What Is The Metric Scale?

If you live in the United States, you can be forgiven for having a less-than-clear understanding of the metric system of measurement, also known as the Système Internationale (SI). The United States is one of only three countries that still uses the Imperial System, and its adherence to British units is the only reason that system isn't obsolete.

The metric system, which you could characterize as the meters scale, originated in France, whose government adopted it in 1795. Although it took almost 200 years, the British eventually did the same, followed by virtually every other country, including the two closest neighbors and most important trading partners of the United States, Canada and Mexico.

Amazingly, some of the British units currently in use in the U.S. are not even the ones adopted by the British government in 1824, but obsolete ones that the British discarded at that time.

Scientists, merchants and governments prefer the metric system for good reasons. For example, it has only seven basic units, from which all others are derived. It uses increments of 10 rather than 12, and the fundamental unit, the meter, is based on physical standard that can be verified anywhere.

The father of the metric system was a church vicar who lived in Lyons, France from 1618 to 1694. Gabriel Mouton had a doctorate in theology, but he was also an active scientist and astronomer. His proposal of a measurement system based on decimal fractions was supported by luminaries such as physicist Christiaan Huygens and mathematician Gottfried Wilhelm von Leibniz, and it was studied by the Royal Society. It took a hundred years, however, for scientists to refine the system and persuade the government of France to adopt it.

The fundamental unit that Mouton proposed was the ​milliare​, which was defined to be one second of longitude on the Earth's surface at the equator. This was subdivided by division by 10 into such sub-units as the ​centuria, decuria​ and ​virga.​ Although none of these units ended up being used, scientists took to heart Mouton's basic idea of basing the measurement system on a geophysical standard.

When the French government first adopted the metric system, the meter became the base unit. The word comes from the Greek word ​metron​, which means "to measure," and it was originally defined as one ten-millionth of the distance between the equator and the North Pole along a meridian passing through Paris.

The definition has changed over the years, and today, it's defined to be the distance light travels through a vacuum in exactly 1/299792458 seconds. This definition is based on the speed of light, which is exactly 299,792,458 meters per second.

The metric system records all length measurements in meters, fractions of meters or multiples of meters, thus avoiding the need for multiple units, such as inches, feet and miles. In the SI system, every increment of 1,000 that moves the decimal of a measurement three places to the right or left, has a prefix. In addition, there are prefixes for one tenth and one hundredth, as well as for 10 and 100.

If you're measuring the distances between cities, you don't have express them in thousands of meters. You can use kilometers. Similarly, scientists measuring atomic distances don't have to express them in billionths of a meter. They can use nanometers. The list of prefixes includes the following:

•10¹⁸ meters: exameter (Em)             10 ⁻¹⁸ meters: attometer (am)
•10¹⁵ meters: petameter (Pm)            10 ⁻¹⁵ meters: femtometer (fm)
•10¹² meters: terameter (Tm)            10 ⁻¹² meters: picometer (pm)
•10⁹   meters: gigameter (Gm)           10 ⁻⁹   meters: nanometer (nm)
•10⁶   meters: megameter (Mm)        10 ⁻⁶   meters: micrometer (µm)
•10³   meters: kilometer (km)             10 ⁻³   meters: millimeter (mm)
•10²   meters: hectometer (hm)         10 ⁻²   meters: centimeter (cm)
•10¹   meters: dekameter (dam)        10 ⁻¹   meters: decimeter (dm)

These prefixes are used throughout the measurement system. They apply to units of mass (grams), time (seconds), electrical current (amperes), luminosity (candela), temperature (kelvins) and amount of matter (moles).

When you measure length, you're measuring in one dimension. Extend your measurements to two dimension to determine area, and the units will be square meters. Add a third dimension and you're measuring volume in cubic meters. You could not do this simple progression when using British units, because the British system has different units for all three quantities, and even has more than one unit for length.

Square meters aren't particularly useful units for measuring small areas, such as the surface area of a solar cell. For small areas, it's customary to convert square meters to square centimeters. For large areas, square kilometers are more useful. The conversion factors are 1 square meter = 10⁴ square centimeters = 10 ⁻⁶ square kilometers.

When measuring volume in the SI system, liters are more useful units than cubic meters, mostly because a cubic meter is too large to carry. A liter is defined as 1,000 cubic centimeters (which are also called milliliters), which makes it equal to 0.001 cubic meters.

Besides the meter, the metric system defines only six other units, and all other units are derived from these. The other units may have names, such a newton (force) or watt (power), but these derived units can always be expressed in terms of the fundamental ones. The six fundamental units are:

•​The second (s)​

–

This is the unit for time. It used to be based on the length of a day, but now that we know that a day is actually less than 24 hours, a more precise definition is needed. The official definition of a second is now based on the vibrations of the cesium-133 atom.

•​The kilogram (kg)​

–

The unit for mass in the system that uses the meter measurement is the kilogram. Because this is 1,000 grams, it doesn't appear to be a fundamental unit, but the gram is useful only when measuring length in centimeters. The system that measures in meters, kilograms and seconds is called the MKS system. The one that measures in centimeters, grams and seconds is the CGS system.

•​The kelvin (K)​

–

Contrary to what you might expect, temperature is not measured on the Celsius scale in the SI system, although countries that use the metric system do tend to measure temperature in degrees Celsius. They do so because the conversion is so simple. The degrees are the same size, and a temperature of 0 degrees Celsius corresponds to 273.15 Kelvins. To convert Celsius to Kelvin, just add 273.15. 

•​The ampere (A)​

–

The unit of electrical current defines the amount of electrical charge passing a point in a conductor in one second. It's defined as one coulomb, which is 6.241 × 10¹⁸ electrons, per second. 

•​The mole (mol)​

– This is a measure of the amount number of atoms in a sample of any particular substance. One mole is the number of atoms in 12 grams (0.012 kg) of a sample of carbon-12. 

•​The candela (cd)​

–

This unit dates back to the days when candles provided the only artificial illumination. It was the amount of illumination provided in one steradian by a single candle, but the modern definition is a bit more complex. One candela is defined as the luminous intensity of a given source emitting monochromatic light at a frequency of 5.4 x 10¹⁴ Hertz and having a radiant intensity of 1/683 watts per steradian. A steradian is a circular cross section of a sphere that has an area equal to the square of the radius of the sphere. 

The metric system has 22 named units which are derived from the seven fundamental ones. Most, but not all, of these are named after prominent scientists who made significant contributions to the field in which the units are relevant. For example, the unit for force is named after Sir Isaac Newton, who laid the groundwork for mechanics, the study of bodies at rest and in motion. Another example is the unit for electrical capacitance, the farad, which is named after Micheal Faraday, a pioneer in the study of electromagnetism.

The derived units are as follows:

•Force                                 ​newton (N)​           m kg

s ⁻²
•Pressure/stress            ​pascal (Pa)​            m ⁻¹ kg  s ⁻²
•Energy/work                ​joule (J)​                  m² kg s ⁻²
•Power/radiant flux         ​watt (W)​                 m² kg s ⁻³
•Electric charge                 ​coulomb (C)​          s A
•Electric potential             ​volt (V)​                    m² kg s ⁻³ A ⁻¹
•Capacitance                       ​farad (F)​                 m ⁻²kg ⁻¹s⁴A²
•Electric resistance           ​ohm (Ω)​                 m²kg s ⁻³A ⁻²
•Electric conductance      ​siemens (S)​            m ⁻² kg ⁻¹ s³ A²
•Magnetic flux                  ​weber (Wb)​            m² kg s ⁻²A ⁻¹
•Magnetic flux density     ​tesla (T)​                   kg s ⁻²A-¹
•Inductance                      ​henry (H)​               m²kg s ⁻²A ⁻²
•Temperature                    ​Celsius (°C)​             K

− 273.15
•Luminous flux                  ​lumen (lm)​             m²m ⁻²cd = cd
•Illuminance (lx)                ​lux (lx)​                     m²m ⁻⁴cd = m ⁻²cd
•Radioactive activity         ​becquerel (Bq)​     s ⁻¹
•Absorbed dose                  ​gray (Gy)​                 m²s ⁻²
•Dose equivalent                ​sievert (Sv)​             m²s ⁻²
•Catalytic activity              ​katal (kat)​              s ⁻¹ mol
•Plane angle                         ​radian (rad)​         m m ⁻¹ = 1
•Solid angle                        ​steradian (sr)​       m²m ⁻² = 1

Compared to the English system, which is a hodgepodge of units created in the English marketplace, the metric system is elegant, accurate and based on universal physical standards.

It's something of a mystery why the English system is still in use in the United States, especially given that Congress passed the Metric Conversion Act in 1975 to coordinate the increasing use of the metric system in that country. A Metric Board was established, and government agencies were required to use the metric system. The problem is that conversion was voluntary for the general public, and most people simply ignored the Board, which disbanded in 1982.

One might say that the only reason for the continued use of the English system in the United States is force of habit. It's a truism that old habits die hard, but given the elegance of the metric system and the fact that the entire world now uses it, it's unlikely that anyone using the English system will continue to do so for much longer.

Change may seem daunting, but the metric system was designed by scientists to be easy to use, and that's a benefit that outweighs stubborn adherence to tradition.