Title :Deived Units

Category: Math

Derived units are formed by powers, products or quotients of the base units and are unlimited in number;Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and distance which, in SI, has the dimensions metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Coherent units are derived units that contain no numerical factor other than 1—quantities such as standard gravity and density of water are absent from their definitions. In the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s−2 respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s−2. Since the newton is part of a coherent set of units, the constant of proportionality is 1.

For the sake of convenience, some derived units have special names and symbols. Such units may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as "newtons per square metre" (N/m2).[39]

Named units derived from SI base units

Name-Symbol-Quantity- Equivalents- Equivalents

hertz Hz frequency 1/s s−1

radian rad angle m/m dimensionless

steradian sr solid angle m2/m2 dimensionless

newton N force, weight kg⋅m/s2 kg⋅m⋅s−2

pascal Pa pressure, stress N/m2 kg⋅m(^−1)⋅s(^−2)

N⋅m

joule J energy, work, C⋅V kg⋅m2⋅s(^−2)

heat W⋅s

J/s

watt W power, radiant, V⋅A kg⋅m2⋅s(^-3)

flux

coulomb C electric charge or s⋅A s⋅A

quantity of electricity

volt V voltage, electrical W/A kg⋅m2⋅s−3⋅A−1

potential difference,

electromotive force

farad F electrical capacitance C/V kg−1⋅m−2⋅s4⋅A2

s/Ω

ohm Ω electrical resistance, V/A kg⋅m2⋅s−3⋅A−2

impedance, reactance

siemens S electrical conductance A/V kg−1⋅m−2⋅s3⋅A2

1/Ω

weber Wb magnetic flux V⋅s/ kg⋅m2⋅s−2⋅A−1

J/A

tesla T magnetic field strength, Wb/m(^2) kg⋅s−2⋅A−1

magnetic flux density or V⋅s/m2

henry H inductance V⋅s/A kg⋅m2⋅s−2⋅A−2

Wb/A

degree °C temperature relative K- 273.15 K - 273.15

Celsius to 273.15 K/

lumen lm luminous flux cd⋅sr cd

lux lx illuminance lm/m2 m−2⋅cd

becquerel Bq radioactivity 1/s s−1

(decays per unit time)

gray Gy absorbed dose J/kg m2⋅s−2

(of ionizing radiation)

sievert Sv equivalent dose J/kg m2⋅s−2

(of ionizing radiation)

katal kat catalytic activity mol/s s−1⋅mol

Category: Math

Derived units are formed by powers, products or quotients of the base units and are unlimited in number;Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and distance which, in SI, has the dimensions metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Coherent units are derived units that contain no numerical factor other than 1—quantities such as standard gravity and density of water are absent from their definitions. In the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s−2 respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s−2. Since the newton is part of a coherent set of units, the constant of proportionality is 1.

For the sake of convenience, some derived units have special names and symbols. Such units may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as "newtons per square metre" (N/m2).[39]

Named units derived from SI base units

Name-Symbol-Quantity- Equivalents- Equivalents

hertz Hz frequency 1/s s−1

radian rad angle m/m dimensionless

steradian sr solid angle m2/m2 dimensionless

newton N force, weight kg⋅m/s2 kg⋅m⋅s−2

pascal Pa pressure, stress N/m2 kg⋅m(^−1)⋅s(^−2)

N⋅m

joule J energy, work, C⋅V kg⋅m2⋅s(^−2)

heat W⋅s

J/s

watt W power, radiant, V⋅A kg⋅m2⋅s(^-3)

flux

coulomb C electric charge or s⋅A s⋅A

quantity of electricity

volt V voltage, electrical W/A kg⋅m2⋅s−3⋅A−1

potential difference,

electromotive force

farad F electrical capacitance C/V kg−1⋅m−2⋅s4⋅A2

s/Ω

ohm Ω electrical resistance, V/A kg⋅m2⋅s−3⋅A−2

impedance, reactance

siemens S electrical conductance A/V kg−1⋅m−2⋅s3⋅A2

1/Ω

weber Wb magnetic flux V⋅s/ kg⋅m2⋅s−2⋅A−1

J/A

tesla T magnetic field strength, Wb/m(^2) kg⋅s−2⋅A−1

magnetic flux density or V⋅s/m2

henry H inductance V⋅s/A kg⋅m2⋅s−2⋅A−2

Wb/A

degree °C temperature relative K- 273.15 K - 273.15

Celsius to 273.15 K/

lumen lm luminous flux cd⋅sr cd

lux lx illuminance lm/m2 m−2⋅cd

becquerel Bq radioactivity 1/s s−1

(decays per unit time)

gray Gy absorbed dose J/kg m2⋅s−2

(of ionizing radiation)

sievert Sv equivalent dose J/kg m2⋅s−2

(of ionizing radiation)

katal kat catalytic activity mol/s s−1⋅mol

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