**SI derived units** are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. **SI coherent derived units** involve only a trivial proportionality factor, not requiring conversion factors.

- Special names
- By field of application
- Kinematics
- Mechanics
- Chemistry
- Electromagnetics
- Photometry
- Thermodynamics
- Other units used with SI
- Supplementary units
- See also
- References
- Bibliography
- External links

The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m^{2}), the SI derived unit of area; and the kilogram per cubic metre (kg/m^{3} or kg⋅m^{−3}), the SI derived unit of density.

The names of SI coherent derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m".^{ [1] }

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Name | Symbol | Quantity | Equivalents | SI base unit Equivalents |
---|---|---|---|---|

hertz | Hz | frequency | 1/s | s^{−1} |

radian | rad | angle | m/m | 1 |

steradian | sr | solid angle | m^{2}/m^{2} | 1 |

newton | N | force, weight | kg⋅m/s^{2} | kg⋅m⋅s^{−2} |

pascal | Pa | pressure, stress | N/m^{2} | kg⋅m^{−1}⋅s^{−2} |

joule | J | energy, work, heat | m⋅N, C⋅V, W⋅s | kg⋅m^{2}⋅s^{−2} |

watt | W | power, radiant flux | J/s, V⋅A | kg⋅m^{2}⋅s^{−3} |

coulomb | C | electric charge or quantity of electricity | s⋅A, F⋅V | s⋅A |

volt | V | voltage, electrical potential difference, electromotive force | W/A, J/C | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

farad | F | electrical capacitance | C/V, s/Ω | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |

ohm | Ω | electrical resistance, impedance, reactance | 1/S, V/A | kg⋅m^{2}⋅s^{−3}⋅A^{−2} |

siemens | S | electrical conductance | 1/Ω, A/V | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

weber | Wb | magnetic flux | J/A, T⋅m^{2},V⋅s | kg⋅m^{2}⋅s^{−2}⋅A^{−1} |

tesla | T | magnetic induction, magnetic flux density | V⋅s/m^{2}, Wb/m^{2}, N/(A⋅m) | kg⋅s^{−2}⋅A^{−1} |

henry | H | electrical inductance | V⋅s/A, Ω⋅s, Wb/A | kg⋅m^{2}⋅s^{−2}⋅A^{−2} |

degree Celsius | °C | temperature relative to 273.15 K | K | K |

lumen | lm | luminous flux | cd⋅sr | cd |

lux | lx | illuminance | lm/m^{2} | cd⋅m^{−2} |

becquerel | Bq | radioactivity (decays per unit time) | 1/s | s^{−1} |

gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

katal | kat | catalytic activity | mol/s | s^{−1}⋅mol. |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

metre per second | m/s | speed, velocity | m⋅s^{−1} |

metre per second squared | m/s^{2} | acceleration | m⋅s^{−2} |

metre per second cubed | m/s^{3} | jerk, jolt | m⋅s^{−3} |

metre per second to the fourth | m/s^{4} | snap, jounce | m⋅s^{−4} |

radian per second | rad/s | angular velocity | s^{−1} |

radian per second squared | rad/s^{2} | angular acceleration | s^{−2} |

hertz per second | Hz/s | frequency drift | s^{−2} |

cubic metre per second | m^{3}/s | volumetric flow | m^{3}⋅s^{−1} |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

square metre | m^{2} | area | m^{2} |

cubic metre | m^{3} | volume | m^{3} |

newton-second | N⋅s | momentum, impulse | m⋅kg⋅s^{−1} |

newton metre second | N⋅m⋅s | angular momentum | m^{2}⋅kg⋅s^{−1} |

newton-metre | N⋅m = J/rad | torque, moment of force | m^{2}⋅kg⋅s^{−2} |

newton per second | N/s | yank | m⋅kg⋅s^{−3} |

reciprocal metre | m^{−1} | wavenumber, optical power, curvature, spatial frequency | m^{−1} |

kilogram per square metre | kg/m^{2} | area density | m^{−2}⋅kg |

kilogram per cubic metre | kg/m^{3} | density, mass density | m^{−3}⋅kg |

cubic metre per kilogram | m^{3}/kg | specific volume | m^{3}⋅kg^{−1} |

joule-second | J⋅s | action | m^{2}⋅kg⋅s^{−1} |

joule per kilogram | J/kg | specific energy | m^{2}⋅s^{−2} |

joule per cubic metre | J/m^{3} | energy density | m^{−1}⋅kg⋅s^{−2} |

newton per metre | N/m = J/m^{2} | surface tension, stiffness | kg⋅s^{−2} |

watt per square metre | W/m^{2} | heat flux density, irradiance | kg⋅s^{−3} |

square metre per second | m^{2}/s | kinematic viscosity, thermal diffusivity, diffusion coefficient | m^{2}⋅s^{−1} |

pascal-second | Pa⋅s = N⋅s/m^{2} | dynamic viscosity | m^{−1}⋅kg⋅s^{−1} |

kilogram per metre | kg/m | linear mass density | m^{−1}⋅kg |

kilogram per second | kg/s | mass flow rate | kg⋅s^{−1} |

watt per steradian square metre | W/(sr⋅m^{2}) | radiance | kg⋅s^{−3} |

watt per steradian cubic metre | W/(sr⋅m^{3}) | radiance | m^{−1}⋅kg⋅s^{−3} |

watt per metre | W/m | spectral power | m⋅kg⋅s^{−3} |

gray per second | Gy/s | absorbed dose rate | m^{2}⋅s^{−3} |

metre per cubic metre | m/m^{3} | fuel efficiency | m^{−2} |

watt per cubic metre | W/m^{3} | spectral irradiance, power density | m^{−1}⋅kg⋅s^{−3} |

joule per square metre second | J/(m^{2}⋅s) | energy flux density | kg⋅s^{−3} |

reciprocal pascal | Pa^{−1} | compressibility | m⋅kg^{−1}⋅s^{2} |

joule per square metre | J/m^{2} | radiant exposure | kg⋅s^{−2} |

kilogram square metre | kg⋅m^{2} | moment of inertia | m^{2}⋅kg |

newton metre second per kilogram | N⋅m⋅s/kg | specific angular momentum | m^{2}⋅s^{−1} |

watt per steradian | W/sr | radiant intensity | m^{2}⋅kg⋅s^{−3} |

watt per steradian metre | W/(sr⋅m) | spectral intensity | m⋅kg⋅s^{−3} |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

mole per cubic metre | mol/m^{3} | molarity, amount of substance concentration | m^{−3}⋅mol |

cubic metre per mole | m^{3}/mol | molar volume | m^{3}⋅mol^{−1} |

joule per kelvin mole | J/(K⋅mol) | molar heat capacity, molar entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1}⋅mol^{−1} |

joule per mole | J/mol | molar energy | m^{2}⋅kg⋅s^{−2}⋅mol^{−1} |

siemens square metre per mole | S⋅m^{2}/mol | molar conductivity | kg^{−1}⋅s^{3}⋅A^{2}⋅mol^{−1} |

mole per kilogram | mol/kg | molality | kg^{−1}⋅mol |

kilogram per mole | kg/mol | molar mass | kg⋅mol^{−1} |

cubic metre per mole second | m^{3}/(mol⋅s) | catalytic efficiency | m^{3}⋅s^{−1}⋅mol^{−1} |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

coulomb per square metre | C/m^{2} | electric displacement field, polarization density | m^{−2}⋅s⋅A |

coulomb per cubic metre | C/m^{3} | electric charge density | m^{−3}⋅s⋅A |

ampere per square metre | A/m^{2} | electric current density | m^{−2}⋅A |

siemens per metre | S/m | electrical conductivity | m^{−3}⋅kg^{−1}⋅s^{3}⋅A^{2} |

farad per metre | F/m | permittivity | m^{−3}⋅kg^{−1}⋅s^{4}⋅A^{2} |

henry per metre | H/m | magnetic permeability | m⋅kg⋅s^{−2}⋅A^{−2} |

volt per metre | V/m | electric field strength | m⋅kg⋅s^{−3}⋅A^{−1} |

ampere per metre | A/m | magnetization, magnetic field strength | m^{−1}⋅A |

coulomb per kilogram | C/kg | exposure (X and gamma rays) | kg^{−1}⋅s⋅A |

ohm metre | Ω⋅m | resistivity | m^{3}⋅kg⋅s^{−3}⋅A^{−2} |

coulomb per metre | C/m | linear charge density | m^{−1}⋅s⋅A |

joule per tesla | J/T | magnetic dipole moment | m^{2}⋅A |

square metre per volt second | m^{2}/(V⋅s) | electron mobility | kg^{−1}⋅s^{2}⋅A |

reciprocal henry | H^{−1} | magnetic reluctance | m^{−2}⋅kg^{−1}⋅s^{2}⋅A^{2} |

weber per metre | Wb/m | magnetic vector potential | m⋅kg⋅s^{−2}⋅A^{−1} |

weber metre | Wb⋅m | magnetic moment | m^{3}⋅kg⋅s^{−2}⋅A^{−1} |

tesla metre | T⋅m | magnetic rigidity | m⋅kg⋅s^{−2}⋅A^{−1} |

ampere radian | A⋅rad | magnetomotive force | A |

metre per henry | m/H | magnetic susceptibility | m^{−1}⋅kg^{−1}⋅s^{2}⋅A^{2} |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

lumen second | lm⋅s | luminous energy | s⋅cd |

lux second | lx⋅s | luminous exposure | m^{−2}⋅s⋅cd |

candela per square metre | cd/m^{2} | luminance | m^{−2}⋅cd |

lumen per watt | lm/W | luminous efficacy | m^{−2}⋅kg^{−1}⋅s^{3}⋅cd |

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

joule per kelvin | J/K | heat capacity, entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1} |

joule per kilogram kelvin | J/(K⋅kg) | specific heat capacity, specific entropy | m^{2}⋅s^{−2}⋅K^{−1} |

watt per metre kelvin | W/(m⋅K) | thermal conductivity | m⋅kg⋅s^{−3}⋅K^{−1} |

kelvin per watt | K/W | thermal resistance | m^{−2}⋅kg^{−1}⋅s^{3}⋅K |

reciprocal kelvin | K^{−1} | thermal expansion coefficient | K^{−1} |

kelvin per metre | K/m | temperature gradient | m^{−1}⋅K |

Some other units such as the hour, litre, tonne, bar, and electronvolt are not SI units, but are widely used in conjunction with SI units.

Until 1995, the SI classified the radian and the steradian as *supplementary units*, but this designation was abandoned and the units were grouped as derived units.^{ [3] }

A **physical quantity** is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a *value*, which is the algebraic multiplication of a *numerical value* and a *unit of measurement*. For example, the physical quantity mass, symbol *m*, can be quantified as *m*=*n* kg, where *n* is the numerical value and kg is the unit symbol.

The **radian**, denoted by the symbol **rad**, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit, defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as rad = m/m. Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.

The **International System of Units**, internationally known by the abbreviation **SI**, is the modern form of the metric system and the world's most widely used system of measurement. Established and maintained by the General Conference on Weights and Measures (CGPM), it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

A **metric prefix** is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix *kilo-*, for example, may be added to *gram* to indicate *multiplication* by one thousand: one kilogram is equal to one thousand grams. The prefix *milli-*, likewise, may be added to *metre* to indicate *division* by one thousand; one millimetre is equal to one thousandth of a metre.

The **steradian** or **square radian** is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a *length* of a circular arc on the circumference, a solid angle in steradians, projected onto a sphere, gives the *area* of a spherical cap on the surface. The name is derived from the Greek στερεός *stereos* 'solid' + radian.

The **mole** (symbol **mol**) is the unit of measurement for *amount of substance*, a quantity proportional to the number of elementary entities of a substance. It is a base unit in the International System of Units (SI). One mole contains exactly 6.02214076×10^{23} elementary entities (602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, or other particles. The number of particles in a mole is the **Avogadro number** (symbol *N*_{0}) and the numerical value of the *Avogadro constant* (symbol *N*_{A}) expressed in **mol ^{-1}**. The value was chosen based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of

The **caesium standard** is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

The **metric system** is a system of measurement that succeeded the decimalised system based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as *metrication*.

A **dimensionless quantity** is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time.

A **base unit of measurement** is a unit of measurement adopted for a *base quantity*. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. The SI base units, or *Systeme International d'unites*, consists of the metre, kilogram, second, ampere, kelvin, mole and candela.

A **geometrized unit system**, **geometric unit system** or **geometrodynamic unit system** is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, *c*, and the gravitational constant, *G*, are set equal to unity.

**Quantity** or **amount** is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.

One **turn** is a unit of plane angle measurement equal to *2π* radians, 360 degrees or 400 gradians. Thus it is the angular measure subtended by a complete circle at its center.

The **radian per second** is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency. The radian per second is defined as the angular frequency that results in the angular displacement increasing by one radian every second.

The **International System of Quantities** (**ISQ**) consists of the quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underlies the International System of Units (SI) but does not itself determine the units of measurement used for the quantities.

The **Unified Code for Units of Measure** (**UCUM**) is a system of codes for unambiguously representing measurement units. Its primary purpose is machine-to-machine communication rather than communication between humans.

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

**Quantity calculus** is the formal method for describing the mathematical relations between *abstract* physical quantities.

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.

A **coherent system of units** is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.

- ↑ Suplee, Curt (2 July 2009). "Special Publication 811".
*Nist*. - ↑ International Bureau of Weights and Measures (2006),
*The International System of Units (SI)*(PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021 - ↑ "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures . Retrieved 23 September 2014.

- Media related to SI derived units at Wikimedia Commons

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.