What the conversion does and why 25.4 is exact
Dividing a millimeter dimension by 25.4 gives inches, and that factor is a definition rather than a measurement. Before 1959 the inch differed slightly between countries — the American inch was 25.4000508 mm under the 1893 Mendenhall Order, the British inch was fixed against a bronze bar in London, and the two disagreed in the seventh figure. The 1959 international yard and pound agreement replaced both with a yard of exactly 0.9144 m, which makes the inch exactly 25.4 mm.
Two consequences follow. First, the conversion introduces no error at all: whatever accuracy your metric dimension carries survives the arithmetic intact. Second, the decimal you get almost never terminates. One millimeter is 0.0393700787401... inches, repeating, because 1/25.4 has factors of five and 127 in the denominator. That is the practical asymmetry of this conversion — inches to millimeters gives clean numbers, millimeters to inches does not.
The fraction is a separate question layered on top. A machine that reads decimals wants 3.93701 in; a tape measure wants 3 15/16 in. Those are different numbers, and the difference is the reason the converter reports the error alongside the fraction rather than quietly presenting the rounded value as the answer.
The formula, the reverse, and the fraction step
Divide millimeters by 25.4 for inches; multiply inches by 25.4 for millimeters. Centimeters and meters route through millimeters first — multiply by 10 and 1,000 respectively — so a meter dimension and a millimeter dimension follow identical arithmetic and no intermediate rounding creeps in.
The fraction step multiplies the decimal inch value by your chosen denominator, rounds it to a whole count of those units, and reduces the resulting fraction by the greatest common divisor. For 3.937007874 in at sixteenths: 3.937007874 × 16 = 62.992, which rounds to 63, so the value is 63 sixteenths. Splitting that into a mixed number, 63 ÷ 16 is 3 with 15 left over, giving 3 15/16 in. Fifteen and sixteen share no common factor, so nothing reduces.
The error is the exact value minus the fraction. Here 3.937007874 − 3.9375 = −0.000492126 in, or −0.49 thousandths, so the fraction is very slightly the larger number. Multiply by 25.4 to see it in metric: 0.0125 mm. That is a twelve-and-a-half micron overshoot, which is negligible for woodwork and material for a bearing fit.
Worst-case bounds are worth memorising, because they tell you whether a fraction can express your tolerance at all. Rounding to sixteenths can be wrong by up to 1/32 in, which is 31.25 thou or 0.794 mm. Thirty-seconds halve that to 15.6 thou or 0.397 mm. Sixty-fourths halve it again to 7.8 thou or 0.198 mm. A drawing toleranced at ±0.1 mm cannot be met by any fraction on a rule.
Worked example: a 100 mm dimension on an imperial machine
A European drawing calls out 100 mm and your mill has an imperial dial.
- Divide by 25.4. 100 ÷ 25.4 = 3.937007874 in. Check the magnitude: four inches is 101.6 mm, so a shade under four inches is right.
- Set the machine. A dial reading to 0.001 in takes 3.937 in. The residual, 0.000007874 in, is two ten-thousandths of a millimeter and below anything the machine can hold.
- Find the tape equivalent. 3.937007874 × 16 = 62.99. Round to 63 sixteenths. 63 ÷ 16 = 3 remainder 15, so the tape reading is 3 15/16 in.
- Price the rounding. 3 15/16 in = 3.9375 in exactly. 3.937007874 − 3.9375 = −0.000492 in = −0.49 thou = −0.0125 mm. Cutting to the tape mark leaves you 0.0125 mm long.
- Test a finer rule. At sixty-fourths: 3.937007874 × 64 = 251.97, rounds to 252, and 252/64 reduces to 63/16 — the same 3 15/16. Going finer changes nothing here, because 100 mm happens to sit within a thousandth of a sixteenth mark.
Reverse the check. 3.9375 in × 25.4 = 100.0125 mm, which is 0.0125 mm above the drawing. The forward and reverse errors agree, which is the sanity check worth doing whenever the number matters.
How to read the result and which number to use
Use the decimal for anything with a dial, a digital readout or a CNC control, and use the fraction only for a hand tool that reads fractions. Copying a fraction into a machine that accepts decimals throws away accuracy for no benefit — the machine does not care that 3.9375 is a rounder number than 3.937008.
Match the decimals to the source. A drawing dimensioned to whole millimeters justifies three decimal places in inches, because one millimeter is 0.039 in and the fourth decimal is below the granularity you were given. A dimension given to 0.01 mm justifies four decimals. Printing six decimals from a whole-millimeter source claims a precision the drawing does not carry.
Read the sign of the error against the fit you need. A negative error means the fraction is larger than the exact value, so a hole cut to it runs oversize and a shaft turned to it runs oversize too. On a clearance hole that is harmless or helpful; on a shaft it is an interference. Rounding to the nearest mark is symmetric and your fit requirement usually is not, so decide the direction before you cut rather than after.
When the error column shows that no available denominator gets you close, stop using fractions. That is not a failure of the converter; it is the fraction system telling you the dimension belongs on a caliper.
Millimeters to inches reference chart
| Millimeters | Decimal inches | Nearest 1/64 |
|---|---|---|
| 1 | 0.0393701 | 3/64 |
| 2 | 0.0787402 | 5/64 |
| 3 | 0.1181102 | 1/8 |
| 5 | 0.1968504 | 13/64 |
| 6 | 0.2362205 | 15/64 |
| 8 | 0.3149606 | 5/16 |
| 10 | 0.3937008 | 25/64 |
| 12 | 0.4724409 | 15/32 |
| 15 | 0.5905512 | 19/32 |
| 20 | 0.7874016 | 25/32 |
| 25 | 0.9842520 | 63/64 |
| 30 | 1.1811024 | 1 3/16 |
| 50 | 1.9685039 | 1 31/32 |
| 100 | 3.9370079 | 3 15/16 |
The fraction column is produced by rounding the decimal to the nearest sixty-fourth and reducing it, which is why several rows show denominators smaller than 64.
Mistakes that put the wrong dimension on the part
- Using 25 mm to the inch. The 1.6 percent shortfall is 1.6 mm on a 100 mm dimension — larger than most assembly tolerances and visible by eye on a joint.
- Rounding twice. Converting 100 mm to 3.94 in and then rounding 3.94 to a fraction stacks two errors. Carry the full decimal into the fraction step.
- Reading the fraction into a digital readout. The decimal is the accurate number; the fraction exists only to be found on a rule.
- Assuming a finer denominator is always closer. At 100 mm, sixteenths and sixty-fourths give exactly the same fraction. Check the error column rather than defaulting to the finest.
- Confusing centimeters with millimeters on a drawing. Metric engineering drawings are dimensioned in millimeters even when the part is a meter long; a 1500 on the drawing is 1.5 m, not 15 m.
- Quoting a converted dimension to more figures than the source has. A drawing that says 100 mm does not support an answer of 3.937008 in; 3.937 in is the honest conversion.
Why one inch is exactly 25.4 mm and not a measured value
The 1959 international yard and pound agreement was signed by the national standards laboratories of the United States, the United Kingdom, Canada, Australia, New Zealand and South Africa. It defined the yard as exactly 0.9144 m and the pound as exactly 0.45359237 kg, replacing six slightly different national standards with one set of definitions. Every imperial length conversion on this site descends from those two lines, which is why the factors terminate and why they are written as exact rather than approximate.
Where this conversion sits among the others
This is the shop-floor end of the length range. If what you have is already a decimal inch and you only want the fraction and the error, the decimal inches to fraction calculator is arranged that way round and lets you enter a fraction to check as well. For dimensions at room and building scale, decimal feet is the working unit and the meters to feet calculator handles it, including the US survey foot for land records. Human height has its own conventions and belongs in the feet and inches to centimeters calculator.
Once you square the dimension the factor squares with it: 25.4 mm per inch becomes 645.16 square millimeters per square inch, and at building scale the tool is the square feet to square meters calculator. Cube it and you are into material quantities, where the cubic yards to cubic feet calculator converts the bulk figures suppliers quote.
A note on drawing conventions that saves more time than any conversion. Metric engineering drawings are dimensioned in millimeters with the unit stated once in the title block, so a bare 1500 means 1500 mm. Imperial drawings are dimensioned in inches with a similar convention, so a bare 1.500 means one and a half inches, not 1,500 of anything. When a number on a foreign drawing seems absurd by three orders of magnitude, the units convention is the first thing to check.