How the Metric System Works

The modern metric system can trace its roots back to Gabriel Mouton, the vicar of St. Paul's Church in Lyon, France, and a notable astronomer and mathematician. In 1670, Mouton conceived of a system of measurement based on the length of one minute of longitude (remember that there are 60 minutes in each degree of longitude and latitude). This unit of length, he further proposed, should be based on decimal arithmetic, or on powers of ten. He also recommended the use of prefixes to make naming conventions less arbitrary.

French scientists continued to modify and refine Mouton's ideas, but they were never formally codified until the French Revolution. Upon its creation in 1790, the National Assembly requested the French Academy of Sciences to "deduce an invariable standard for all measures and all weights." The academy in turn appointed a commission to develop the system, with the stipulation that the final solution should be at once simple, yet scientific. Borrowing from Mouton, the commission established three basic principles:

The commission named the unit of length "metre" ("meter" in the U.S.), after the Greek word metron, which means "to measure." Next came the task of actually determining the exact length of a meter. This fell to two men, Pierre Mechain and Jean Delambre, who spent six painstaking years measuring the distance on the meridian from Barcelona, Spain, to Dunkirk in northern France. Their survey resulted in a value for the meter equal to "one ten-millionth part of a meridional quadrant of the earth." Other units came from the precisely defined meter. For example, the gram was made equal to the mass of a cubic centimeter of pure water at the temperature of its maximum density; the liter was made equal to the volume of a cube 10 centimeters (4 inches) on a side.

This was the first incarnation of the metric system, which France officially adopted in 1795. Four years later, scientists fashioned standards for the meter and kilogram out of platinum. These, too, were officially recognized by the French government and stored in a safe place so copies could be made as needed.

Next, the metric system takes the whole world by storm.

Thanks to Napoleon's conquest of Europe throughout the early 19th century, other countries adopted -- some more grudgingly than others -- the metric system as their national system of measurement.

In 1875, a special assembly in Paris brought together representatives from 17 nations, including the U.S. These nations were busy during the assembly, signing the Treaty of the Meter and setting up the International Bureau of Weights and Measures, an International Committee for Weights and Measures to run the bureau and the General Conference on Weights and Measures to consider and adopt changes. The treaty also directed that a lab be maintained in Sèvres, by Paris, to house international metric standards and allowed for these standards to be distributed to each ratifying nation. The U.S. received its copies of the International Prototype Metre and the International Prototype Kilogram in 1890.

In 1954, the 10th General Conference on Weights and Measures initiated a redesign of the metric system to better accommodate the needs of the scientific and technical communities. The revision established seven base units and simplified metric unit definitions, symbols and terminology. The work extended into the 11th Conference, and in 1960, conference members ratified and approved the new system, calling it the International System of Units, or SI for short.

The International System of Units is the modern form of the metric system, and although the two names are used interchangeably, SI is more accurate technically. Up next, we'll look at the building blocks of SI -- the seven base units.

Before we dive into the fundamental SI units, let's review measurement as a concept. When you measure something, you use an instrument or device to determine some physical quantity of an object. For example, you use a ruler to measure length, a scale to measure mass and a thermometer to measure temperature. Each of those instruments comes marked in standard units to make sure the measurement of one observer matches that of another observer. In theory, each standard unit would trace its lineage back to a single prototype -- the archetypal example of that particular unit.

In earlier versions of the metric system, the prototypes were physical objects, such as a standard meter stick or a standard kilogram bar. When the General Conference on Weights and Measures revamped the metric system in 1960, it replaced units based on physical objects with physical descriptions of the units based on stable properties of the universe.

With that in mind, let's introduce the seven SI base units. The table lists each unit, the physical quantity that unit measures and the standard upon which the unit is based, as defined by the International Bureau of Weights and Measures.

If you don't fully understand the definition for each standard, don't worry. Instead of trying to picture two straight parallel conductors of infinite length or a cesium-133 atom vacillating between two hyperfine levels of its ground state, just remember this: The fundamental SI units are based on immutable properties of the universe, and they are mutually independent. All other units in the modern metric system come by multiplying or dividing these base units. We'll get into that more in the next section.

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.

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.

A few derived units are significant enough to have earned special SI names and symbols. Force serves as a great example. Isaac Newton defined force as the mass of an object times its acceleration. When you multiply these two quantities together, you get a derived unit of kilogram meter per second squared (kg-m/s²). Because kg-m/s² is a little cumbersome and because force is such an important quantity in physics, SI bigwigs decided to call the derived unit a newton, in honor of Sir Isaac. In all, there are 22 derived SI units with special names and symbols. Some of the most important ones appear in the accompanying table.

Finally, it's important to know that a few units are not officially part of the metric system but make frequent appearances. As such, the SI accepts these units for use with its family of measures. Some of the common time quantities -- the minute, hour and day -- fall into this category, as do the metric ton and astronomical unit. All of these units, however, can be defined according to SI base units. For example, a day is 86,400 seconds. And an astronomical unit (AU) -- a unit of length equal to the mean distance between the Earth and the sun -- is 1.495978 × 10¹¹ meters.

Of course, a base unit may be too large or too small to describe an object adequately. In the SI, making units larger and smaller requires nothing more than adding a prefix. We'll cover those on the next page.

As we've hammered home by now, each physical quantity -- length, mass, volume and so on -- is represented by a specific SI unit. Sometimes, though, the base units have limitations when they're used to measure very small or very large objects. For example, let's say you wanted to measure the length of an ant. Expressed in the SI base unit, an ant's length is 0.003 meters. Now imagine expressing the width of a human hair or an atom in meters: Your numbers would become smaller and smaller -- and increasingly cumbersome. The same holds true for large measurements. The distance between New York City and Los Angeles is 4,493,288 meters, another unwieldy number.

To get around this issue, the General Conference on Weights and Measures adopted a series of prefix names and symbols to designate the decimal multiples and submultiples of SI units. In 1960, enough prefixes existed to cover multiples ranging from 10¹² to 10^-12. But over the years, new prefixes entered the system to accommodate ever larger and smaller values. The accompanying table lists some of the approved prefix names and symbols.

Now we can go back to our examples to see the advantage of using a prefix system based on powers of 10. An ant's length may be 0.003 meters, but it's much more practical to describe something that small in millimeters. To convert meters to millimeters, you simply multiply the length by 1,000, or move the decimal point to the right three spaces. That tells us that an ant is 3 millimeters (3 mm) from its head to its abdomen. And what about our trip between New York City and Los Angeles? You'd be much better off measuring such a great distance in kilometers. To convert meters to kilometers, you simply divide the distance by 1,000, or move the decimal to the left three spaces. That makes your final distance 4,493 kilometers (4,493 km).

All of the prefixes operate in a similar way. The one curveball you need to worry about is the kilogram, the only SI base unit whose name and symbol include a prefix. You might be tempted to add a prefix to kilogram (microkilogram, for example), but that would be incorrect. Instead, you should attach prefix names to the unit name "gram" to represent larger and smaller values of an object's mass. So, for example, 10^-6 kilograms would be equal to 1 milligram (1 mg).

Armed with the SI units and prefixes, you have everything you need to start measuring metric. In fact, most of the world has been doing so for decades. Up next, we'll discover why nations have enthusiastically embraced the modern metric system and what can happen when a country (yeah, we're looking at you, America) fails to make the switch.

If taking a tour of SI units and prefixes hasn't convinced you of the metric system's advantages, then tackle this exercise: convert 5 miles to inches. Quick. In your head. Even if you remember how many feet are in a mile (5,280) and how many inches are in a foot (12), you still have some complex arithmetic to do. Here's what the math would look like:

(5 miles)(5,280 feet/1 mile)(12 inches/1 foot) = 316,800 inches

The metric system makes life much easier. A similar conversion would be to find how many centimeters exist in 5 kilometers. A kilometer is 10³ meters; a centimeter is 10^-2 meters. To make the conversion, you simply move the decimal point to the right five times:

5 kilometers = 5,000 meters = 500,000 centimeters

See why SI units are easier?

Because of its elegance and simplicity, the International System of Units can be found throughout the world. The United States is the only industrialized nation that still clings to its legacy measures and, as a result, wrestles with a confusing array of unrelated units. Of course, cost factors into why the U.S. has been slow to adopt the metric system. As an example, consider NASA's space shuttle program, which still adheres to the inch-pound system of measurement. NASA engineers recently reported that converting the relevant drawings, software and documentation to SI units would cost a total of $370 million -- a big chunk of change, even for a government agency that easily spends $760 million to get a shuttle into the air [source: Marks].

Of course, not converting comes with its own financial risks. Take NASA again. In 1999, the space agency lost its $125 million Mars Climate Orbiter probe when a unit mismatch caused a malfunction [source: Marks]. The mismatch occurred because its attitude-control system used imperial units, but its navigation software used SI units. As a result, the probe swung too close to the planet, overheated and then ceased to function properly. Now it's a million-dollar piece of space junk, thanks to America's lagging commitment to SI.

Many U.S. companies have paid attention to these cautionary tales. John Deere, Proctor & Gamble, Kodak, Ingersoll-Rand and numerous other businesses have converted all or some of their operations to use SI units. That means their overseas factories and supply chains use the same measuring system -- and the same parts -- as their American counterparts. That may seem minor, but the savings can be significant. Cost reductions come from two principal sources: increases in productivity resulting from the use of a decimal-based measurement system and the ability to compete more effectively in global markets.

Eventually, the U.S. will make the metric system compulsory for its citizens. When that time comes, it will change the look of road signs, gas pumps and food labels, but it won't affect some hallowed expressions. Why? Because a country kilometer and a 30-centimeter-long hotdog simply don't echo the American experience.