Fraction to Decimal Converter
Fractional inches, decimal inches, millimetres and centimetres — all at once.
Exact at 1/16
A tape measure is usually marked in 16ths; 32nds and 64ths are machinist and drill-index territory. Only the fraction is rounded to the mark — the decimal, millimetre and centimetre values are always the number you entered.
| Fraction | Inches | Millimetres |
|---|---|---|
| 1/16 | 0.0625 | 1.5875 |
| 3/16 | 0.1875 | 4.7625 |
| 5/16 | 0.3125 | 7.9375 |
| 7/16 | 0.4375 | 11.1125 |
| 9/16 | 0.5625 | 14.2875 |
| 11/16 | 0.6875 | 17.4625 |
| 13/16 | 0.8125 | 20.6375 |
| 15/16 | 0.9375 | 23.8125 |
Marks in lowest terms only — on a 16ths rule the 8/16 mark is the 1/2 mark, so it belongs to the coarser rule and is listed there.
A fraction is a division waiting to happen. To convert 3/8 to a decimal,
divide the numerator by the denominator: 3 ÷ 8 = 0.375. That is the whole
method, and it works for any fraction — 7/16 is 7 ÷ 16 = 0.4375, and a mixed
number like 1 3/8 is 1 + (3 ÷ 8) = 1.375.
Going the other way is where the interesting part is, because most decimals are not any fraction you would find on a rule. Converting a decimal to a fraction means choosing a precision first — the denominator you are willing to work to — and then finding the nearest multiple of it. 0.375 inches is exactly 6/16, which reduces to 3/8, so nothing is lost. But 0.333 inches is not any number of 16ths: the nearest mark is 5/16 (0.3125) and the next is 3/8 (0.375). The converter above says which case you are in rather than quietly rounding, because the difference between "this is the answer" and "this is within half a mark of the answer" starts to matter as soon as you cut something.
Why fractions at all? Because a tape measure is divided by repeated halving, not by tens. Fold a length in half and you have halves; fold again for quarters, then eighths, sixteenths, thirty-seconds. Every mark on an imperial rule has a power of two underneath it, which is why 3/8 and 11/16 are ordinary numbers to a carpenter and 3/10 is not — there is no mark for it. It is also why the conversion is exact in one direction and approximate in the other: every fraction with a power-of-two denominator has an exact decimal, because halving a decimal always terminates, while almost no decimal lands exactly on a mark.
Terminating and repeating decimals. A fraction converts to a terminating
decimal when its denominator, in lowest terms, has no prime factor other than 2 and 5 — the
factors of ten. So every workshop fraction terminates: 1/64 is exactly 0.015625, no rounding
involved. But 1/3 is 0.333… forever, and 5/12 is 0.41666… with the 6 repeating, because 3
divides their denominators and no power of ten ever will. On the per-fraction pages linked
above a repeating decimal is written with the repeating part bracketed — 0.41(6) — which is exact, where any number of 6s written out is not.
Metric alongside. One inch is exactly 25.4 millimetres. That is a definition, not a measurement: the international yard was fixed at 0.9144 metres in 1959, which makes the inch exactly 25.4 mm by construction. So every fraction-to-millimetre conversion is exact too — 3/8" is 9.525 mm on the nose. The millimetre and centimetre panes are converted from the value you entered, never from the rounded fraction, so changing the precision moves the fraction and leaves the metric values where they were.
How do I convert a fraction to a decimal?
Divide the top number by the bottom number. 3/8 = 3 ÷ 8 = 0.375. For a mixed number like 1 3/8, convert the fraction part and add the whole number: 1 + 0.375 = 1.375. Every fraction with a power-of-two denominator — halves, quarters, eighths, sixteenths, thirty-seconds, sixty-fourths — gives an exact decimal with no rounding at all.
How do I convert a decimal to a fraction?
Choose the precision you want (1/16 for most woodworking, 1/32 or 1/64 for machining), multiply the decimal by that denominator, round to the nearest whole number, and reduce. For 0.375 at 1/16: 0.375 × 16 = 6, giving 6/16, which reduces to 3/8 — exact. For 0.333 × 16 = 5.33, you round to 5/16, which is close but not equal. This converter marks that difference rather than hiding it.
What is 3/8 as a decimal?
3/8 is exactly 0.375 inches, or 9.525 millimetres. It is one of the fractions that converts perfectly, because 8 is a power of two: 3 ÷ 8 = 0.375 with no remainder.
Why does my decimal not convert to an exact fraction?
Because most decimals fall between the marks. A rule marked in 16ths can only express multiples of 0.0625, so a decimal that is not a multiple of that has to be rounded to the nearest mark. Going to 1/32 or 1/64 narrows the gap but rarely closes it — one third of an inch has no exact representation at any power-of-two precision, because 3 is not a power of two.
How many millimetres is a 16th of an inch?
One sixteenth of an inch is exactly 1.5875 mm, since an inch is defined as exactly 25.4 mm. A 32nd is 0.79375 mm and a 64th is 0.396875 mm. These are exact values rather than rounded ones — the inch has been defined in terms of the metre since 1959.
What does the bracketed repeating decimal mean?
The bracket marks the digits that repeat forever: 0.(3) is 0.3333… and 0.41(6) is 0.41666…. Written that way it is exact, whereas six or eight digits written out is not. A fraction repeats when its denominator in lowest terms has a prime factor other than 2 or 5 — so thirds, sixths, sevenths and twelfths repeat, while halves, quarters, fifths, eighths and tenths terminate.