the conversion itself introduces no error at all.

What it does introduce is an awkward fact. Because 25.4 is not a power of two and not a round number in the other direction, no round metric size is a clean binary fraction, and no common inch fraction is a whole number of millimetres.

The 25 mm row is the one that catches people. It is within a hundredth of an inch of 63/64 and within two hundredths of a whole inch, so “25 mm is about an inch” is a fine everyday statement — and a 1.6% error, which on a metre of material is sixteen millimetres.

The practical consequence: when a dimension crosses between systems, carry the exact value as far as you can and round once, at the end, to the precision the job needs. Rounding early and then converting compounds two errors that did not have to be compounded.

The spanner near-misses have no pattern

Because the two fastener series were developed independently, the inch sizes land at essentially random points among the metric ones. Some pairs are close enough to be genuinely interchangeable; some will round a fastener off. Nothing about the numbers tells you which.

Look at 5/16″ and 3/8″ — adjacent sizes in the same set. The first is six hundredths of a millimetre from an 8 mm nut and fits properly. The second is nearly half a millimetre from a 10 mm nut and will chew the corners off it. There is no way to reason your way to that; it has to be looked up.

The thresholds used here are about consequence rather than arithmetic. Around a tenth of a millimetre is ordinary manufacturing slop and nobody notices. Around a third starts to matter on a tight or soft fastener, especially with a twelve-point socket that bears on the corners. Approaching half a millimetre the spanner is turning the corners rather than the flats, and the fastener rounds.

And 3/4″ against a 19 mm nut is the famous one: five hundredths apart, which is inside the tolerance of both. They are treated as the same size in practice, and that is correct.

Fractions and thousandths are different languages

A tape measure and a micrometer both measure inches, and they cannot express the same thing.

An ordinary machining tolerance of ±0.005″ — five thou — is twelve and a half times finer than the finest mark on a standard tape measure. Even a 1/64 rule, which is a fine one, is only about three times coarser than that tolerance band.

Which means a dimension written as a fraction cannot carry a thousandths-level tolerance. “3/16″” and “0.1875 ±0.005″” are the same number and different instructions: the first says mark it here, the second says hold it to here. Drawing conventions encode this — a fractional dimension implies a loose, nominal fit, and a decimal dimension with places implies the precision those places suggest.

This is why shops that work to thousandths abandon fractions internally even when their stock is sold in them. A 3/4″ bar is bought as 3/4″ and turned to 0.7480″, and nobody writes the second number as a fraction because there is no useful way to.

Reading a fractional dimension

A few habits make fractional work less error-prone, most of them about not throwing away precision you already had.

• Convert once, at the end. Carry the exact decimal through a calculation and round only the final dimension. Rounding each intermediate value to a fraction stacks errors that had no need to meet.
• Say which denominator you rounded to. “3/8, to the nearest sixteenth” tells the next person how much to trust the number. “3/8” alone does not.
• Watch for a fraction that did not reduce. A drawing showing 8/16″ rather than 1/2″ is often signalling that the dimension was measured to the sixteenth, not that someone forgot to simplify. Both readings occur, so it is worth asking.
• Do not round a metric dimension into a fraction to work in inches. If the part is metric, work in metric. The conversion is exact; the rounding is not, and the rounding is the only part that costs you anything.

One arithmetic note that saves grief: to add fractions with different denominators, convert both to the finer one first. Sixteenths and thirty-seconds add cleanly once everything is in thirty-seconds — 3/16 becomes 6/32, and 6/32 + 5/32 is 11/32. The calculator’s ladder is useful here too, because it shows at a glance whether a result even needs the finer denominator.

Related calculators

Related measurement and machining tools:

More in Conversion, or browse all calculators.

Sources and methodology

The inch has been exactly 25.4 millimetres since 1959, which is the fact everything on this page rests on — the conversions are exact and only the roundings are approximate. The two fastener series were developed independently rather than derived from one another, which is why the gaps between them follow no pattern and have to be tabulated rather than reasoned about.

• NIST — the international yard and pound agreement of 1959National Institute of Standards and Technology, US · verified 2026-09-07 · That the inch is defined as exactly 25.4 millimetres, which is why 25.4 mm is the only round metric size that is a clean inch and every other crossing is an approximation
• ISO 272 — Fasteners: hexagon products, widths across flatsInternational Organization for Standardization · verified 2026-09-07 · The metric across-flats sizes used in the spanner comparison table, which is what makes the imperial-metric gaps computable rather than anecdotal
• ASME B18.2.2 — Nuts for general applications, inch seriesAmerican Society of Mechanical Engineers · verified 2026-09-07 · The inch-series across-flats sizes paired against the metric ones here, and the fact that the two series were developed independently rather than derived from each other
• ASME Y14.5 — Dimensioning and tolerancingAmerican Society of Mechanical Engineers · verified 2026-09-07 · The convention that a dimension carries a tolerance and that the number of decimal places implies precision — the basis for the point that a fractional dimension cannot express a thousandths-level tolerance