A converter cannot know how precise your input was
Type "12.5" into a unit converter and it will multiply by a stored factor carried to fifteen or sixteen digits of double-precision accuracy, then hand back a result formatted to several decimal places. Nothing about that arithmetic is wrong. What can be wrong is treating the output as more trustworthy than the input, because a converter has no way to know whether "12.5" meant exactly 12.500000… or was a tape-measure reading good to three significant figures and no more. This site's own Methodology page states the display policy — up to 8 decimal places, trailing zeros stripped, scientific notation outside roughly 1e-6 to 1e9. That is a formatting rule. It says nothing about which of those displayed digits are meaningful for a specific input, which is a judgement only the person holding the original measurement can make.
What "significant figures" actually count
A significant figure is a digit that carries real information about a measured quantity, as opposed to a digit that only marks the number's scale. In 0.0250, the two leading zeros are not significant — they only place the decimal point — but the trailing zero after the 5 is significant, because someone chose to write it, implying the value is known to that fourth digit and not, say, 0.02 with an unstated rounding. This is also where ambiguity creeps in without decimal notation: "200 kg" could mean precisely known to three significant figures, or a rough figure known only to one. Scientific notation removes the ambiguity outright — 2 × 10² kg versus 2.00 × 10² kg cannot be misread.
Two different rules, depending on the operation
Combining measured quantities loses precision differently depending on whether the operation is multiplicative or additive, and applying the wrong rule is a common error:
- Multiplication and division (which is what every unit conversion is): the result carries no more significant figures than the least-precise input. Converting a length known to 3 significant figures into a different unit still leaves you with 3 significant figures of real information, no matter how many digits the arithmetic produces.
- Addition and subtraction: the result carries no more decimal places than the least-precise input, regardless of significant-figure count. 12.5 m + 0.084 m is limited to one decimal place by the first term, giving 12.6 m, not 12.584 m.
A unit conversion is always the first case: value × factor. The factor's own precision matters too, which is where "exact by definition" becomes important.
Exact factors do not cost you significant figures; measured ones do
Multiplying by an exact conversion factor — 1 inch = 2.54 cm exactly, 1 lb = 0.45359237 kg exactly — does not degrade precision, because an exact-by-definition number carries no uncertainty of its own to propagate; every digit of the factor is available if you want it. A measured conversion factor is different: before the 1983 redefinition of the metre in terms of the speed of light, the speed of light itself was a measured quantity with an experimental uncertainty attached, and any calculation using it inherited that uncertainty the same way it would inherit uncertainty from a measured length. After 1983, the speed of light is fixed at exactly 299,792,458 m/s by definition and contributes zero additional uncertainty to anything computed from it. The lesson generalises: the limiting factor in a conversion's precision is almost always the measured input, not the stored constant, provided the constant genuinely is exact. Where this site uses a non-exact, context-dependent figure — the carbon-emissions factor documented on the Methodology page is the clearest example — that figure, not the arithmetic, is the actual precision ceiling.
Worked example: converting a room measurement
A room measured with a tape measure at 12.5 ft by 10.25 ft — three and four significant figures respectively, typical of a tape read to the nearest quarter-inch on a longer wall and a shorter one measured slightly more carefully. Converting each side to metres using the exact factor 1 ft = 0.3048 m:
| Measurement | Sig figs | Raw product | Correctly rounded | Falsely precise (typical calculator display) |
|---|---|---|---|---|
| 12.5 ft × 0.3048 | 3 | 3.81 m | 3.81 m | 3.81000000 m |
| 10.25 ft × 0.3048 | 4 | 3.1242 m | 3.124 m | 3.12420000 m |
| Area: 3.81 m × 3.124 m | 3 (limited by the 3-sig-fig side) | 11.90244 m² | 11.9 m² | 11.90244000 m² |
The area figure is the one that matters: a calculator will happily report 11.90244 m², eight-digit precision inherited from nothing more than floating-point arithmetic having no opinion about measurement quality. The tape measure never supported more than three significant figures on its shorter reading, so the honest answer is 11.9 m² — the other five digits are arithmetic noise, not information about the room.
Where error actually compounds: chained conversions
A single multiplication by an exact factor does not add error. A chain of conversions can still lose accuracy, but the mechanism is rounding at intermediate steps, not the conversions themselves. Converting 12.5 ft to metres, rounding that result to 3.81 m, then converting 3.81 m to millimetres gives 3,810 mm — and looks identical to converting 12.5 ft straight to millimetres (3,810.0 mm), because in this case the intermediate rounding happened to fall on a round number. It does not always work out that cleanly: round 10.25 ft to metres at 2 decimal places first (3.12 m, dropping the true 3.1242 m), then convert that rounded figure onward to compute area with the 3.81 m side, and the area comes out to 3.81 × 3.12 = 11.8872 m² — a different fourth significant figure than the 11.90244 m² obtained from carrying full precision through and rounding only once, at the end. Neither number is "more wrong" in an absolute sense at 3 significant figures (11.9 m² either way), but the discrepancy grows with each additional rounded intermediate step in a longer chain, which is exactly why this site stores every factor at full floating-point precision and rounds only at the final display step, never in between.
The practical rule
Carry full precision through every intermediate step of a calculation and round exactly once, at the end, to the number of significant figures your least-precise input actually supports. A converter that shows eight decimal places is not claiming eight decimal places of real-world accuracy for your specific input — it is declining to guess how many of those digits you need, which is the reader's judgement to make, not the tool's.