# International System of Units(SI)

The modernized metric system, what most people mean by “the metric system,” 1960 – present. The official symbol of the system, which is the way scientists usually refer to it, is “SI,” from the French “Système International d'Unités.”

SI consists of 7 base units and a number of derived units, some with special names. It is coherent.

Any one of 20 decimal multiplier or submultiplier prefixes, such as kilo-, milli- and so on, may be attached to the names of the base and derived units.

## Base units in SI

In the original metric system the key base units, the meter and kilogram, were defined by actual physical objects, called prototypes. The meter, for example, was the distance between two scratches on a certain bar. If something happens to a prototype, its system is in trouble. In the 19th century the British lost their prototypes in a fire in the House of Commons. Making certain that the newly-made replacements were a close match to the vanished originals took years. Depending on a prototype can be problematical even if it isn’t lost or destroyed; for some unknown reason the closely-guarded prototype of the kilogram appears to be losing mass.

Over the years improvements in technology have made it possible to redefine SI’s base units in terms of physical constants like the speed of light. From the information in the definition, anyone with the right tools can re-create the unit. A second advantage of the new definitions is that they make possible more precise measurements. (Here, by “more precise” we mean the measurement can have a greater number of meaningful decimal places after the decimal point.) Imagine determining the length of the meter from scratches on a bar. Even with a powerful microscope, it is very, very difficult, if not impossible, to determine where within the width of the scratch the meter ends. Trying to use a meter so defined to measure objects very much smaller than the scratch itself is lunacy. The improved definitions are one reason it has been necessary to add prefixes like zepto- and yotta-. More precise definitions make possible more precise measurements that sometimes reveal previously undiscovered phenomena. Now (2011) only the kilogram is still defined by an object, and that is expected to change in a year or two. At present, the second is the unit that can be measured to the largest number of significant decimal places.

The “Year adopted” column in the table shows those years in which the CGPM approved a new definition of the unit. For details, click on the names of the individual units.

by CGPM
Measured
Property
meter m 1889, 1927,
1960, 1983
length
kilogram kg 1889, 1960 mass
second s 1960, 1967 time
ampere A 1948 electric current
kelvin K 1967 thermodynamic
temperature
mole mol 1971 amount of
substance
candela cd 1948, 1967,
1979
luminous
intensity

## Derived units with special names

Car drivers often use the term “miles per hour.” “Miles per hour” is, in fact, a unit, but one defined simply by a mathematical relationship between the units mile and hour. Some such units are used so often that it is worthwhile to give them their own names. SI has a class of such units, ones completely defined in terms of base units, but with their own names. Examples include the

Unit Symbol Year
by CGPM
Properties measured
becquerel Bq 1975 activity
coulomb C 1960 electric charge, quantity of electricity
degree Celsius °C 1948 Celsius temperature
gray Gy 1975 absorbed dose, specific energy imparted, kerma, absorbed dose index
henry H 1960 inductance
hertz Hz 1960 frequency
joule J 1960 energy, work, quantity of heat
katal kat 1999 catalytic activity
lumen lm 1960 luminous flux
lux lx 1960 illuminance
newton N 1960 force
ohm Ω 1960 electric resistance
pascal Pa 1971 pressure, stress
siemens S 1971 electric conductance
sievert Sv 1980 dose equivalent, dose equivalent index
tesla T 1960 magnetic flux density
volt V 1960 electric potential, potential difference, electromotive force
watt W 1960 power, radiant flux
weber Wb 1960 magnetic flux

Courtesy NIST Special Publication 814.

## Supplementary units in SI

This class of units (but not the radian and steradian themselves!) was abolished in 1995.

## Prefixes in the International System of Units

Prefix Sym-
bol
Year
by CGPM
Meaning
(using American names of numbers)
Example
yotta- Y 1990 10²⁴ = 1 000 000 000 000 000 000 000 000 = 1 septillion
zetta- Z 1990 10²¹ = 1 000 000 000 000 000 000 000 = 1 sextillion
exa- E 1975 10¹⁸ = 1 000 000 000 000 000 000 = 1 quintillion
peta- P 1975 10¹⁵ = 1 000 000 000 000 000 = 1 quadrillion
tera- T 1960 10¹² = 1 000 000 000 000 = 1 trillion
giga- G 1948,
1960
10⁹ = 1 000 000 000 = 1 billion gigajoule
mega- M 1960 10⁶ = 1 000 000 = 1 million megawatt
kilo- k 1960 10³ = 1 000 = 1 thousand kilowatt
hecto- h 1960 10² = 100 = 1 hundred hectare
deka-* da 1960 10¹ = 10 = ten
10⁰ = 1 = one
deci- d 1960 10⁻¹ = .1 = a tenth of a decibel
centi- c 1960 10⁻² = .01 = a hundredth of a centimeter
milli- m 1960 10⁻³ = .001 = a thousandth of a milliliter
micro- μ 1960 10⁻⁶ = .000 001 = a millionth of a microfarad
nano- n 1960 10⁻⁹ = .000 000 001 = a billionth of a nanometer
pico- p 1960 10⁻¹² = .000 000 000 001 = a trillionth of a picofarad
femto- f 1964 10⁻¹⁵ = .000 000 000 000 001 = a quadrillionth of a femtosecond
atto- a 1964 10⁻¹⁸ = .000 000 000 000 000 001 = a quintillionth of a
zepto- z 1990 10⁻²¹ = .000 000 000 000 000 000 001 = a sextillionth of a
yocto- y 1990 10⁻²⁴ = .000 000 000 000 000 000 000 001 = a septillionth of a

* The spelling “deca-” is often used (but not in the United States).

Since the prefixes are all decimal multiples or submultiples, it is easy to convert a measurement in a unit with one prefix to one with another: just move the decimal point (or add and subtract powers of ten).

-somethings to -somethings,

move the decimal point __ places to the _____.

For your convenience, this little utility is also provided as a small separate page.

### Miscellaneous notes

The metric prefixes have been used for units whose magnitudes are based on powers of 2 not 10, for example kilobytes and megabytes. To avoid confusion, a separate set of prefixes has been defined for them. See prefixes for binary multiples.

A number of bogus prefixes have been described, mostly on the Internet. These hoaxes are being tracked by Gérard Michon.

We offer, just for fun, a silly quiz mostly based on the SI prefixes.

In combining the prefix with the unit name, the prefixes' final vowel is retained, except in the case of “hectare”. The American National Standard* also calls for the spellings “megohm” and “kilohm”, but the spelling “megaohm” is often encountered.

* American National Standard for Metric Practice.
ANSI/IEEE Standard 268-1992.
New York: IEEE, Oct. 1992.

## written usage in SI

The following recommendations are based on those of the United States' National Institute of Standards and Technology:

For a detailed, more rigorous treatment of written usage in SI, see Taylor, 1995 (a PDF file, 539KB).

### Capitalization

When written out, the names of units start with a lowercase letter, except at the beginning of a sentence or in a title. The only exception is “degree Celsius.”

Symbols for units are lowercase unless they come from a person's name, in which case the first letter of the symbol is capitalized. The exception, in the United States, is L for liter. See liter. Click here for a list of the symbols in the United States.

Symbols for numerical prefixes are lowercase, except for those representing multipliers of 106 or more: mega- (M), giga- (G), tera- (T), peta- (P), exa- (E), zetta- (Z), and yotta- (Y). When spelled out, all prefixes are lowercase.

### Plurals

When the names of units are written out, they should be made plural when the number to which they refer is greater than 1. Fractions are always singular. Symbols are never made plural.

correct incorrect
3 kilograms 3 kilogram
3 kg 3 kgs
1.46 kg
1.46 kilograms 1.46 kilogram
0.46 kilogram 0.46 kilograms

### Periods

A period or full stop is not used after a symbol, except at the end of a sentence.

### Numerals

In scientific and technical writing, all numbers expressing physical quantities should be represented by numerals.

In newspapers, it is usual to spell out the numbers from one to nine and use numerals for everything else.

In ordinary magazines and books, whole numbers from one through ninety-nine, and any of these followed by “hundred,” “thousand,” “million,” etc., are written out. If the unit is represented by an abbreviation or symbol, the associated number should be written as numerals.

### Decimal marker

In the United States, the dot is used as the decimal marker and is placed on the line. In the rest of the world, the comma is used as the decimal marker. (A centered dot was formerly used in Great Britain. e. g. “0·14”.)

### Grouping of digits

Digits should be separated by spaces into groups of 3, counting from the decimal marker. The use of a space, and not a comma, is necessary because in the United States, in nontechnical writing a period is used as the decimal marker and a comma is used to separate groups of three digits, while in other countries the comma is used as the decimal marker. Using a space avoids crosscultural confusion. No space should be put in a number that has only 4 digits.

correct incorrect
3.141 592 3.141592
176 000 176,000
1568 1 568

### Spaces

A prefix should not be separated from the name of the unit by a space or hyphen.

A space should be left between a symbol and the number to which it refers, with the exception of the symbols for degree, minute, and second of angles.

correct incorrect
3 kg 3kg
3° 27′ 59″ 3 ° 27 ′ 59 ″
5 nanoseconds 5 nano-seconds

### Mathematical operations

When the SI units are used with symbols for mathematical operations, the units should also be represented by symbols, not by their written-out names. This principle also applies to compound units like the newton meter.

correct incorrect
joules per mole joules/mole
J/mol
j·mol−1 joules·mol−1
N·m newton·meter
newton meter
newton-meter

For the official position on usage, see 9th CGPM, 1948, resolution 7.

## spoken usage in SI

Reading numbers aloud is simplified by the written usage rule that numbers are to be broken into groups of three digits, starting from the decimal point. Read aloud, starting at the left, each group of three digits consists of:

• the name of the first digit
• “hundred”
• the name of the number represented by the next two digits
• for numbers greater than 999, the name of the order of magnitude for that group of three, such as “thousand”, “million”, and so on.

For example, the number “123 456” is read aloud as “one hundred twenty-three thousand four hundred fifty-six.”

Such expressions as “fifteen hundred” and “a hundred twenty-three” should not be used.

### Decimal fractions

In numbers with a decimal fraction, the digits after the decimal point are to be spoken as a series of the names of the individual digits. For example, “123.456 millimeters” would be read aloud as “one hundred twenty-three point four five six.” It should not be read as “one hundred twenty-three and four hundred fifty-six thousandths.”

The decimal prefixes in SI greatly simplify, and hence clarify, spoken numbers. A number that contains many trailing zeros can usually be simplified by choosing a larger unit, for example, not “one million two hundred thirty thousand centimeters” but “one point two three kilometers.” Of course, this cannot be done when the trailing zeros indicate significant figures.

## History of SI

See metric system for the development  of the basic units prior to the Conference on the Meter in 1879, and spread of the metric system for country by country notes on adoption.

The Conference on the Meter led to the formation of permanent international bodies (the CGPM, BIPM, and CIPM) with a commitment to the meter and kilogram, and a mandate to standardize and improve the world's weights and measures. In the early years, the organizations' attention was focused mainly on units, rather than systems of units.

In the late 19th and early 20th century, most scientists used centimeter-gram-second systems, which proliferated because there were various ways of handling electromagnetic quantities. Alongside these systems were others, also ostensibly “metric,” which defined other electric and magnetic units for practical use. A subject which involved both electric and magnetic quantities required treatment in two and possibly three different systems of units. Furthermore, as new sciences developed they tended to extemporize new units, for example, the study of radioactivity led to nuclear physics and to curies, rads, rems, barns, and other units, all “metric.”

In 1901, the Italian physicist G. Giorgi proposed a meter-kilogram-second-electrical unit system, presenting it to the International Electrotechnical Commission (IEC) in 1904. Giorgi originally suggested that the electric unit be a unit of resistance, but later that was replaced by a unit of current, the ampere. The great advantage of Giorgi's proposal was that it used familiar units of mass, length, and time and, with rationalized units (and the right choice of a value for the permeability of free space), it preserved the sizes of the practical electric units, even though they were defined in absolute rather than material terms. It was an absolute practical system. In 1935, the IEC passed a resolution adopting the Giorgi system (but without deciding whether the units should be rationalized or not) and recommending it be named after him. But it was too late; almost everywhere it was referred to as the MKSA system.

Also in 1935, the Commission on Symbols, Units and Nomenclature of the International Union of Pure and Applied Physics (IUPAP) recommended basing a system on the meter and kilogram, and proposed the name newton for the unit of force based on the kilogram, second and meter. The IEC confirmed their 1935 decision in 1938 (still without deciding the rationalization issue), and the IUPAP repeated their recommendation in 1948.

In 1948 the Ninth CGPM, prodded by the French government and noting that the IUPAP had asked the CIPM “to adopt for international use a practical international system of units” and had recommended “the MKS system and one electric unit of the absolute practical system,” formally requested the CIPM “to make recommendations on the establishment of a practical system of units of measurement suitable for adoption by all signatories” (Resolution 6).

In July, 1950, the IEC's Technical Committee No. 24 on Electrical and Magnetic Magnitudes and Units chose the ampere to be the fourth, electric, unit and finally recommended rationalized units.

The 10th CGPM (1954) adopted as base units the meter, kilogram, second, ampere, degree Kelvin, and candela, thus adopting the Giorgi system. The remaining base unit, the mole, was added by the 14th CGPM in 1971 (Resolution 3).

The 11th CGPM (1960) named the new system “International System of Units;” adopted the “international abbreviation” SI and the prefixes from tera- through pico-; and added two supplementary units and 27 derived units, 13 of which had special names. So 1960 may be taken as the birth year of SI. Since then, one base unit, 11 derived units (including five with special names) and eight prefixes have been added; the second, meter and candela have been redefined; the liter and micron have been discarded, and the “degree Kelvin” changed to “Kelvin.”

The 21st CGPM (1999) adopted the “katal.”

## resources

Bureau International des Poids et Mesures.
The International System of Units (SI). 8th edition.
Organisation Intergouvernementale de la Convention du Mètre, 2006.

The authoritative (though the French version is more authoritative), comprehensive description of SI. The English version is available on the Web as a pdf file at
www.bipm.org/utils/en/pdf/si-brochure_8_en.pdf