Inch Fraction to Decimal Converter

How it works

A tape-measure fraction is just a division: 3/16 in is 3 ÷ 16 = 0.1875 in. With a whole-inch part, the whole inches are added on, so 1 5/16 in is 1 + 5 ÷ 16 = 1.3125 in. Millimetres follow from the definition of the inch, exactly 25.4 mm, so 0.1875 in is 4.7625 mm.

Going the other way there is usually no exact fraction, so the calculator finds the nearest mark at the precision your tape reads to. It multiplies the decimal by the denominator (16 for sixteenths), rounds to the nearest whole number of marks, and reduces: 0.3 in × 16 = 4.8 → 5 sixteenths = 5/16 in. The rounding error is the decimal minus the fraction, here 0.3 − 0.3125 = −0.0125 in, meaning the mark is a little over the true length. The error is never more than half a step: 1/32 in at sixteenths, 1/128 in at sixty-fourths.

Use the finest precision your tape actually shows. Rounding a machinist's decimal to sixty-fourths is pointless if you will cut to a tape marked in sixteenths, and the error figure tells you whether the nearest mark is close enough for the job.

Formula

fraction → decimal:  inches = whole + numerator ÷ denominator
                     mm = inches × 25.4
decimal → fraction:  marks = round(inches × d)         d = 8, 16, 32 or 64
                     fraction = marks / d, reduced
                     error = inches − marks ÷ d        |error| ≤ 1 ÷ (2d)

Example

3/16 in, the default, is 3 ÷ 16 = 0.1875 in, which is 0.1875 × 25.4 = 4.7625 mm. 1 1/2 in is 1.5 in = 38.1 mm, and 1 in is exactly 25.4 mm.

0.3 in to the nearest sixteenth: 0.3 × 16 = 4.8, which rounds to 5, so the nearest mark is 5/16 in (0.3125 in). The error is 0.3 − 0.3125 = −0.0125 in, and 0.3 in is 7.62 mm. To the nearest sixty-fourth, 0.3 × 64 = 19.2 → 19/64 in with an error of +0.0031 in.

Assumptions and limitations

• 1 in = 25.4 mm exactly, by the international yard and pound agreement of 1959.
• Enter decimal inches. To find the nearest fraction for a millimetre measurement, divide it by 25.4 first.
• The nearest-fraction mode rounds to the nearest mark; a decimal exactly halfway between two marks rounds up. The rounding error is the decimal minus the fraction, so a negative error means the fraction is larger than the measurement.
• Lengths are non-negative. In fraction mode the numerator may exceed the denominator (18/16 in is read as 1 1/8 in) and any whole-number denominator is accepted, not only the tape sizes.
• The decimal inch is shown to four places and millimetres to three; the working line shows six.

Frequently asked questions