Metric system
The metric system is an international system of measurement that was first introduced in France in the 1790s, and has since undergone revision. In the mid-20th century, it was standardized by an international standards body, and became officially known by the French abbreviation SI (System International), or the International System of Units.
The metric system is built around the basic units of the meter, liter, gram, Kelvin (for temperature) and a few other core units. The system is based on several core principles. The units are based on natural, physical, and scientific principles, that is, they are defined precisely and scientifically based on scientific phenomena in the natural world that can always be measured consistently. This stands in contrast to older systems like the imperial system used in the US, consisting of units like inches, miles, and gallons, which are arbitrary and not defined by natural principles. Another principle of the metric system is that the units are related to each other consistently, and they are coherent, that is, based on natural orders of magnitude, or factors of ten (e.g., 1 meter = 100 centimeters, 1 centimeter = 10 millimeters), and this is expressed with regular prefixes (e.g., centi-, milli-).
This system serves as the official system of weights and measures internationally, except in Myanmar, Liberia, and the United States.
Contents
1 Base units and derived units
The following are the base units of the metric system and their formal scientific definitions.^{[1]}
Unit name | Symbol | Dimension | Definition |
---|---|---|---|
second | s | time (T) | The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. |
meter | m | length (L) | The distance travelled by light in a vacuum in 1/299792458 seconds. |
kilogram | kg | mass (M) | The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10^{−34} J⋅s (J = kg⋅m2⋅s^{−2}), given the definitions of the metre and the second. |
ampere | A | electric current (I) | The flow of exactly 1/1.602176634×10^{−19} times the elementary charge e per second, equalling approximately 6.2415090744×10^{18} elementary charges per second. |
kelvin | K | thermodynamic temperature (Θ) | The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10^{−23} J⋅K−1, (J = kg⋅m2⋅s^{−2}), given the definition of the kilogram, the meter, and the second. |
mole | mol | amount of substance (N)) | The amount of substance of exactly 6.02214076×10^{23} elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol^{−1}. |
candela | cd | luminous intensity (J) | The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×10^{14} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. |
1.1 Derived units
The following units are commonly used derived units, often formed from combinations of base units.
Name | Symbol | Quantity | In SI base units | In other SI units |
---|---|---|---|---|
radian* | rad | plane angle | m/m | * |
steradian* | sr | solid angle | m^{2}/m^{2} | * |
hertz | Hz | frequency | s^{−1} | |
newton | N | force, weight | kg⋅m⋅s^{−2} | |
pascal | Pa | stress | kg⋅m^{−1}⋅s^{−2} | N/m^{2} |
joule | J | work, heat | kg⋅m^{2}⋅s^{−2} | N⋅m = Pa⋅m^{3} |
watt | W | power, radiant flux | kg⋅m^{2}⋅s^{−3} | J/s |
coulomb | C | electric charge | s⋅A | |
volt | V | emf | kg⋅m^{2}⋅s^{−3}⋅A^{−1} | W/A = J/C |
farad | F | capacitance | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} | C/V = C^{2}/J |
ohm | Ω | resistance, electrical impedance, (electronics) reactance | kg⋅m^{2}⋅s^{−3}⋅A^{−2} | V/A = J⋅s/C^{2} |
siemens | S | electrical conductance | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} | Ω^{−1} |
weber | Wb | magnetic flux | kg⋅m^{2}⋅s^{−2}⋅A^{−1} | V⋅s |
tesla | T | magnetic flux density | kg⋅s^{−2}⋅A^{−1} | Wb/m^{2} |
henry | H | inductance | kg⋅m^{2}⋅s^{−2}⋅A^{−2} | Wb/A |
degree Celsius | °C or ℃ | temperature relative to 273.15 K | K | |
lumen | lm | luminous flux | cd⋅sr | cd⋅sr |
lux | lx | illuminance | cd⋅sr⋅m^{−2} | lm/m^{2} |
becquerel | Bq | activity referred to a radionuclide (decays per unit time) | s^{−1} | |
gray | Gy | absorbed dose (of ionising radiation) | m^{2}⋅s^{−2} | J/kg |
sievert | Sv | equivalent dose (of ionising radiation) | m^{2}⋅s^{−2} | J/kg |
katal | kat | catalytic activity | mol⋅s^{−1} | |
*Note: The radian and steradian are defined as dimensionless derived units. |
1.2 Unofficial SI units
A number of units are accepted and commonly used in science and other fields, though these are not officially part of the SI system. However, these units are defined according to official SI units.
Quantity | Name | Symbol | Value in SI units |
---|---|---|---|
time | minute | min | 1 min = 60 s |
hour | h | 1 h = 60 min = 3600 s | |
day | d | 1 d = 24 h = 86400 s | |
length | astronomical unit | au | 1 au = 149597870700 m (mean distance of Earth from Sun) |
lane and phase angle |
degree | ° | 1° = π/180 rad |
arcminute | ′ | 1′ = 1/60 ° = π/10800 rad | |
arcsecond | ″ | 1″ = 1/60 ′ = π/648000 rad | |
area | hectare | ha | 1 ha = 1 hm^{2} = 10^{4} m^{2} |
volume | litre | l, L | 1 l = 1 L = 1 dm^{3} = 10^{3} cm^{3} = 10^{−3} m^{3} |
mass | tonne (metric ton) | t | 1 t = 1 Mg = 10^{3} kg |
dalton | Da | 1 Da = 1.660539040 x 10^{-27} kg | |
energy | electronvolt | eV | 1 eV = 1.602176634 x 10^{-19} J |
logarithmic ratio quantities |
neper | Np | For these units, the type of quantity should be specified, with appropriate reference values. |
bel | B | ||
decibel | dB |
2 Prefixes
The following are official SI prefixes that are attached to SI units, along with several proposed new prefixes.
Prefix | Base 10 | English equivalent | ||
---|---|---|---|---|
Name | Symbol | Short scale | Long scale (UK) | |
quetta* | Q* | 10^{30} | nonillion | quintillion |
ronna* | R* | 10^{27} | octillion | quadrilliard |
yotta | Y | 10^{24} | septillion | quadrillion |
zetta | Z | 10^{21} | sextillion | trilliard |
exa | E | 10^{18} | quintillion | trillion |
peta | P | 10^{15} | quadrillion | billiard |
tera | T | 10^{12} | trillion | billion |
giga | G | 10^{9} | billion | milliard |
mega | M | 10^{6} | million | |
kilo | k | 10^{3} | thousand | |
hecto | h | 10^{2} | hundred | |
deca | da | 10^{1} | ten | |
10^{0} | one | |||
deci | d | 10^{−1} | tenth | |
centi | c | 10^{−2} | hundredth | |
milli | m | 10^{−3} | thousandth | |
micro | μ | 10^{−6} | millionth | |
nano | n | 10^{−9} | billionth | milliardth |
pico | p | 10^{−12} | trillionth | billionth |
femto | f | 10^{−15} | quadrillionth | billiardth |
atto | a | 10^{−18} | quintillionth | trillionth |
zepto | z | 10^{−21} | sextillionth | trilliardth |
yocto | y | 10^{−24} | septillionth | quadrillionth |
ronto* | r* | 10^{−27} | octillionth | quadrilliard |
quecto* | q* | 10^{−30} | nonillionth | quintillionth |
The prefixes quetta, ronna, quecto and ronto have been proposed and are under consideration as of 2022^{[2]}. For newer prefixes beyond sextillion and sextillionth, the names large scale and fractional orders of magnitude are deliberately named to be similar to each other, e.g., yotto (septillion) and yocto (septillionth)^{[3]}. The prefixes yotta, yocto, zetta, and zepto are the most recently added official prefixes, which were added in 1991. The prefix deca is nowadays less commonly used. One might see a few older prefixes, namely, myria for 10,000, but this never became popular, and was removed from the SI system in 1960.
The long scale numerals are those traditionally used in the UK and British Commonwealth nations, but are increasingly less common, especially in math, science and engineering, where the North American short scale is more common. In the long scale, 10^{9} is one million, while 10^{12} is one milliard, corresponding to one billion in the short scale; thus, 10^{15} is one billion in the long scale and one trillion in the short scale, and 10^{18} is one billiard in the long scale, and one quadrillion in the short scale, and so on.
3 See also
3.1 References
- ↑ The information in these tables is compiled from various Wikipedia pages for your convenience.
- ↑ Draft Resolutions of the General Conference for Weights and Measures, 27th meeting (15–18 November 2022), page 22. Retrieved 2022-02-16
- ↑ Brown, R. J. (2019), "On the nature of SI prefixes and the requirements for extending the available range", Measurement, 137: 339–343, Bibcode:2019Meas..137..339B, doi:10.1016/j.measurement.2019.01.059, S2CID 117531445