Why inch fractions are all powers of two
Every mark on an imperial tape is a halving of the one before it: half, quarter, eighth, sixteenth, thirty-second, sixty-fourth. That is not an accident of tradition, it is the only way to subdivide a length repeatedly by folding it, which is how graduated rules were made before machines made them. It also has a convenient consequence: any fraction whose denominator is a power of two converts to a decimal that terminates. Three-sixteenths is exactly 0.1875, not 0.1875 rounded. Nothing is lost going either direction, as long as the denominator stays a power of two.
The moment a measurement comes from somewhere else, that stops being true. A third of 10 inches is 3.3333 and there is no tape mark for it. A metric drawing converted to inches lands wherever it lands. The calculator tells you which case you are in: if the total is an exact shop fraction it shows it, and if it is not, it says so and gives you the nearest marks instead.
| Fraction | Decimal | Millimetres | Fraction | Decimal | Millimetres |
|---|---|---|---|---|---|
| 1/64 | 0.015625 | 0.397 | 9/16 | 0.5625 | 14.288 |
| 1/32 | 0.03125 | 0.794 | 5/8 | 0.625 | 15.875 |
| 1/16 | 0.0625 | 1.588 | 11/16 | 0.6875 | 17.463 |
| 1/8 | 0.125 | 3.175 | 3/4 | 0.75 | 19.050 |
| 3/16 | 0.1875 | 4.763 | 13/16 | 0.8125 | 20.638 |
| 1/4 | 0.25 | 6.350 | 7/8 | 0.875 | 22.225 |
| 5/16 | 0.3125 | 7.938 | 15/16 | 0.9375 | 23.813 |
| 3/8 | 0.375 | 9.525 | 1 | 1.0 | 25.400 |
| 7/16 | 0.4375 | 11.113 | A sixteenth is 1.5875 mm | ||
| 1/2 | 0.5 | 12.700 | A sixty-fourth is 0.397 mm, about 16 thou | ||
The subtraction that everyone does in their head and gets wrong
The most common piece of shop arithmetic is taking framing thicknesses off a measured opening, and it is exactly the kind of sum that is easy in decimals and awkward in fractions. A 48 inch opening less two studs at 1-1/2, plus a 3/16 gap: in decimals that is 48 minus 1.5 minus 1.5 plus 0.1875, which is 45.1875, and 45.1875 is 45-3/16. In fractions you are converting to sixteenths, adding 768 minus 24 minus 24 plus 3 of them, and dividing back. Both give the same answer and the second one is where a sixteenth goes missing.
The list format on this page exists so that you can type the sum the way you would say it out loud, one measurement per line with a sign, rather than converting anything first. Mixed numbers, plain fractions, decimals and the hyphenated 1-1/2 form all parse, and they can be mixed in the same list. What comes back is the exact total as a fraction where one exists, the decimal, and the nearest marks at each of the denominations a tape actually shows.
Rounding, and the thousandth that matters
A sixty-fourth is 0.0156 inches, about 16 thousandths. A sixteenth is 62.5 thousandths. Whether the difference matters depends entirely on what you are doing, and the honest answer is that it matters far less often than machinists assume and far more often than framers do.
On a stud wall, a sixteenth is nothing; the lumber is not that straight and the drywall covers it. On a face frame, a sixteenth is a visible gap in a light-coloured finish. On a cumulative layout, where you are stepping off the same dimension repeatedly, rounding error compounds and that is where it gets expensive: five parts each rounded up by a sixty-fourth put the last one a sixteenth out of place, and twenty of them put it a quarter inch out. The divide function on this page shows exactly that. It gives the exact part size, the rounded one, and how far the rounded parts drift from the total when you add them back up. If the drift is more than you can live with, the fix is to lay out cumulatively from one end with a tape rather than stepping off a single measurement with a gauge.
Inches and millimetres
The inch has been defined as exactly 25.4 millimetres since 1959, so the conversion is not an approximation and there is no rounding involved in the definition. What is approximate is anything that comes back the other way: 100 mm is 3.937 inches, which is not a fraction, and rounding it to 3-15/16 puts you 0.0245 inches, about 0.6 mm, under. That is invisible in carpentry and disqualifying in machining.
The practical advice is to pick one system for a project and stay in it. Mixed drawings, where the sheet goods are metric and the framing is imperial, are common and manageable, but the conversion should happen once at the start rather than at every cut. Every round trip between the systems introduces error that has nowhere to go but into the joint.
One thing this cannot fix
Arithmetic accuracy and measurement accuracy are unrelated problems, and this page only helps with the first. A total carried to six decimal places is worth nothing if the original measurement was taken with the tape hooked over a burr, or read at an angle, or taken from a wall that is not straight. Shop wisdom about measuring twice is really about the fact that the second measurement is the only check you have on a reading, and no amount of exact fraction handling downstream will tell you the first one was wrong. Use this to keep the sums honest, then go back and measure the opening again.
Questions people ask
What is 0.4375 as a fraction of an inch?
Seven-sixteenths. The conversion is to multiply by 16 and see whether you land on a whole number: 0.4375 times 16 is exactly 7, so it is 7/16. If the result is not whole, try 32 and then 64. Numbers you meet constantly are worth knowing cold: 0.0625 is a sixteenth, 0.125 an eighth, 0.1875 three-sixteenths, 0.25 a quarter, 0.3125 five-sixteenths, 0.375 three-eighths, 0.4375 seven-sixteenths, 0.5 a half, and then the same sequence again above the half. Anything that does not resolve at 64 is not a tape measure number, and this calculator will say so rather than pretending otherwise.
How do I add fractions with different denominators?
Convert both to the smallest denominator that divides evenly into each, add the numerators, and reduce. Adding 3/8 and 5/16 means turning the 3/8 into 6/16, adding to get 11/16, which is already reduced. With inch fractions this is easier than general fraction arithmetic because every denominator is a power of two, so the common denominator is always just the larger of the two. Most people find it faster to convert to decimals, add, and convert back, which is what this page does internally while also tracking the exact fraction so nothing is lost to rounding along the way.
What does the exact value line mean when it says the total is not a shop fraction?
It means the total has landed on a value whose denominator is not a power of two, so there is no tape mark that hits it exactly. That happens when a decimal that is not a clean binary fraction goes into the list, such as a metric conversion or a third of something. The decimal shown is still exact; what does not exist is a fraction to express it in sixty-fourths or anything coarser. In that case the rounded rows are the useful ones, and the thousandths figure beside each tells you how far the nearest mark actually is from where the number wants to be.
How accurate is a sixty-fourth?
A sixty-fourth of an inch is 0.015625 inches, or 0.397 millimetres, or a bit under 16 thousandths. For context, a sheet of ordinary printer paper is around 4 thousandths, so a sixty-fourth is about four sheets. It is roughly the finest graduation printed on a good tape or rule, and it is at the edge of what most people can read reliably without magnification. In woodworking it is a fine fit; in metalwork it is coarse. If your work needs better than a sixty-fourth, you are past the point where a tape measure and a fraction are the right tools and should be working from decimals with a caliper.
Can I use this for feet and inches?
Enter everything in inches and read the feet-and-inches line in the results, which converts the total for you. The list itself takes inches only, deliberately, because allowing mixed feet-and-inches entry means guessing at what someone meant by an ambiguous entry and getting it wrong twelve times out of twelve. Twelve feet six and a half is 150.5 in the box. If you routinely work from a rod or a story pole in feet, multiply once on the way in and let the results convert on the way out.
Why do my rounded parts not add up to the whole?
Because rounding is applied to each part and the errors add. Split 47 inches five ways and each part is 9.4 inches exactly; round each to the nearest sixteenth, 9-3/8, and the five together come to 46-7/8, an eighth short of where you started. The larger the number of parts and the coarser the rounding, the worse the drift. The fix in the shop is not better arithmetic but a different layout method: mark cumulatively from a single end, so that each mark is measured from the datum rather than from the last mark, and the error stops accumulating. The split section on this page shows the drift explicitly so you can see whether it matters before you start marking.