How this instrument works
Centimetre and kilometre are both a metre wearing a prefix, and those two prefixes are among the oldest in the system. France's decimal measures law of 18 Germinal, Year III — 7 April 1795 — named milli-, centi-, deci-, deca-, hecto-, kilo- and myria- at one stroke. Myria- (ten thousand) fell out of use and was left off the SI prefix list in 1960; centi- (one hundredth) and kilo- (one thousand) came through unchanged. Their ratio is 10³ ÷ 10⁻², which is 10⁵ — so one kilometre holds exactly one hundred thousand centimetres.
That ratio has never moved, though the metre itself has been redefined three times over. It began in 1793 as a ten-millionth of the quarter meridian through Paris, became a platinum-iridium bar in 1889, a count of krypton-86 wavelengths in 1960, and since 1983 the distance light covers in 1⁄299,792,458 of a second. Each redefinition rescaled centimetre and kilometre together by identical amounts, leaving their relationship untouched. Prefix arithmetic is not measurement, so this conversion carries no uncertainty whatever.
In practice these units rarely meet. Centimetres run everyday life across metric countries: body height, sewing patterns, A4 paper at 21.0 by 29.7 cm, a schoolchild's 30 cm rule, furniture that must clear a doorway. Kilometres belong to road signs, odometers, map scales and race distances — 5 km, 10 km, the marathon's 42.195 km. Crossing five orders of magnitude in one hop usually means industrial length counters, cable and pipe runs, survey chainage, or classroom drills on decimal places, and it is precisely that jump which trips people up.
- Type your measurement into the Centimetres (cm) field; 100000 is preloaded as a reference.
- Read your answer on the Kilometres (km) line, recomputed as you type and shown to six decimals.
- Sanity-check by eye: the decimal point moves five places left, so 250 cm should read 0.0025 km.
- Working backwards from kilometres? Multiply by 100,000 first, then enter that figure as centimetres.
Worked example — a cable drum counter
An installer pulls fibre off a drum whose mechanical counter reads in centimetres, because that is what its wheel encoder resolves. At the end of a run the counter shows 100000. Type it into the Centimetres (cm) field and the Kilometres (km) line returns 1.0 — a clean kilometre of cable, with the decimal point simply walked five places left.
Scale it either way and that shift stays honest. Half the reel, 50000 cm, reads 0.5 km; a 250 cm patch lead reads 0.0025 km; a 42.195 km marathon route works back to 4,219,500 cm. No factor changes anywhere along that range, because there is only ever one factor.
Questions
How many centimetres are in a kilometre?
Exactly 100,000 — no rounding, no measurement involved. Take it in two hops: 100 centimetres make a metre, and 1,000 metres make a kilometre, so 100 × 1,000 = 100,000. Reverse that and one centimetre is 0.00001 km, which is where the 1e-05 factor comes from. Because both units are decimal prefixes hung on one base unit, this figure is fixed by definition and cannot drift.
Is the factor 1e-05 exact or rounded?
Exact. 1e-05 is scientific notation for ten raised to minus five — one hundred-thousandth, written compactly. It is a definitional ratio between two SI prefixes, not a measured quantity, so it carries no uncertainty and no significant-figure limit. Any rounding you meet on this page happens in six displayed decimals of your Kilometres (km) result, never in arithmetic behind it.
Why does my hand-calculated answer come out 100 times too large?
Almost always because only one of two divisions got applied. Going from centimetres to kilometres needs a division by 100 to reach metres, then another by 1,000 to reach kilometres — 100,000 altogether. Stopping after that ÷1,000 step leaves a figure 100 times too big; dividing by 10,000 instead leaves it 10 times too big. Quick check: 100,000 cm must read 1 km, and 100 cm must read 0.001 km.
Are centimetres and kilometres imperial or US customary units?
Neither — both are metric, and no imperial or US customary system claims them. Those systems do link to this one exactly, though: since the 1959 international yard and pound agreement, an inch is 2.54 cm and a statute mile is 160,934.4 cm, both exact. One kilometre therefore works out at 100,000 ÷ 160,934.4 = 0.6213712 miles, a decimal running on forever yet a plain fraction underneath.
How many decimal places should I keep?
Six covers millimetre resolution, which is why Kilometres (km) shows that many. One centimetre lands in the fifth decimal place (0.00001 km) and one millimetre in the sixth (0.000001 km); anything finer than that outruns what tapes, measuring wheels and drum counters can actually resolve. For road distances or race planning, two or three decimals — tens of metres — is usually plenty.
Why do engineering drawings skip centimetres entirely?
Because SI practice favours prefixes in steps of a thousand, and centi- breaks that rhythm. Mechanical and construction drafting conventions dimension in millimetres and metres instead, leaving cm to tailoring, medicine, retail and schoolrooms. The centimetre remains a fully legal SI unit — it was even a base unit under the older CGS system — but on drawings its presence invites exactly the ambiguity draughtsmen work hardest to avoid.