Convert meters to kilometers

The meter is the SI base unit of length, the one every other length unit is counted from. Since 1983 its value has been set by the speed of light: a meter is the distance light travels in a vacuum in 1/299,792,458 of a second[1]. A definition built on a physical constant has an advantage over the old bar standard, because any laboratory can reproduce it on its own bench.

A kilometer is a multiple of the meter. The prefix kilo- multiplies a unit by a thousand, so a kilometer holds 1,000 meters. The same rule runs through the whole system: a kilogram is a thousand grams, and a kilobyte a thousand bytes.

Which unit you use comes down to convenient numbers. Meters describe distances on a track, the length of a pool and the height of a building. Kilometers describe a road race, the mileage on a car and the gap between two cities.

One thousand meters is 1 kilometer. Five hundred meters works out to 0.5 kilometers. One hundred meters is 0.1 kilometers. Every conversion in this direction comes down to dividing the number of meters by a thousand.

Beyond the round thousand, three values come up in search more often than the rest. Two hundred and fifty meters is 0.25 kilometers. Seven hundred and fifty meters gives 0.75 kilometers. Two thousand five hundred meters works out to 2.5 kilometers.

The converter above runs both ways and shows the result as you type, so none of these numbers is worth memorizing.

The conversion rests on a fixed relationship: one kilometer is 1,000 meters. To turn meters into kilometers, you divide their number by a thousand.

The full formula: kilometers = meters ÷ 1000. The other way round: meters = kilometers × 1000.

Three numbers follow from that formula more often than any others. Five hundred meters divided by a thousand gives 0.5 kilometers. One thousand five hundred meters comes out at 1.5 kilometers the same way. Ten thousand meters gives an even 10 kilometers.

When you divide by a thousand the digits stay as they are and the decimal point moves three places to the left. From 42,195 meters you get 42.195 kilometers. When there are not enough places to move through, you add zeros in front, so five meters turn into 0.005 kilometers.

The same arithmetic reversed, multiplying by a thousand, is what the kilometers to meters converter does.

The factor of a thousand comes from the prefix, but the length of the meter itself came from a survey of the Earth. When France settled on the new unit in the 1790s, a meter was to be one ten-millionth of the distance from the equator to the North Pole, measured along the meridian through Paris[4].

That starting point produces a figure which is easy to hold on to. If a meter is a ten-millionth of the distance, then the whole distance is ten million meters. Divided by a thousand, that comes to an even 10,000 kilometers.

Today's measurement lands slightly higher. On the WGS84 ellipsoid, the model of the Earth that GPS works on, the quarter meridian measures 10,001,965.729 meters[5]. That is a little under two kilometers more than the makers of the meter had assumed.

The gap traces back to a survey carried out two centuries ago. The expedition led by Delambre and Méchain left out the deflection of the vertical at the southern end of the arc they measured, and the finished meter came out 0.197 millimeters shorter than intended[4]. That fraction of a millimeter repeated ten million times accounts for roughly those two kilometers.