# How the Metric System Works

SI Derived Units: We Need More Than Plain, Old Meters

The fundamental SI units cover all of the basic measuring needs. There are times, however, when it's necessary to relate measurements mathematically. For example, let's say you measure the length of a soccer field and find it to be 120 meters (394 feet) long. Then you determine its width to be 90 meters (295 feet). If you wanted to find the area of the field, you would need to multiply its length by its width. But you don't just multiply the numbers in front of the units; you multiply the units, too. So, the math would look like this:

area = length × width = 120 m × 90 m = 10,800 m2

Notice that the final unit is a meter times a meter, which results in what metrologists, or measuring experts, call a square meter.

Now let's say you have a cube measuring 1 meter on each side. If you wanted to find the volume of the cube, you would need to multiply three dimensions -- length, width and height. Here's the math:

volume = length × width × height = 1 m × 1 m × 1 m = 1 m3 = m3

Notice again that the base unit gets multiplied along with the numerical factor. In this case, it's a meter times a meter times a meter, resulting in a cubic meter. Also observe that when the numerical factor is 1, you can drop the number and simply show the unit. Metrologists call this a coherent unit.

The table lists some of the most common derived units.

Area and volume are derived units because they are defined in terms of an SI base unit and a specific quantity equation. The table lists some of the most common derived units.

Some of the most important SI derived units