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

EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT^{–2}.

EXAMPLE 2 In the same system of quantities, dim ρ_{B} = ML^{–3} is the quantity dimension of mass concentration of component B, and ML^{–3} is also the quantity dimension of mass density, ρ (volumic mass).

EXAMPLE 3 The period T of a pendulum of length l at a place with the local acceleration of free fall g is

or

where

Hence dim C(g) = L^{–1/2} T.

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 Q is denoted by dim Q.

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 quantity dimension,

- quantities of different quantity dimensions are always of different kinds, and

- quantities having the same quantity dimension are not necessarily of the same kind.

NOTE 5 Symbols representing the dimensions of the base quantities in the ISQ are:

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^{β}T^{γ}I^{δ}Θ^{ε}N^{ζ}J^{η} where the exponents, named dimensional exponents, are positive, negative, or zero.

- 1.1 quantity
- 1.2 kind of quantity
- 1.3 system of quantities
- 1.4 base quantity
- 1.5 derived quantity
- 1.6 International System of Quantities
- 1.7 quantity dimension
- 1.8 quantity of dimension one
- 1.9 measurement unit
- 1.10 base unit
- 1.11 derived unit
- 1.12 coherent derived unit
- 1.13 system of units
- 1.14 coherent system of units
- 1.15 off-system measurement unit
- 1.16 International System of Units
- 1.17 multiple of a unit
- 1.18 submultiple of a unit
- 1.19 quantity value
- 1.20 numerical quantity value
- 1.21 quantity calculus
- 1.22 quantity equation
- 1.23 unit equation
- 1.24 conversion factor between units
- 1.25 numerical value equation
- 1.26 ordinal quantity
- 1.27 quantity-value scale
- 1.28 ordinal quantity-value scale
- 1.29 conventional reference scale
- 1.30 nominal property

- 2.1 measurement
- 2.2 metrology
- 2.3 measurand
- 2.4 measurement principle
- 2.5 measurement method
- 2.6 measurement procedure
- 2.7 reference measurement procedure
- 2.8 primary reference measurement procedure
- 2.9 measurement result
- 2.10 measured quantity value
- 2.11 true quantity value
- 2.12 conventional quantity value
- 2.13 measurement accuracy
- 2.14 measurement trueness
- 2.15 measurement precision
- 2.16 measurement error
- 2.17 systematic measurement error
- 2.18 measurement bias
- 2.19 random measurement error
- 2.20 repeatability condition of measurement
- 2.21 measurement repeatability
- 2.22 intermediate precision condition of measurement
- 2.23 intermediate measurement precision
- 2.24 reproducibility condition of measurement
- 2.25 measurement reproducibility
- 2.26 measurement uncertainty
- 2.27 definitional uncertainty
- 2.28 Type A evaluation of measurement uncertainty
- 2.29 Type B evaluation of measurement uncertainty
- 2.30 standard measurement uncertainty
- 2.31 combined standard measurement uncertainty
- 2.32 relative standard measurement uncertainty
- 2.33 uncertainty budget
- 2.34 target measurement uncertainty
- 2.35 expanded measurement uncertainty
- 2.36 coverage interval
- 2.37 coverage probability
- 2.38 coverage factor
- 2.39 calibration
- 2.40 calibration hierarchy
- 2.41 metrological traceability
- 2.42 metrological traceability chain
- 2.43 metrological traceability to a measurement unit
- 2.44 verification
- 2.45 validation
- 2.46 metrological comparability of measurement results
- 2.47 metrological compatibility of measurement results
- 2.48 measurement model
- 2.49 measurement function
- 2.50 input quantity in a measurement model
- 2.51 output quantity in a measurement model
- 2.52 influence quantity
- 2.53 correction

- 3.1 measuring instrument
- 3.2 measuring system
- 3.3 indicating measuring instrument
- 3.4 displaying measuring instrument
- 3.5 scale of a displaying measuring instrument
- 3.6 material measure
- 3.7 measuring transducer
- 3.8 sensor
- 3.9 detector
- 3.10 measuring chain
- 3.11 adjustment of a measuring system
- 3.12 zero adjustment of a measuring system

- 4.1 indication
- 4.2 blank indication
- 4.3 indication interval
- 4.4 nominal indication interval
- 4.5 range of a nominal indication interval
- 4.6 nominal quantity value
- 4.7 measuring interval
- 4.8 steady-state operating condition
- 4.9 rated operating condition
- 4.10 limiting operating condition
- 4.11 reference operating condition
- 4.12 sensitivity of a measuring system
- 4.13 selectivity of a measuring system
- 4.14 resolution
- 4.15 resolution of a displaying device
- 4.16 discrimination threshold
- 4.17 dead band
- 4.18 detection limit
- 4.19 stability of a measuring instrument
- 4.20 instrumental bias
- 4.21 instrumental drift
- 4.22 variation due to an influence quantity
- 4.23 step response time
- 4.24 instrumental measurement uncertainty
- 4.25 accuracy class
- 4.26 maximum permissible measurement error
- 4.27 datum measurement error
- 4.28 zero error
- 4.29 null measurement uncertainty
- 4.30 calibration diagram
- 4.31 calibration curve

- 5.1 measurement standard
- 5.2 international measurement standard
- 5.3 national measurement standard
- 5.4 primary measurement standard
- 5.5 secondary measurement standard
- 5.6 reference measurement standard
- 5.7 working measurement standard
- 5.8 travelling measurement standard
- 5.9 transfer measurement device
- 5.10 intrinsic measurement standard
- 5.11 conservation of a measurement standard
- 5.12 calibrator
- 5.13 reference material
- 5.14 certified reference material
- 5.15 commutability of a reference material
- 5.16 reference data
- 5.17 standard reference data
- 5.18 reference quantity value