Significant Figures: Why Your Converter Shows More Digits Than You Should Use

Convert 5 feet to metres and you get 1.524. Convert 5.7 inches to centimetres and you get 14.478. Both look precise. Only one of them is honest — and possibly neither, depending on how you measured.

Conversion does not create precision. It cannot. If you measured to the nearest inch, your answer is good to the nearest inch no matter how many decimal places the arithmetic produces.

What a significant figure is

Significant figures are the digits in a number that carry actual information about the measurement.

• All non-zero digits are significant. 247 has three.
• Zeros between non-zero digits are significant. 2007 has four.
• Leading zeros are not. 0.0034 has two.
• Trailing zeros after a decimal point are significant. 2.400 has four — the writer is asserting those zeros were measured.
• Trailing zeros in a whole number are ambiguous. 1500 might have two, three or four. Scientific notation removes the doubt: 1.5 × 10³ is unambiguously two.

The rule for multiplication

When multiplying or dividing — which is what unit conversion is — the result carries as many significant figures as the least precise input.

Convert 5 inches to centimetres. The factor 2.54 is exact, so it does not limit anything. Your measurement of "5 inches" has one significant figure. The honest answer is 10 cm, not 12.7 cm.

If you actually measured 5.0 inches — two significant figures, meaning you are confident to a tenth — then 13 cm is appropriate.

Why our converters show many digits

This site displays up to ten significant figures. That is deliberate, and it is not a claim about your precision.

A converter cannot know how you measured. Showing extra digits means the tool never silently discards precision you actually had. If you are converting a machined tolerance, you need those digits. If you are converting a rough estimate, you should discard them.

Rounding is your job, because only you know your measurement uncertainty.

False precision in practice

Unit conversion is the most common source of fake precision in technical writing, and it usually goes like this:

A press release says a building is "about 500 feet tall". A translated article states "152.4 metres". The original was accurate to perhaps the nearest fifty feet. The translation implies accuracy to a tenth of a metre. Three significant figures appeared from nowhere.

The honest version is "about 150 metres". It preserves the vagueness of the source, which is information in itself.

You see this constantly in recipe conversions too: "1 cup (236.5882365 mL)". No cook measures to a ten-millionth of a millilitre. The useful figure is 240 mL, or 235 mL if you want to be fussy.

Round once, at the end

If a calculation has several steps, carry full precision throughout and round only the final answer. Rounding intermediate results compounds error — each rounding introduces a small bias and those biases accumulate.

This is why our conversion engine defines every unit against a single base unit. Converting furlongs to fathoms is one multiplication and one division, not a chain through metres, feet and yards, each hop shedding precision.

A practical procedure

1. Decide how precisely you actually measured.
2. Convert at full precision.
3. Round the result to match your input precision.
4. If the rounded figure hides something important, say "approximately" rather than adding digits you did not earn.

And one caution: for safety-critical tolerances, round in the direction that preserves safety rather than the direction the arithmetic suggests. A clearance rounded the wrong way is a clearance you no longer have.