How this calculator works
The decimal distance is converted to inches, multiplied by the chosen denominator, and rounded to the nearest whole number of that fraction. The whole inches and the leftover fraction are then displayed, and the fraction is reduced by the greatest common divisor. A value that rounds up to a full inch is carried into the whole number, so 11.99 inches at half-inch precision becomes 12 in rather than 11 2/2 in.
Formula
fraction units = round(inches x denominator). whole inches = floor(fraction units / denominator). numerator = fraction units - whole inches x denominator, reduced by the greatest common divisor with the denominator. millimetres = inches x 25.4.
Worked example
2.375 in at 1/16 inch precision is 2 6/16 in, reduced to 2 3/8 in. 0.375 in at 1/8 precision is 3/8 in. 0.5 in at 1/2 precision is 1/2 in, while 0.6 in at 1/2 precision rounds to 1/2 in.
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Frequently asked questions
Why round to a fraction at all?
Woodworking, plumbing and construction use standard fraction markings. A fraction that matches the tape or drill chart is easier to work with than a long decimal, even though it carries a small rounding error.
How much error does rounding introduce?
At most half of the chosen fraction. A 1/16 inch precision can be off by 1/32 inch, while 1/64 inch precision can be off by 1/128 inch. Choose the finest precision your measuring tools can support.
What does reducing the fraction mean?
A fraction such as 6/16 is divided by the common factor 2 to give 3/8. The length is unchanged; the fraction is simply written in its simplest form.