FractionReference

Simplest fraction within tolerance

The site's signature question. State how much error you can live with, and get the simplest fraction inside that window — not the closest complicated one.

Try: — also accepts +/- and mixed units.

Presets are conveniences, not standards: they pick which denominators count as “usable.” School stops at twelfths; machining runs to 128ths.

Common questions

What fraction fits 10 mm within half a millimetre?
3/8″. It measures 9.525 mm, which is 0.475 mm under 10 mm — inside the ±0.5 mm window — and no simpler fraction qualifies. Tighten the tolerance to ±0.1 mm and the answer becomes 25/64″ at 9.921875 mm.
How is “simplest” decided?
By a documented ranking: only candidates inside the tolerance qualify; an exact hit wins outright; otherwise the smaller reduced denominator wins; equal denominators go to the smaller error; a dead tie goes undersize. No hidden weighting.
What if nothing fits?
The tool says so — “no fraction in the selected denominator set falls within this tolerance” — and suggests widening the window or allowing finer marks. It never rounds its way to a false fit.
Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. The ranking is stated in full on the methodology page and pinned by the test suite. See the full methodology.