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The International System of Units, the SI, is the system of units in which
Here are basic data associated with the International System of Units, commonly known as the "metric system". The abbreviation "SI" is from the French expression Système Internationale [d'Unités].
The chart gives the originally intended idea behind the measurement unit and the current official definition which is intended to reflect the same value while eliminating various ambiguities in the original by fixing the value of various physical constants to exact values (previously the measurements were fixed to standard prototypes and the physical constants were not precisely known, now it is the other way around, and the constants are fixed, yet the precise magnitude of the measurements are the unknown factor.)
| SI base units | ||||||
|---|---|---|---|---|---|---|
| quantity | name | symbol | original basis | pre-2019 definition | current definition | conversions |
| length | metre | m | One ten thousandth (1/10 000) of the distance from the North Pole to the equator along a meridian line running through Paris, France. | length of the path travelled by light in vacuum during a time interval of 1/299 792 458 second. | defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m⋅s⁻¹, where the second is defined in terms of the cæsium frequency ΔνCs. | 1 m ≅ 3 feet 3⅜ inches 1 foot = 0.3048 m 1 mile = 1609.344 m |
| mass | kilogram | kg | Mass of one litre of water, one litre being a cubic decimetre or one thousandth (1/1 000) of a cubic metre. | mass of a particular international prototype kept in France | defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15×10⁻³⁴ when expressed in the unit J⋅s, which is equal to kg⋅m²⋅s⁻¹, where the metre and the second are defined in terms of c and ΔνCs. |
1 kg ≅ 2 pounds 3¼ ounces 1 pound = 0.453 592 37 kg 1 stone = 6.350 293 18 kg 1 grain ≅ 64.8 mg |
| time | second | s | 1/60 of 1/60 of 1/24 of a day on Earth, that is a second-level 1/60 division of an hour | 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 cæsium-133 atom. | defined by taking the fixed numerical value of the cæsium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cæsium-133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹. | 1 s ≅ 1 (traditional) second |
| electric current | ampere | A | the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 metre apart in vacuum would produce between these conductors a force equal to 2 × 10⁻⁷ newtons per square metre of length. | the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 metre apart in vacuum would produce between these conductors a force equal to 2 × 10⁻⁷ newton per square metre of length. | defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634×10⁻¹⁹ when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of ΔνCs. | 1 A = 1 amp |
| thermodynamic temperature |
kelvin | K | An absolute temperature corresponding to the centigrade temperature where 0° centigrade is the freezing point of water at normal atmospheric pressure on earth, and 100° centigrade is the boiling point of water at normal atmospheric pressure on earth. | the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. | defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10⁻²³ J⋅K⁻¹, where the kilogram, metre and second are defined in terms of h, c and ΔνCs. |
0 K = -273.15°C = -459⅔°F 273.15 K = 0°C = 32°F 293.15 K = 20°C = 68°F 310.15 K = 37°C = 98.6°F 373.15 K = 100°C = 212°F |
| amount of substance | mole | mol | the amount of substance of a system which contains as many elementary entities as there are atoms in 16 grams of oxygen-16. | the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. | One mole contains exactly 6.022 140 76×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol⁻¹ and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. | 1 mol = 50,184,506,333,333,333,333,333⅓ dozen 1 dozen ≅ 20 ymol 1 gross ≅ 239 ymol |
| luminous intensity | candela | cd | intensity of light given off by a candle | the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. | defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×10¹² Hz, Kcd, to be 683 when expressed in the unit lm⋅W⁻¹, which is equal to cd⋅sr⋅W⁻¹, or cd⋅sr⋅kg⁻¹⋅m⁻²⋅s³, where the kilogram, metre and second are defined in terms of h, c and ΔνCs. | 1 cd ≅ 1 candlepower |
| SI derived units | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| quantity | name | symbol | definition | conversions | ||||||||||||||||||||||||
| plane angle | radian | rad | the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius | 1 rad = 1/(2⋅π) circle = (180/π)° ≅ 57°17′45″ 1° ≅ 0.01745 rad | ||||||||||||||||||||||||
| solid angle | steradian | sr | solid angle that, having its vertex in the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. | |||||||||||||||||||||||||
| frequency | hertz | Hz | 1 / s | 1 Hz = 1 cycle per second (cps) | ||||||||||||||||||||||||
| force | newton | N | m⋅kg / s² | 1 N ≅ 0.22481 pounds ≅ 7.233 poundals 1 pound = 4.44822 N 1 poundal = 0.138255 N | ||||||||||||||||||||||||
| pressure | pascal | Pa | N / m² | 1 millibar = 100 Pa 1 pound per square inch (psi) ≅ 6897 Pa 1 kPa = 0.145 psi 1 mm of Mercury (Hg) ≅ 0.13332 kPa | ||||||||||||||||||||||||
| energy | joule | J | N⋅m | 1 J ≅ 0.000948 British thermal units (BTU) 1 J ≅ 6.24×10¹⁸ eV 1 kilowatt-hour (kW⋅h)= 3.6 MJ 1 J ≅ 2.778×10⁻⁷ kW⋅h 1 (real) calorie = 4.184 J 1 (U.S. nutrition label) calorie = 4184 J | ||||||||||||||||||||||||
| power | watt | W | J / s | 1 horsepower ≅ 745.7 W 1 kW ≅ 1.341 horsepower | ||||||||||||||||||||||||
| electric charge | coulomb | C | A⋅s | |||||||||||||||||||||||||
| electric potential | volt | V | W / A | |||||||||||||||||||||||||
| capacitance | farad | F | C / V | |||||||||||||||||||||||||
| resistance | ohm | Ω | V / A | |||||||||||||||||||||||||
| conductance | siemens | S | A / V | 1 siemens = 1 mho (℧) | ||||||||||||||||||||||||
| magnetic flux | weber | Wb | V⋅s | |||||||||||||||||||||||||
| magnetic flux density | tesla | T | Wb / m² | |||||||||||||||||||||||||
| inductance | henry | H | Wb / A | |||||||||||||||||||||||||
| relative temperature | degree Celsius | °C | K (temperature of TK K is (TK - 273.15) °C) | TFahrenheit = (TCelsius × 9°F/5°C) + 32°F TCelsius = (TFahrenheit - 32°F) × 5°C/9°F TCelsius = Tcentigrade × °C/°Centigrade luminous flux
| lumen
| lm
| cd⋅sr
| illuminance
| lux
| lx
| lm / m²
| nuclear activity
| becquerel
| Bq
| Hz
| radiation dose
| sievert
| Sv
| J / kg
| absorbed dose
| gray
| Gy
| Sv
| catalytic enzyme activity
| katal
| kat
| mol / s
| |
| Other non-SI metric units | ||||
|---|---|---|---|---|
| quantity | name | symbol | definition | conversions |
| time | minute | min | 60 s | ≅ 1 (traditional) minute |
| time | hour | h | 3600 s = 60 min | ≅ 1 (traditional) hour |
| time | day | d | 86 400 s | ≅ 1 (traditional) day |
| length | astronomical unit | au | 149 597 870 700 m | 1 au ≅ 499 light seconds 1 au 3.168 8×10⁻⁸ light years 1 light year ≅ 63 241 au 1 parsec = (648 000)/π au ≅ 206 264.8 au |
| angle | degree | ° | (π/180) rad = 1/360 circle | |
| angle | minute | ′ | (1/60)° = (π/10 800) rad | |
| angle | second | ″ | (1/60)′ = (1/3600)° = (π/10 800) rad | |
| area | hectare | ha | hm² = 10 000 m² | 1 ha ≅ 2.4711 acres ≅ 107 639 sq. ft. 1 km² = 100 ha 1 acre ≅ 0.404687 ha |
| volume | litre | ℓ, L | dm³ = 0.001 m³ | 1 ℓ = 1000 cm³ = 1000 c.c. 1 U.S. cup = 236.588 236 5 mℓ 1 U.S. pint = 473.176 473 mℓ 1 U.S. quart = 0.946 352 946 ℓ 1 U.S. gallon = 3.785 411 784 ℓ 1 ℓ ≅ 1 quart 1 13⁄16 fluid ounces (U.S.) 1 ℓ ≅ 1¾ imperial pint |
| mass | tonne, metric ton | t | 1 Mg | 1 t ≅ 2204 pounds 10 ounces 1 t ≅ 68½ slugs 1 t ≅ 1.1023 (short or U.S.) tons 1 t ≅ 0.984 (long or imperial) tons 1 short or U.S. ton ≅ 0.907 t 1 long or imperial ton ≅ 1.016 t |
| mass | dalton | Da | 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state | 1 Da ≅ 1.66 yg |
| energy | electronvolt | eV | 1.602 176 634 × 10⁻¹⁹ J | |
| logarithmic ratio | neper | Np | natural-base logarithm of ratio | |
| logarithmic ratio | bel | B | decimal-base logarithm of ratio | |
| logarithmic ratio | decibel | dB | one tenth of decimal-base logarithm of ratio | |
| Prefixes used with SI units | |||||||
|---|---|---|---|---|---|---|---|
| Factor | Prefix | Symbol | multiplier | Factor | Prefix | Symbol | |
| 10¹ | deca | da | ten | 10⁻¹ | deci | d | |
| 10² | hecto | h | hundred | 10⁻² | centi | c | |
| 10³ | kilo | k | thousand | 10⁻³ | milli | m | |
| 10⁶ | mega | M | million | 10⁻⁶ | micro | µ | |
| 10⁹ | giga | G | billion | 10⁻⁹ | nano | n | |
| 10¹² | tera | T | trillion | 10⁻¹² | pico | p | |
| 10¹⁵ | peta | P | quadrillion | 10⁻¹⁵ | femto | f | |
| 10¹⁸ | exa | E | quintillion | 10⁻¹⁸ | atto | a | |
| 10²¹ | zetta | Z | sextillion | 10⁻²¹ | zepto | z | |
| 10²⁴ | yotta | Y | septillion | 10⁻²⁴ | yocto | y | |
| 10²⁷ | ronna | R | octillion | 10⁻²⁷ | ronto | r | |
| 10³⁰ | quetta | Q | nonillion | 10⁻³⁰ | quecto | q | |
Prefixes are usually added to the beginning of the names of the base or derived units to create additional related measurements of various magnitudes. For instance, centimetre is one hundredth of a metre, and kilometre is one thousand metres. For multiples of the kilogram, prefixes are applied to the word gram (where one gram is 0.001 kilogram). So, 1000 kilograms is 1 megagram (and not 1 kilokilogram, which is not a proper unit at all). One microgram (1 µg) is one billionth of a kilogram (0.000000001 kg). Prefixes are properly accented on the first syllable, but there are many English speakers who utter kilometre as [kəˈlɑːmɪɾɹ̩ ] (kə·lä′·mĭ·tər) rather than the usual [ˈkɪləˌmitɹ̩] (kĭl′·ə·mēt′·ər).
Some persons historically abbreviated units with the micro- prefix by using a u as the prefix symbol due to its similarity to the proper prefix, namely µ, using an excuse that their typewriter didn't have a µ key (fortunately, no one in this millennium can use that lame excuse as computer keyboards can generate a vast repertoire of characters including emojis ☺). A certain disreputable pharmaceutical company was once guilty of using the nonsensical abbrevation "mcg" to mean microgram which is more likely to be interpreted as a millicentigram (an improper term suggesting 10⁻⁵ g); to this day, it is still uncertain how many fatalities such outlandishly wrong symbol usage brought about. If you are indeed using a Teletype or some other antique device which cannot generate lowercase letters, don't even try to abbreviate — just spell out the name of the unit in full.
Official SI reference documents make no particular comment about using prefixes with unit names that begin with a vowel, but in practical English usage, the final vowel of the prefix is sometimes dropped, especially when it is the same letter as the first letter of the base unit name or when the last letter of the prefix is an -a-. For instance, kilohm (kΩ), megohm (MΩ), and megampere (MA); but milliampere (mA). Dropping the final vowel in the deca- or deci- prefixes would lead to ambiguity, so do not do so.
A hectare is 100 ares, where one are is an essentially defunct term for one square decametre (1 dm²) or one hundred square metres (100 m²). The unprefixed term are (pronounced [ɛɹ] (ĕr) like the word "air") by itself is not generally used in English as it can be easily confused with the verb are (form of to be), so areas given in "square metres" (m²) are generally used instead. Although hectare the unit symbol (ha), that does not imply that are has a symbol (a) or that other prefixes could be applied to either are or hectare.
SI unit symbols also are traditionally not considered abbreviations, so they are not followed by a period or full stop unless the context would otherwise require one such as at the end of a sentence. Also, the unit symbols do not change for number, gender, case, or other grammatical criteria: so, one metre is (1 m) and two metres is (2 m); do not add "s" to make a symbol plural.
In the real world, people use measurement abbreviations improperly all the time, so you have to use your judgment and figure out that "MM" probably means "millimetre" (which should be "mm") rather than "megametre" (which should be "Mm"), or that a GVWR (Gross Vehicle Weight Rating) in "KGS" on a truck means "kilograms" (should be "kg").