﻿ The International System of Units

## The International System of Units (SI)

All systems of weights and measures, metric and non-metric, are linked through a network of international agreements supporting the International System of Units. The International System is called the SI, using the first two initials of its French name Système International d'Unités. The key agreement is the Treaty of the Meter (Convention du Mètre), signed in Paris on May 20, 1875. 48 nations have now signed this treaty, including all the major industrialized countries. The United States is a charter member of this metric club, having signed the original document back in 1875.
 The SI is maintained by a small agency in Paris, the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures), and it is updated every few years by an international conference, the General Conference on Weights and Measures (CGPM, for Conférence Générale des Poids et Mesures), attended by representatives of all the industrial countries and international scientific and engineering organizations. The first CGPM met in 1889. The 25th CGPM met in 2014 and the 26th is scheduled for November 2018. As BIPM states on its web site, "The SI is not static but evolves to match the world's increasingly demanding requirements for measurement." At the heart of the SI is a concept called coherence. In a coherent unit system, a limited number of units are identified as base units, and all other units are created by combining the base units algebraically (by multiplication and division). For example, with the meter and the second as the base units of distance and time, respectively, the system's unit of velocity will automatically be meter/second. In the International System the base units are consistent with the part of the metric system called the MKS system. There are only seven SI base units: the meter for distance, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for intensity of light. SI logo copyright BIPM

The other SI units, called SI derived units, are then defined algebraically in terms of these base units. For example, the SI unit of force, the newton, is defined to be the force that accelerates a mass of one kilogram at the rate of one meter per second per second. This means the newton is equal to one kilogram meter per second squared, so the algebraic relationship is N = kg·m·s-2. Currently there are 22 SI derived units that have special names and symbols. They include:

• the newton for force and the pascal for pressure;
• the joule for energy and the watt for power;
• the degree Celsius for everyday measurement of temperature;
• units for measurement of electricity: the coulomb (charge), volt (potential), farad (capacitance), ohm (resistance), and siemens (conductance);
• units for measurement of magnetism: the weber (flux), tesla (flux density), and henry (inductance);
• the lumen for flux of light and the lux for illuminance;
• the hertz for frequency of regular events and the becquerel for rates of radioactivity and other random events;
• the gray and sievert for radiation dose; and
• the katal, a unit of catalytic activity used in biochemistry.

Future meetings of the CGPM may make additions to this list; the katal was added by the 21st CGPM in 1999.

In addition to the 29 base and derived units, the SI permits the use of certain additional units, including:

The SI currently accepts the use of certain other metric and non-metric units traditional in various fields. These units are supposed to be "defined in relation to the SI in every document in which they are used," and "their use is not encouraged." These barely-tolerated units could be prohibited by future meetings of the CGPM. They include:

• the nautical mile and knot, units traditionally used at sea and in meteorology;
• the are and hectare, common metric units of area;
• the bar, a pressure unit, and its commonly-used multiples such as the millibar in meteorology and the kilobar in engineering;
• the angstrom and the barn, units used in physics and astronomy.
 The SI does not allow use of any units other than those listed above and their multiples. In particular, it does not allow use of any of the English traditional units (the horsepower, for example), nor does it allow the use of any of the algebraically-derived units of the former CGS system, such as the erg, gauss, poise, stokes, or gal. In addition, the SI does not allow use of other traditional scientific and engineering units, such as the torr, curie, calorie, or rem. Certain scientific fields have defined units more or less compatible with the SI, but not part of the SI. The use of the jansky in astronomy is a good example. There is always the chance that future meetings of the CGPM could add these units to the SI, but for the present they are not approved. The National Institute of Standards and Technology establishes measurement standards and presides over the implementation of the SI in the U.S.

For multiples of approved units, the SI includes a list of prefixes. This list has been extended several times, most recently by the 19th CGPM in 1991. Prefixes now range from yotta- at 1024 (one septillion) to yocto- at 10-24 (one septillionth). The SI does not allow these prefixes to be used for binary multiples, such as the use of "kilobit" to mean 1024 bits instead of 1000. For binary multiples a new list of special prefixes has been established by the International Electrotechnical Commission.

Each SI unit is represented by a symbol, not an abbreviation. These symbols are the same in every language of the world. However, the names of the units themselves vary in spelling according to national conventions. Therefore, it is correct for Americans to write meter and Germans to write Meter, and it is also correct for the British to write metre, Italians to write metro, and Poles to write metr. See Spelling of Metric Units for additional comments.