Unit Conversion, Exactness and Rounding

A conversion factor is a definition, not a measurement

An inch is 25.4 millimetres. Not approximately, not to within a tolerance — by definition, and has been since the international yard and pound agreement of 1959 fixed the yard at exactly 0.9144 metres. Every length conversion between the imperial and metric systems descends from that one line, and none of them has an error bar.

This matters more than it sounds, because it separates two things that get muddled. The arithmetic of a conversion is exact. The number you feed it is not. All of the uncertainty in a converted result was already present in the measurement, and the conversion neither adds to it nor removes any of it.

The one famous exception is instructive. The United States retained a second, slightly different foot for land survey — the survey foot, larger than the international foot by two parts in a million — until it was formally retired at the end of 2022. Two parts per million is nothing across a room and about 3.2 millimetres across a kilometre, which is why it survived in cadastral work and nowhere else. Every conversion on this site uses the international definitions.

Three tiers, and only the first is exact

EXACT BY DEFINITION. The inch, the foot, the yard and the mile against the metre. The pound against the kilogram, fixed at exactly 0.45359237 kg by the same 1959 agreement. The US liquid gallon, defined as exactly 231 cubic inches. The acre, defined as exactly 43,560 square feet. The therm, defined as exactly 100,000 British thermal units. For any of these, there is no assumption to state and no condition under which the number is wrong.

EXACT BY DERIVATION. A pound-force per square inch against the pascal is exact, because the pound-force, the standard acceleration of gravity and the inch are each defined exactly — it simply takes three definitions rather than one. Foot-candles against lux are exact for the same reason: both are lumens per unit area, and the foot is defined. These read as though they ought to be approximations and are not.

CONVENTIONAL, AND NOT A CONVERSION AT ALL. A cubic yard of gravel weighs what it weighs because of what the gravel is, how graded it is and how wet it was when it was loaded. A board foot assumes nominal rather than dressed timber. A ton is one of two different masses depending on which side of an ocean it was quoted on. These look like conversions, are named like conversions, and are material assumptions wearing a conversion's clothes.

The site's rule follows from the split rather than from tidiness: a calculator in the first two tiers ships with no limitations note, and is listed in `exact-conversions.ts` as the record of why. A calculator in the third tier gets its assumption written out. The reason for refusing to pad the exact ones is that a warning on a page with nothing to warn about does real harm — it teaches a reader that the limitations block is boilerplate, and the next block they skip is one that mattered.

A U-value belongs in the second tier. Watts per square metre per kelvin against BTU per hour per square foot per degree Fahrenheit is exact because the International Table BTU (1055.05585262 J), the foot and the Fahrenheit degree are each defined, so 5.678263 is a truncation of an exact ratio — and a thermal conversion that crosses a factor of nearly six, not a rounding step.

Converting cannot create precision

A wall measured to the nearest foot at twelve feet is not 3.6576 metres. That figure implies the measurement was good to a tenth of a millimetre; the tape was good to perhaps half a foot. The conversion is exact and the claim is nonsense, and the nonsense was manufactured entirely by the number of digits printed after it.

The magnitude is worth stating plainly, because it is larger than people expect. A measurement of ±0.5 ft carries a relative uncertainty of about 4%. Printing its conversion to five decimal places asserts a relative uncertainty of about 0.004% — an overstatement of roughly a thousandfold, in the direction that makes an estimate look like a survey.

So the output of a conversion carries the precision of its input, and the site's converters round to a sensible number of significant figures rather than echoing the full float. Where an exact fractional answer is what the reader actually wants — an inch measurement expressed in sixteenths, a fraction for a tape rather than a decimal for a spreadsheet — the site has separate calculators that return the fraction, because rounding a decimal by eye to the nearest sixteenth is a second, avoidable error.

Where it fails: soft conversion against hard conversion

The arithmetic being exact does not make the ANSWER useful, and the gap between those two is where construction conversions actually go wrong. Converting a dimension is a soft conversion: it re-expresses the same physical thing. Replacing a dimension with the nearest convenient one in the other system is a HARD conversion, and it changes the thing.

A nominal 2×4 is not 50.8 × 101.6 mm. It is a name for a piece dressed to roughly 38 × 89 mm, and the arithmetic conversion of the name gives a stick that does not exist. The same trap sits inside pipe sizes, sheet thicknesses and fastener gauges: the designation is a label, not a measurement, and converting a label produces a number with no referent.

The modular cases carry a magnitude worth knowing. A 4 ft × 8 ft sheet is 1219 × 2438 mm; the metric sheet sold alongside it is 1200 × 2400 mm, about 1.6% smaller in each direction and 3.1% smaller in area — on a job needing fifty imperial sheets, the metric equivalent is one and a half sheets more. A 600 mm stud centre is not 24 in, which is 609.6 mm; the 1.6% difference accumulates, so over a twelve-metre wall the twentieth stud lands nearly 200 mm — most of a stud bay — away from where the other system would put it.

This is why a converted dimension should be treated as a starting point for a modular decision rather than as the decision. The site converts; it does not silently substitute the nearest standard size, because that substitution is a design choice and belongs to whoever is responsible for the design.

Where it fails: the round trip

Converting a value out and back through a rounded intermediate does not return it. One hundred millimetres is 3.937 inches; rounded for a drawing to 3.9 inches and converted back it is 99.06 mm — a millimetre lost in a single round trip, and lost silently because both numbers look right.

On a single dimension that is tolerable. On a schedule it is not: a set of thirty openings each round-tripped through a rounded imperial intermediate accumulates a systematic bias, always in the same direction if the rounding rule is consistent, and the cumulative discrepancy turns up when the last unit will not fit the last opening.

The defence is procedural rather than arithmetic: convert once, from the original measurement, and keep the original alongside the converted value. A drawing that carries both and states which one governs cannot drift; one that carries only the converted figure has already thrown away the thing that would settle an argument.

The alternative method, and why this site does not use it

The obvious alternative to rounding a converted value by significant figures is to round it to a PREFERRED increment — the nearest 5 mm, the nearest sixteenth, the nearest standard modular size. Manufacturing and drafting standards do exactly that, and for a shop drawing it is the right answer.

This site does not do it automatically. Rounding to an increment is a decision about what is buildable, and it depends on the trade, on the tolerance available and on which direction the error is allowed to fall — a door opening rounds up, a beam length rounds down, and neither rule generalises. Applying one silently would turn an arithmetic tool into a design tool without saying so.

So the conversions here return a converted measurement at appropriate precision, and the rounding to something orderable is left where it belongs: in the calculator that models the ordering, with its waste factor and its ceiling function exposed as inputs.