Definitions of the SI base and derived units

GUIDE: Definitions of the SI base and derived units

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(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 quantityNameSymbolDescription
lengthmetermThe meter is the length of the path travelled by light in vacuum during a time interval of 1299 792 458 of a second.
masskilogramkgThe kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram - Pavillon de Breteuil (Sèvres).
timesecondsThe second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
electric currentampereAThe 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 2 x 10-7 newton per meter of length.
thermodynamic temperaturekelvinKThe kelvin, unit of thermodynamic temperature, is the fraction 1273.16 of the thermodynamic temperature of the triple point of water.
amount of substancemolemol1. 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 intensitycandelacdThe candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1683 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 quantityName SymbolExpression
in terms of
other SI units
in terms of
SI base units
plane angleradian (a) rad  -m·m-1 = 1 (b)
solid anglesteradian (a)sr ©  -m2·m-2 = 1 (b)
frequencyhertzHz  -s-1
forcenewtonN  -m·kg·s-2
pressure, stresspascalPaN/m2 m-1·kg·s-2
energy, work, quantity of heat  jouleJN·m m2·kg·s-2
power, radiant fluxwattWJ/s m2·kg·s-3
electric charge, quantity of electricitycoulomb C  -s·A
electric potential difference,
electromotive force
volt VW/A m2·kg·s-3·A-1
capacitancefaradFC/V m-2·kg-1·s4·A2
electric resistanceohmΩV/A m2·kg·s-3·A-2
electric conductancesiemens SA/V m-2·kg-1·s3·A2
magnetic fluxweberWbV·s m2·kg·s-2·A-1
magnetic flux densityteslaTWb/m2 kg·s-2·A-1
inductancehenryHWb/A m2·kg·s-2·A-2
Celsius temperaturedegree Celsius (e) °C  -K
luminous fluxlumenlmcd·sr © m2·m-2·cd = cd
illuminance luxlxlm/m2 m2·m-4·cd = m-2·cd
activity (of a radionuclide)becquerelBq  -s-1
absorbed dose, specific energy (imparted), kermagrayGyJ/kgm2·s-2
dose equivalent (d) sievertSvJ/kgm2·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)

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 log10(P1/P2)

where P1 and P2 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 = I2Z = E2/Z

Thus dB is also given by

dB = 10 log10[(E12/Z1)/(E22/Z2)] = 10 log10[(I12Z1)/(I22Z2)]

If Z1 = Z2, these become

dB = 20 log10(E1/E2) = 20 log10(I1/I2)

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.


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