Kilometers to Centimeters

Expressing kilometers in centimeters sounds odd, but it comes up wherever two very different scales meet. Geology is a good example. The Atlantic Ocean widens by roughly 2.5 cm a year as the plates on either side of the Mid-Atlantic Ridge move apart. Over a million years that is 2,500,000 cm, or 25 km, and over the roughly 180 million years since the ocean began to open, thousands of kilometers. Converting both sides to one unit is what makes such comparisons possible.

Physics has its own reason. The older CGS system of units, built on the centimeter, gram and second, is still used in parts of astrophysics, so a distance of 1 km appears in papers as 10⁵ cm.

When the meter was created in the 1790s, it was meant to be one ten-millionth of the distance from the North Pole to the equator. By that definition the quarter meridian is 10,000 km, which is 1,000,000,000 cm, a billion centimeters. The survey behind it was slightly off, so the real figure is about 10,002 km, but the round number explains why the Earth's circumference is close to 40,000 km.

Since 1983 the meter has been defined by the speed of light instead, and the kilometer and centimeter follow from it exactly, so the factor of 100,000 involves no rounding.

Going up the metric ladder from kilometers to centimeters takes five steps of ten: kilometer, hectometer, decameter, meter, decimeter, centimeter. Each step adds one zero, so the factor has five. Writing 2.5 km as 25,000 cm, a common slip, drops one step and leaves the answer ten times too small; the correct figure is 250,000 cm.

If the numbers get unwieldy, convert to meters first by multiplying by 1,000, then to centimeters by multiplying by 100. For the reverse, use centimeters to kilometers, or pick any pair in the unit converter.