(Definitions of the SI base units, SI derived units, Other not SI units)

The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. The SI was established in 1960 by the 11th General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures). The CGPM is the international authority that ensures wide dissemination of the SI and modifies the SI as necessary to reflect the latest advances in science and technology.

**Definitions of the SI base units**

- The SI is founded on seven

*SI base units*for seven

*base quantities*assumed to be mutually independent

Base quantity | Name | Symbol | Description |
---|---|---|---|

length | meter | m | The meter is the length of the path travelled by light in
vacuum during a time interval of ^{1}⁄_{299}
792 458 |

mass | kilogram | kg | The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram - Pavillon de Breteuil (Sèvres). |

time | second | s | The second is the duration of |

electric current | ampere | A | The ampere is that constant current which, if maintained in two
straight parallel conductors of infinite length, of negligible
circular cross-section, and placed 1 meter apart in vacuum, would
produce between these conductors a force equal to ^{-7} newton |

thermodynamic temperature | kelvin | K | The kelvin, unit of thermodynamic temperature, is the fraction
^{1}⁄_{273}.16 of the thermodynamic temperature of
the triple point of water. |

amount of substance | mole | mol | 1. The mole is the amount of substance of a system which
contains as many elementary entities as there are atoms in 0.012
kilogram of carbon 12; its symbol is “mol.” 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. |

luminous intensity | candela | cd | The candela is the luminous intensity, in a given direction, of
a source that emits monochromatic radiation of frequency ^{12} hertz^{1}⁄_{683} watt per
steradian. |

**SI derived units**

- Other quantities, called

*derived quantities*, are defined in terms of the seven base quantities via a system of quantity equations. The

*SI derived units*for these derived quantities are obtained from these equations and the seven SI base units.

For ease of understanding and convenience, 21 SI derived units have been given special names and symbols, as shown in Table. The special names and symbols of the 21 SI derived units with special names and symbols given in Table may themselves be included in the names and symbols of other SI derived units.

Derived quantity |
Name |
Symbol |
Expressionin terms of other SI units |
Expressionin terms of SI base units |
---|---|---|---|---|

plane angle | radian ^{(a)} |
rad | - | m·m^{-1} = 1 ^{(b)} |

solid angle | steradian ^{(a)} |
sr ^{©} |
- | m^{2}·m^{-2} = 1
^{(b)} |

frequency | hertz | Hz | - | s^{-1} |

force | newton | N | - | m·kg·s^{-2} |

pressure, stress | pascal | Pa | N/m^{2} |
m^{-1}·kg·s^{-2} |

energy, work, quantity of heat | joule | J | N·m | m^{2}·kg·s^{-2} |

power, radiant flux | watt | W | J/s | m^{2}·kg·s^{-3} |

electric charge, quantity of electricity | coulomb | C | - | s·A |

electric potential difference, electromotive force |
volt | V | W/A |
m^{2}·kg·s^{-3}·A^{-1} |

capacitance | farad | F | C/V |
m^{-2}·kg^{-1}·s^{4}·A^{2} |

electric resistance | ohm | Ω | V/A |
m^{2}·kg·s^{-3}·A^{-2} |

electric conductance | siemens | S | A/V | m^{-2}·kg^{-1}·s^{3}·A^{2} |

magnetic flux | weber | Wb | V·s | m^{2}·kg·s^{-2}·A^{-1} |

magnetic flux density | tesla | T | Wb/m^{2} |
kg·s^{-2}·A^{-1} |

inductance | henry | H | Wb/A | m^{2}·kg·s^{-2}·A^{-2} |

Celsius temperature | degree Celsius ^{(e)} |
°C | - | K |

luminous flux | lumen | lm | cd·sr ^{©} |
m^{2}·m^{-2}·cd = cd |

illuminance | lux | lx | lm/m^{2} |
m^{2}·m^{-4}·cd =
m^{-2}·cd |

activity (of a radionuclide) | becquerel | Bq | - | s^{-1} |

absorbed dose, specific energy (imparted), kerma | gray | Gy | J/kg | m^{2}·s^{-2} |

dose equivalent ^{(d)} |
sievert | Sv | J/kg | m^{2}·s^{-2} |

^{(a)} The radian and
steradian may be used advantageously in expressions for derived
units to distinguish between quantities of a different nature but
of the same dimension.Radian is the measure of a central plane angle that subtends
an arc that is the same length as the radius of the circle. Equal
to 57.2958°.Steradian is the measure of a central solid angle that
subtends a surface that is the same area as the square radius of
the sphere.^{(b)} In practice, the symbols rad and sr are used where
appropriate, but the derived unit “1” is generally omitted.^{©} In photometry, the unit name steradian and the unit
symbol sr are usually retained in expressions for derived
units.^{(d)} Other quantities expressed in sieverts are ambient
dose equivalent, directional dose equivalent, personal dose
equivalent, and organ equivalent dose.^{(e)} The unit of Celsius temperature is the degree
Celsius, symbol °C. The numerical value of a Celsius temperature
t expressed in degrees Celsius is given by t/°C = T/K
- 273.15. |

**Other not SI units**

Bit, nibble, byte, word, Decibel (dB), Neper (Np)

**Bit:**

A **bit** is the smallest unit of data in a computer. A bit has
a single binary value, either 0 or 1. Although computers usually
provide instructions that can test and manipulate bits, they
generally are designed to store data and execute instructions in
bit multiples called **bytes**. In most computer systems, there
are eight bits in a byte. The value of a bit is usually stored as
either above or below a designated level of electrical charge in a
single capacitor within a memory device. Half a byte (four bits) is
called a **nibble**. In some systems, the term **octet** is
used for an eight-bit unit instead of byte. In many systems, four
eight-bit bytes or octets form a 32-bit word. In such systems,
instruction lengths are sometimes expressed as **full-word** (32
bits in length) or **half-word** (16 bits in length).

**Decibel (dB):**

One tenth of the common logarithm of the ratio of relative powers,
equal to 0.1 B (bel).

*Note 1:* The decibel is the conventional relative power
ratio, rather than the bel, for expressing relative powers because
the decibel is smaller and therefore more convenient than the bel.
The ratio in dB is given by

*dB* = 10
log_{10}(*P*_{1}/*P*_{2})

where *P*_{1} and *P*_{2} are the
actual powers. Power ratios may be expressed in terms of voltage
and impedance, *E* and *Z* , or current and impedance,
*I* and *Z* , since

*P* = *I*^{2}Z =
*E*^{2}/*Z*

Thus dB is also given by

*dB* = 10
log_{10}[(*E*_{1}^{2}/*Z*_{1})/(*E*_{2}^{2}/*Z*_{2})]
= 10
log_{10}[(*I*_{1}^{2}*Z*_{1})/(*I*_{2}^{2}*Z*_{2})]

If *Z*_{1} = *Z*_{2}, these become

*dB* = 20
log_{10}(*E*_{1}/*E*_{2}) = 20
log_{10}(*I*_{1}/*I*_{2})

Note 2: The dB is used rather than arithmetic ratios or
percentages because when circuits are connected in tandem,
expressions of power level, in dB, may be arithmetically added and
subtracted. For example, in an optical link, if a known amount of
optical power, in dBm, is launched into a fiber, and the losses, in
dB, of each component (*e.g.* , connectors, splices, and
lengths of fiber) are known, the overall link loss may be quickly
calculated with simple addition and subtraction.

**Neper (Np):**

A unit used to express ratios, such as gain, loss, and relative
values.

*Note 1:* The neper is analogous to the decibel, except that
the Naperian base 2.718281828… is used in computing the ratio in
nepers.

*Note 2:* The value in nepers, *Np* , is given by
*Np* = ln(*x* _{1}/*x* _{2}), where
*x* _{1} and *x* _{2} are the values of
interest, and ln is the natural logarithm, *i.e.,* logarithm
to the base e.

*Note 3:* One neper (Np) = 8.686 dB, where 8.686 = 20/(ln
10).

*Note 4:* The neper is often used to express voltage and
current ratios, whereas the decibel is usually used to express
power ratios.

*Note 5:* Like the dB, the Np is a dimensionless unit.

*Note 6:* The ITU recognizes both units.