The
Contents 1 Base quantities 2 Derived quantities 2.1 Dimensions of derived quantities 2.2 Logarithmic quantities 2.2.1 Level 2.2.2 Information entropy 3 See also 4 References 5 Further reading Base quantities[edit] A base quantity is a physical quantity in a subset of a given system of quantities that is chosen by convention, where no quantity in the set can be expressed in terms of the others. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics.[4] The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif[5] type. Base quantity
Symbol for quantity[6]
Symbol for dimension
SI unit
length l displaystyle l L displaystyle mathsf L metre m mass m displaystyle m M displaystyle mathsf M kilogram kg time t displaystyle t T displaystyle mathsf T second s electric current I displaystyle I I displaystyle mathsf I ampere A thermodynamic temperature T displaystyle T Θ displaystyle mathsf Theta kelvin K amount of substance n displaystyle n N displaystyle mathsf N mole mol luminous intensity I v displaystyle I_ text v J displaystyle mathsf J candela cd Derived quantities[edit] See also: Dimensional analysis A derived quantity is a quantity in a system of quantities that is a defined in terms of the base quantities of that system. The ISQ defines many derived quantities. Dimensions of derived quantities[edit] The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by L a M b T c I d Θ e N f J g displaystyle mathsf L ^ a mathsf M ^ b mathsf T ^ c mathsf I ^ d mathsf Theta ^ e mathsf N ^ f mathsf J ^ g , where the dimensional exponents are positive, negative, or zero. The symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted L T − 1 displaystyle mathsf LT ^ -1 . The following table lists some quantities defined by the ISQ. A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is 1 displaystyle 1 . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension. Derived quantity Symbol for dimension plane angle 1 displaystyle 1 solid angle 1 displaystyle 1 frequency T − 1 displaystyle mathsf T ^ -1 force L M T − 2 displaystyle mathsf LMT ^ -2 pressure L − 1 M T − 2 displaystyle mathsf L ^ -1 mathsf MT ^ -2 velocity L T − 1 displaystyle mathsf LT ^ -1 area L 2 displaystyle mathsf L ^ 2 volume L 3 displaystyle mathsf L ^ 3 acceleration L T − 2 displaystyle mathsf LT ^ -2 Logarithmic quantities[edit] Level[edit] In the ISQ, the level of a quantity is a logarithmic quantification of the ratio of the quantity with a stated reference value of that quantity. It is differently defined for a root-power quantity (also known by the deprecated term field quantity) and for a power quantity. It is not defined for ratios of quantities of other kinds. The level of a root-power quantity F textstyle F with reference to a reference value of the quantity F 0 textstyle F_ 0 is defined as L F = ln F F 0 , displaystyle L_ F =ln frac F F_ 0 , where ln displaystyle ln is the natural logarithm. The level of a power quantity quantity P textstyle P with reference to a reference value of the quantity P 0 textstyle P_ 0 is defined as L P = ln P P 0 = 1 2 ln P P 0 . displaystyle L_ P =ln sqrt frac P P_ 0 = frac 1 2 ln frac P P_ 0 . When the natural logarithm is used, as it is here, use of the neper (symbol Np) is recommended, a unit of dimension 1 with Np = 1. The neper is coherent with SI. Use of the logarithm base 10 in association with a scaled unit, the bel (symbol B), where B = ( 1 2 ln 10 ) Np ≈ 1.151293 Np textstyle text B =( frac 1 2 ln 10) text Np approx text 1.151293 Np . An example of level is sound pressure level. All levels of the ISQ are treated as derived quantities of dimension 1. Information entropy[edit] The ISQ recognizes another logarithmic quantity: information entropy, for which the coherent unit is the natural unit of information (symbol nat).[citation needed] See also[edit] List of physical quantities Quantity Observable quantity References[edit] ^ "1.16". International vocabulary of metrology – Basic and general
concepts and associated terms (VIM) (PDF) (3rd ed.). International
Bureau of Weights and Measures (BIPM):Joint Committee for Guides in
Metrology. 2012. Retrieved 28 March 2015.
^
Further reading[edit] B. N. Taylor, Ambler Thompson,
v t e SI base quantities Base quantity Quantity SI unit Name Symbol Dimension symbol Unit name (symbol) Example length l, x, r, (etc.) L metre (m) r = 10 m mass m M kilogram (kg) m = 10 kg time, duration t T second (s) t = 10 s electric current I , i I ampere (A) I = 10 A thermodynamic temperature T Θ kelvin (K) T = 10 K amount of substance n N mole (mol) n = 10 mol luminous intensity Iv J candela (cd) Iv = 10 cd Specification The quantity (not the unit) can have a specification: Tmax = 300 K Derived quantity Definition A quantity Q is expressed in the base quantities: Q = f ( l , m , t , I , T , n , I v ) displaystyle Q=fleft( mathit l,m,t,I,T,n,I mathrm _ v right) Derived dimension dim Q = La · Mb · Tc · Id · Θe · Nf · Jg (Superscripts a–g are algebraic exponents, usually a positive, negative or zero integer.) Example
See also History of the metric system International System of Quantities Proposed redefinitions Systems of measurement Book |

The
Contents 1 Base quantities 2 Derived quantities 2.1 Dimensions of derived quantities 2.2 Logarithmic quantities 2.2.1 Level 2.2.2 Information entropy 3 See also 4 References 5 Further reading Base quantities[edit] A base quantity is a physical quantity in a subset of a given system of quantities that is chosen by convention, where no quantity in the set can be expressed in terms of the others. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics.[4] The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif[5] type. Base quantity
Symbol for quantity[6]
Symbol for dimension
SI unit
length l displaystyle l L displaystyle mathsf L metre m mass m displaystyle m M displaystyle mathsf M kilogram kg time t displaystyle t T displaystyle mathsf T second s electric current I displaystyle I I displaystyle mathsf I ampere A thermodynamic temperature T displaystyle T Θ displaystyle mathsf Theta kelvin K amount of substance n displaystyle n N displaystyle mathsf N mole mol luminous intensity I v displaystyle I_ text v J displaystyle mathsf J candela cd Derived quantities[edit] See also: Dimensional analysis A derived quantity is a quantity in a system of quantities that is a defined in terms of the base quantities of that system. The ISQ defines many derived quantities. Dimensions of derived quantities[edit] The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by L a M b T c I d Θ e N f J g displaystyle mathsf L ^ a mathsf M ^ b mathsf T ^ c mathsf I ^ d mathsf Theta ^ e mathsf N ^ f mathsf J ^ g , where the dimensional exponents are positive, negative, or zero. The symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted L T − 1 displaystyle mathsf LT ^ -1 . The following table lists some quantities defined by the ISQ. A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is 1 displaystyle 1 . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension. Derived quantity Symbol for dimension plane angle 1 displaystyle 1 solid angle 1 displaystyle 1 frequency T − 1 displaystyle mathsf T ^ -1 force L M T − 2 displaystyle mathsf LMT ^ -2 pressure L − 1 M T − 2 displaystyle mathsf L ^ -1 mathsf MT ^ -2 velocity L T − 1 displaystyle mathsf LT ^ -1 area L 2 displaystyle mathsf L ^ 2 volume L 3 displaystyle mathsf L ^ 3 acceleration L T − 2 displaystyle mathsf LT ^ -2 Logarithmic quantities[edit] Level[edit] In the ISQ, the level of a quantity is a logarithmic quantification of the ratio of the quantity with a stated reference value of that quantity. It is differently defined for a root-power quantity (also known by the deprecated term field quantity) and for a power quantity. It is not defined for ratios of quantities of other kinds. The level of a root-power quantity F textstyle F with reference to a reference value of the quantity F 0 textstyle F_ 0 is defined as L F = ln F F 0 , displaystyle L_ F =ln frac F F_ 0 , where ln displaystyle ln is the natural logarithm. The level of a power quantity quantity P textstyle P with reference to a reference value of the quantity P 0 textstyle P_ 0 is defined as L P = ln P P 0 = 1 2 ln P P 0 . displaystyle L_ P =ln sqrt frac P P_ 0 = frac 1 2 ln frac P P_ 0 . When the natural logarithm is used, as it is here, use of the neper (symbol Np) is recommended, a unit of dimension 1 with Np = 1. The neper is coherent with SI. Use of the logarithm base 10 in association with a scaled unit, the bel (symbol B), where B = ( 1 2 ln 10 ) Np ≈ 1.151293 Np textstyle text B =( frac 1 2 ln 10) text Np approx text 1.151293 Np . An example of level is sound pressure level. All levels of the ISQ are treated as derived quantities of dimension 1. Information entropy[edit] The ISQ recognizes another logarithmic quantity: information entropy, for which the coherent unit is the natural unit of information (symbol nat).[citation needed] See also[edit] List of physical quantities Quantity Observable quantity References[edit] ^ "1.16". International vocabulary of metrology – Basic and general
concepts and associated terms (VIM) (PDF) (3rd ed.). International
Bureau of Weights and Measures (BIPM):Joint Committee for Guides in
Metrology. 2012. Retrieved 28 March 2015.
^
Further reading[edit] B. N. Taylor, Ambler Thompson,
v t e SI base quantities Base quantity Quantity SI unit Name Symbol Dimension symbol Unit name (symbol) Example length l, x, r, (etc.) L metre (m) r = 10 m mass m M kilogram (kg) m = 10 kg time, duration t T second (s) t = 10 s electric current I , i I ampere (A) I = 10 A thermodynamic temperature T Θ kelvin (K) T = 10 K amount of substance n N mole (mol) n = 10 mol luminous intensity Iv J candela (cd) Iv = 10 cd Specification The quantity (not the unit) can have a specification: Tmax = 300 K Derived quantity Definition A quantity Q is expressed in the base quantities: Q = f ( l , m , t , I , T , n , I v ) displaystyle Q=fleft( mathit l,m,t,I,T,n,I mathrm _ v right) Derived dimension dim Q = La · Mb · Tc · Id · Θe · Nf · Jg (Superscripts a–g are algebraic exponents, usually a positive, negative or zero integer.) Example
See also History of the metric system International System of Quantities Proposed redefinitions Systems of measurement Book |

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