SI derived unit

Encyclopedia

The International System of Units

(SI) specifies a set of seven base units

from which all other units of measurement

are formed, by products of the powers of base units. These other units are called

The names of SI units are always written in lowercase. The symbols of units named after persons, however, are always written with an uppercase initial letter (e.g., the symbol of hertz is Hz; but metre is m).

derived units radian

(rad) and steradian

(sr), 20 other derived units have special names.

, are not SI units, but are accepted for use with the SI

.

International System of Units

The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI) specifies a set of seven base units

SI base unit

The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

from which all other units of measurement

Units of measurement

A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

are formed, by products of the powers of base units. These other units are called

**SI derived units**, for example, the SI derived unit of area is square metre (m^{2}), and of density is kilograms per cubic metre (kg/m^{3}). The number of derived units is unlimited.The names of SI units are always written in lowercase. The symbols of units named after persons, however, are always written with an uppercase initial letter (e.g., the symbol of hertz is Hz; but metre is m).

## Derived units with special names

In addition to the two dimensionlessDimensionless quantity

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

derived units radian

Radian

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

(rad) and steradian

Steradian

The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane...

(sr), 20 other derived units have special names.

Name | Symbol Symbol A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for... |
Quantity Physical quantity A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:... |
Expression in terms of other units | Expression in terms of SI base unit SI base unit The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length... s |
---|---|---|---|---|

hertzHertz The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications.... |
Hz |
frequency Frequency Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency... |
1/s | s^{−1} |

radianRadian Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit... |
rad |
angle Angle In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc... |
m/m | dimensionless |

steradianSteradian The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane... |
sr |
solid angle Solid angle The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point... |
m^{2}/m^{2} |
dimensionless |

newton |
N |
force Force In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform... , weight Weight In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:... |
kg⋅m/s^{2} |
kg⋅m⋅s^{−2} |

pascalPascal (unit) The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre... |
Pa |
pressure Pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :... , stress Stress (physics) In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body... |
N/m^{2} |
kg⋅m^{−1}⋅s^{−2} |

jouleJoule The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second... |
J |
energy Energy In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems... , work Mechanical work In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work... , heat Heat In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between... |
N⋅m = C⋅V = W⋅s | kg⋅m^{2}⋅s^{−2} |

wattWatt The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:... |
W |
power Power (physics) In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit... , radiant flux Radiant flux In radiometry, radiant flux or radiant power is the measure of the total power of electromagnetic radiation... |
J/s = V⋅A | kg⋅m^{2}⋅s^{−3} |

coulomb |
C |
electric charge Electric charge Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two... or quantity of electricity Quantity of electricity In physics the term quantity of electricity refers to the quantity of electric charge. It is designated by the letter Q and in the SI system is measured in derived units called Coulombs.- Pre-English origins :... |
s⋅A | s⋅A |

voltVolt The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the... |
V |
voltage Voltage Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points... , electrical potential difference, electromotive force Electromotive force In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a... |
W/A = J/C | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

faradFarad The farad is the SI unit of capacitance. The unit is named after the English physicist Michael Faraday.- Definition :A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt. A coulomb is 1 ampere second... |
F |
electric capacitance | C/V | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |

ohm |
Ω |
electric resistance, impedance Electrical impedance Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit... , reactance |
V/A | kg⋅m^{2}⋅s^{−3}⋅A^{−2} |

siemensSiemens (unit) The siemens is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term... |
S |
electrical conductance | 1/Ω = A/V | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

weber |
Wb |
magnetic flux Magnetic flux Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber... |
J/A | kg⋅m^{2}⋅s^{−2}⋅A^{−1} |

teslaTesla (unit) The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla... |
T |
magnetic field Magnetic field A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;... strength, magnetic flux density |
V⋅s/m^{2} = Wb/m^{2} = N/(A⋅m) |
kg⋅s^{−2}⋅A^{−1} |

henry |
H |
inductance Inductance In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit... |
V⋅s/A = Wb/A | kg⋅m^{2}⋅s^{−2}⋅A^{−2} |

degree Celsius |
°C |
temperature Temperature Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot... relative to 273.15 K |
K | K |

lumenLumen (unit) The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux... |
lm |
luminous flux Luminous flux In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of... |
cd⋅sr | cd |

luxLux The lux is the SI unit of illuminance and luminous emittance, measuring luminous flux per unit area. It is used in photometry as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface... |
lx |
illuminance Illuminance In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per... |
lm/m^{2} |
m^{−2}⋅cd |

becquerelBecquerel The becquerel is the SI-derived unit of radioactivity. One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. The Bq unit is therefore equivalent to an inverse second, s−1... |
Bq |
radioactivity (decays per unit time) | 1/s | s^{−1} |

grayGray (unit) The gray is the SI unit of absorbed radiation dose of ionizing radiation , and is defined as the absorption of one joule of ionizing radiation by one kilogram of matter .... |
Gy |
absorbed dose Absorbed dose Absorbed dose is a measure of the energy deposited in a medium by ionizing radiation per unit mass... (of ionizing radiation Ionizing radiation Ionizing radiation is radiation composed of particles that individually have sufficient energy to remove an electron from an atom or molecule. This ionization produces free radicals, which are atoms or molecules containing unpaired electrons... ) |
J/kg | m^{2}⋅s^{−2} |

sievertSievert The sievert is the International System of Units SI derived unit of dose equivalent radiation. It attempts to quantitatively evaluate the biological effects of ionizing radiation as opposed to just the absorbed dose of radiation energy, which is measured in gray... |
Sv |
equivalent dose Equivalent dose The equivalent absorbed radiation dose, usually shortened to equivalent dose, is a computed average measure of the radiation absorbed by a fixed mass of biological tissue, that attempts to account for the different biological damage potential of different types of ionizing radiation... (of ionizing radiation Ionizing radiation Ionizing radiation is radiation composed of particles that individually have sufficient energy to remove an electron from an atom or molecule. This ionization produces free radicals, which are atoms or molecules containing unpaired electrons... ) |
J/kg | m^{2}⋅s^{−2} |

katalKatal The katal is the SI unit of catalytic activity. It is a derived SI unit for expressing quantity values of catalytic activity of enzymes and other catalysts. Its use is recommended by the General Conference on Weights and Measures and other international organizations. It replaces the non-SI enzyme... |
kat |
catalytic activity | mol/s | s^{−1}⋅mol |

## Examples of derived quantities and units

Some other metric units, such as the litreLitre

pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

, are not SI units, but are accepted for use with the SI

Non-SI units accepted for use with SI

This is a list of units that are not defined as part of the International System of Units , but are otherwise mentioned in the SI, because either the General Conference on Weights and Measures accepts their use as being multiples or submultiples of SI-units, they have important contemporary...

.

## See also

- International Vocabulary of MetrologyInternational vocabulary of metrologyThe International vocabulary of metrology is an attempt to find a common language and terminology in metrology, e.g. the science of measurements, across different fields of science, legislature and commerce...
- International System of Quantities
- International System of UnitsInternational System of UnitsThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
- SI base units
- SI prefixesSI prefixThe International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...
- Non-SI units accepted for use with the SINon-SI units accepted for use with SIThis is a list of units that are not defined as part of the International System of Units , but are otherwise mentioned in the SI, because either the General Conference on Weights and Measures accepts their use as being multiples or submultiples of SI-units, they have important contemporary...
- Planck unitsPlanck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...