(Untitled) | (Untitled) | (Untitled) | (Untitled) | (Untitled) | Examples |

IEVref: | 112-01-11 | ID: | |||||||||||||||||

Language: | en | Status: Standard | |||||||||||||||||

Term: | dimension of a quantity | ||||||||||||||||||

Synonym1: | quantity dimension [Preferred] | ||||||||||||||||||

Synonym2: | dimension [Preferred] | ||||||||||||||||||

Synonym3: | |||||||||||||||||||

Symbol: | |||||||||||||||||||

Definition: | expression of the dependence of a quantity on the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factor
NOTE 1 – A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity. NOTE 2 – The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. 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 NOTE 3 – In deriving the dimension of a quantity, no account is taken of its scalar, vector or tensor character. NOTE 4 – In a given system of quantities,
– quantities of the same kind have the same dimension,
– quantities of different dimensions are always of different kinds, and
– quantities having the same dimension are not necessarily of the same kind. For example, in the ISQ, pressure and energy density (volumic energy) have the same dimension L NOTE 5 – In the International System of Quantities (ISQ), the symbols representing the dimensions of the base quantities are:
Thus, the dimension of a quantity T^{β}I^{γ}Θ^{δ}N^{ε}J^{ζ}, where the exponents, named dimensional exponents, are positive, negative, or zero. Factors with exponent 0 are usually omitted. When all exponents are zero, the symbol 1, printed in sans-serif type, is used to represent the dimension. Examples are:
^{η}- The dimension of force is dim
*F*= LMT^{–2}. - Mass concentration of a given component and mass density (volumic mass) have the same dimension ML
^{–3}. - Electric current and scalar magnetic potential have the same dimension I
^{1}= I, although they are not quantities of the same kind.
NOTE 6 – An exponent can be fractional. The period $T=2\pi \sqrt{\frac{1}{g}}$ or $T=C(g)\sqrt{l}$ where $C(g)=\frac{2\pi}{\sqrt{g}}$ Hence dim | ||||||||||||||||||

Publication date: | 2010-01 | ||||||||||||||||||

Source: | ISO/IEC GUIDE 99:2007 1.7 | ||||||||||||||||||

Replaces: | |||||||||||||||||||

Internal notes: | 2015-05-07: Version with images replaced by character-based version, and table put into html. JGO 2016-03-09: Math images replaced by MathML. JGO | ||||||||||||||||||

CO remarks: | |||||||||||||||||||

TC/SC remarks: | |||||||||||||||||||

VT remarks: | |||||||||||||||||||

Domain1: | |||||||||||||||||||

Domain2: | |||||||||||||||||||

Domain3: | |||||||||||||||||||

Domain4: | |||||||||||||||||||

Domain5: |

Base quantity |
Symbol for dimension |

length | L |

mass | M |

time | T |

electric current | I |

thermodynamic temperature | Θ |

amount of substance | N |

luminous intensity | J |

Thus, the dimension of a quantity *Q* is denoted by dim *Q* = L* ^{α}*M

- The dimension of force is dim
*F*= LMT^{–2}. - Mass concentration of a given component and mass density (volumic mass) have the same dimension ML
^{–3}. - Electric current and scalar magnetic potential have the same dimension I
^{1}= I, although they are not quantities of the same kind.

$T=2\pi \sqrt{\frac{1}{g}}$ or $T=C(g)\sqrt{l}$ where $C(g)=\frac{2\pi}{\sqrt{g}}$

Hence dim *C*(*g*) = T·L^{−1/2}.