SI unit definitions

Ampere (A)

2019

The ampere, symbol A, is the SI unit of electric current. It is 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 ∆ν_Cs. [26th CGPM, Resolution 1]

Previous definitions

1948

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 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10⁻⁷ newtons per metre of length. [9th CGPM; 1946 CIPM]

Are (a)

1879

Are is an obsolete special name for 100 m².

Note

The are, pronounced like “air”, is obsolete, but the hectare, equal to 10 000 m², is still used for measuring areas of land.

Becquerel (Bq)

1975

The special name for the SI unit of activity: becquerel, symbol Bq, equal to one reciprocal second. [15th CGPM, Resolution 8]

Candela (cd)

1979

The candela is 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. [16th CGPM, Resolution 3]

Previous definitions

1968

The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 pascals. [13th CGPM, Resolution 5]

1948

The value of the candela is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 candelas per square centimetre. [9th CGPM; 1946 CIPM]

Note

This unit was originally called the new candle, but it was renamed candela, generally pronounced with the accent on the second syllable, in 1948. The name new candle was officially declared obsolete in 1968.

Coulomb (C)

1948

The coulomb is the quantity of electricity carried in 1 second by a current of 1 ampere. [9th CGPM; 1946 CIPM]

Day (d)

1 day is 24 hours or 86 400 seconds.

Degree Celsius (°C)

2019

Since the kelvin was redefined in the 26th CGPM using the Boltzmann constant, and the degree Celsius was fixed at the triple point of water that was defined in kelvins, it was transitively redefined from the triple point of water to exactly the difference between the temperature in kelvins and 273.15.

Previous definitions

1954

The 10th Conférence Générale des Poids et Mesures decides to define the thermodynamic temperature scale by choosing the triple point of water as the fundamental fixed point, and assigning to it the temperature 273.16 kelvins, exactly. [10th CGPM, Resolution 3]

1948

The zero of the centesimal thermodynamic scale must be defined as the temperature 0.0100 degree below that of the triple point of water. [9th CGPM, Resolution 3]

Notes

The plural of “degree Celsius” is “degrees Celsius”. The word “Celsius” should be capitalized. There should be no space between the characters of its unit symbol, °C, although there should be space before it.

The term degree centigrade was a synonym for this unit until 1948: From three names (‘degree centigrade’, ‘centesimal degree’, ‘degree Celsius’) proposed to denote the degree of temperature, the CIPM [and 9th CGPM] has chosen ‘degree Celsius’.

Farad (F)

1948

The farad is the capacitance of a capacitor between the plates of which there appears a potential difference of 1 volt when it is charged by a quantity of electricity of 1 coulomb. [9th CGPM; 1946 CIPM]

Gray (Gy)

1975

[The] special name for the SI unit of ionizing radiation: gray, symbol Gy, equal to one joule per kilogram. [15th CGPM, Resolution 9]

Hectare (ha)

1879

Are is an obsolete special name for 100 m². The hectare, which is not obsolete, is 100 ares (10 000 m²) and is used for measuring land area.

Notes

“Hectare” is normally pronounced so as to rhyme with “air.”

“Hectare” is one of the few cases in which a vowel is elided from what would otherwise be spelled “hectoare.”

Henry (H)

1948

The henry is the inductance of a closed circuit in which an electromotive force of 1 volt is produced when the electric current in the circuit varies uniformly at the rate of 1 ampere per second. [9th CGPM; 1946 CIPM]

Hertz (Hz)

1960

The SI unit of frequency, 1 hertz is 1/s. [11th CGPM, Resolution 12]

Note

The plural of “hertz” is “hertz”.

Hour (h)

1 hour is 60 minutes or 3600 seconds.

Joule (J)

1948

The joule is the work done when the point of application of 1 newton moves a distance of 1 metre in the direction of the force. [9th CGPM; 1946 CIPM]

Katal (kat)

1999

Adopts the special name katal, symbol kat, for the SI unit mole per second to express catalytic activity, especially in the fields of medicine and biochemistry. [21st CGPM, Resolution 7]

Kelvin (K)

2019

The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10^–23 when expressed in the unit J K^–1, which is equal to kg m² s^–2 K^–1, where the kilogram, metre and second are defined in terms of h, c and ∆ν_Cs. [26th CGPM, Resolution 1]

Previous definitions

1967

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. [13th CGPM, Resolution 4]. In addition, the same name and the same symbol are used to express a temperature interval, [although] a temperature interval may also be expressed in degrees Celsius. [13th CGPM, Resolution 3]

Because the temperature of the triple point depends on the relative amount of isotopes of hydrogen and oxygen present in the sample of water used [and] this effect is now one of the major sources of the observed variability between different realizations of the water triple point, the definition of the kelvin was clarified in 2007 by adding a note:

This definition refers to water having the isotopic composition defined by the following amount-of-substance ratios: 0.000 155 76 mole of ²H per mole of ¹H, 0.000 379 9 mole of ¹⁷O per mole of ¹⁶O, and 0.002 005 2 mole of ¹⁸O per mole of ¹⁶O. [23rd CGPM, Resolution 10]

1954

The 10th Conférence Générale des Poids et Mesures decides to define the thermodynamic temperature scale by choosing the triple point of water as the fundamental fixed point, and assigning to it the temperature 273.16 kelvins, exactly. [10th CGPM, Resolution 3]

Notes

This unit was called the degree Kelvin, symbol °K, until 1967, when the name kelvin, symbol K, replaced it. The old forms, as well as the symbol “deg”, were officially declared obsolete in 1980.

Kilogram (kg)

2019

The kilogram, symbol kg, is the SI unit of mass. It is 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 ∆ν_Cs. [26th CGPM, Resolution 1]

Previous definitions

1889

This prototype shall henceforth be considered as the unit of mass, referring to a prototype made of an alloy of platinum with 10% iridium. [1st CGPM]

Notes

In 1901, the 3rd CGPM emphasized that the kilogram is a unit of mass and defined a standard value for the constant g, declaring that:

1. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram;
2. The word “weight” denotes a quantity of the same nature as a “force”: the weight of a body is the product of its mass and the acceleration due to gravity; in particular, the standard weight of a body is the product of its mass and the standard acceleration due to gravity;
3. The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s², a value already stated in the laws of some countries.

In everyday use, “weight” is a synonym for “mass”: You weigh something to determine its mass, which you call its “weight”, measured in grams, kilograms, megagrams, or the like. See Is it “weight” or “mass”? in the FAQ.

Litre (L)

1964

The word ‘litre’ may be employed as a special name for the cubic decimetre [replacing its previous definition]. [12th CGPM, Resolution 6]

Previous definitions

1901

The unit of volume, for high accuracy determinations, is the volume occupied by a mass of 1 kilogram of pure water, at its maximum density and at standard atmospheric pressure: this volume is called ‘litre’. [3rd CGPM]

1795

Litre is defined as a special name for the cubic decimetre.

Note

The original symbol for litre, adopted by the CIPM in 1879, was l (lowercase letter ell), and that was confirmed in Resolution 7 of the 9th CGPM in 1948. However, several countries later adopted a capital L to avoid confusion with the digit 1, and in 1979, Resolution 6 of the 16th CGPM decided as an exception, to adopt the two symbols l and L as symbols to be used for the unit litre, but said that in the future only one of these two symbols should be retained. As of 2013, no decision has been made, so both symbols remain correct.

Lumen (lm)

1948

The lumen is the luminous flux emitted in unit solid angle (steradian) by a uniform point source having a luminous intensity of 1 candela. [9th CGPM; 1946 CIPM]

Note

This unit was originally called the new lumen, but the “new” qualifier was later dropped.

Lux (lx)

1948

The unit of illuminance, the lux is 1 lm/m².

Metre (m)

1983

The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. [17th CGPM, Resolution 1]

Previous definitions

1960

The metre is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p₁₀ and 5d₅ of the krypton 86 atom. [11th CGPM, Resolution 6]

1927

The unit of length is the metre, defined by the distance, at 0°, between the axes of the two central lines marked on the bar of platinum-iridium kept at the Bureau International des Poids et Mesures and declared Prototype of the metre by the 1st Conférence Générale des Poids et Mesures, this bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other. [7th CGPM]

1889

This prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length, referring to a prototype made of an alloy of platinum with 10% iridium. [1st CGPM]

1799

A platinum prototype.

1795

A brass prototype.

1793

The metre was defined as 1/10 000 000 of the distance from an Earth pole to the equator.

Metric ton (t)

1879

The metric ton, known officially as the tonne, is 1 Mg or 1000 kg.

Micron (µ)

1879

Micron, symbol µ, was a special name for the micrometre, but it was officially declared obsolete in 1968. [13th CGPM, Resolution 7]

Minute (min)

1 minute is 60 seconds.

Mole (mol)

2019

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number. [26th CGPM, Resolution 1]

Previous definitions

1971

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. [14th CGPM, Resolution 3]

Newton (N)

1948

The newton is the force which gives to a mass of 1 kilogram an acceleration of 1 metre per second, per second. [9th CGPM; 1946 CIPM]

Note

Although the SI unit of force has always been the kg⋅m/s², the name newton was not adopted until 1948.

Ohm (Ω)

1948

The ohm is the electric resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force. [9th CGPM; 1946 CIPM]

Note

The final vowel of the prefix is normally elided in “megohm” (MΩ) and “kilohm” (kΩ).

Pascal (Pa)

1971

The 14th CGPM adopted “pascal” as a special name for the SI unit newton per square metre.

Radian (rad)

1960

The unit of plane angle, one radian is the angle subtended at the center of a circle by an arc of length equal to the radius of the circle. As such, its units are m/m, and so technically the radian is a special name for the number 1. For example, angular velocity in rad/s is, in base units, s^-1.

Notes

The symbol rad was adopted at least as early as 1960, but the radian itself dates back at least as far as 1879.

The radian was originally categorized as a supplementary unit, distinct from the SI base units and derived units. In 1995 the CGPM officially eliminated the supplementary unit category, adopting a 1980 CIPM recommendation to classify the radian as a derived unit.

Second (s)

1967

The 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 [at rest at a thermodynamic temperature of 0 K]. [13th CGPM, Resolution 1]

Previous definition

1960

The second is the fraction 1/31 556 925.9747 of the tropical year for 0 January 1900 at 12 hours ephemeris time. [11th CGPM, Resolution 9; 1956 CIPM]

Siemens (S)

1971

The 14th CGPM adopted “siemens” as a special name for the SI unit of conductance, reciprocal ohm.

Sievert (Sv)

1980

[The] special name sievert, symbol Sv, for the SI unit of dose equivalent in the field of radioprotection. The sievert is equal to the joule per kilogram. [16th CGPM, Resolution 5]

Steradian (sr)

1960

The unit of solid angle, one steradian is the solid angle subtended at the center of the sphere by a portion of the surface whose area is equal to the square of the radius of the sphere. As such, its units are m²/m², and so technically the steradian is a special name for the number 1.

Notes

The symbol sr was adopted at least as early as 1960.

The steradian was originally categorized as a supplementary unit, distinct from the SI base units and derived units. In 1995 the CGPM officially eliminated the supplementary unit category, adopting a 1980 CIPM recommendation to classify the steradian as a derived unit.

Stere (st)

1879

Stere is an obsolete special name for 1 m³, once used for measuring firewood.

Note

The symbol for stere originally was s, later changed to st so as not to conflict with the symbol for the second. But the stere is now obsolete.

Tesla (T)

1960

The unit of magnetic flux density, the tesla is 1 Wb/m². [11th CGPM, Resolution 12]

Volt (V)

1948

The volt is the potential difference between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these points is equal to 1 watt. [9th CGPM; 1946 CIPM]

Watt (W)

1948

The watt is the power which in one second gives rise to energy of 1 joule. [9th CGPM; 1946 CIPM]

Weber (Wb)

1948

The weber is the magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second. [9th CGPM; 1946 CIPM]

Year

The year is not an SI unit and it is not approved for use with the SI. In practice, it is an important unit that is, ironically, directly relevant to SI in contexts such as, Delegates from all Member States of the Metre Convention attend the General Conference which, at present, meets every four years.

In common use, “year” usually refers to a calendar (or “civil”) year, i.e., the period of time between successive occurrences of a calendar date such as “1 January”. The actual duration of such a year varies due to leap years, among other things.

There is no official symbol for the year, but y, yr, and a are probably the most common; note that “a” conflicts with the symbol for the are.

Other definitions of the year, based on the interval between two successive passages of the Sun through a reference point, include the sidereal year, tropical year, and anomalistic year, all based on different astronomical reference points. These and other definitions of the year are explicitly identified when relevant.