Derived scientific quantities with special names

Several derived quantities are so important that convenient names are given for them such as rate, flux, moment, wavelength, etcetera. These are summarized in the following table.

Recommended names and symbols; standard definitions; and quantity dimensions of derived scientific quantities of relevance for physics, chemistry, biology, and other disciplines

name	symbols	definition	dimension
† also flow or current †† formerly specific quantity; the lower case letter is the symbol of the massic quantity when the symbol of the quantity is a capital letter, otherwise it is not predefined ††† formerly quantity density †‡ formerly surface density of quantity ‡ formerly linear density of quantity
rate of scalar quantity	\( \dot{Q} \)	\( \displaystyle \frac{\mathrm{d} Q}{\mathrm{d} t} \)	\( \mathrm{Q} \;\mathrm{T}^{−1} \)
flux† of vector quantity	\( \dot{\mathbf{Q}} \)	\( \displaystyle \frac{\mathrm{d} \mathbf{Q}}{\mathrm{d} t} \)	\( \mathrm{Q} \;\mathrm{T}^{−1} \)
molar quantity	\( Q_m \)	\( \displaystyle \frac{Q}{n} \)	\( \mathrm{Q} \;\mathrm{N}^{-1} \)
massic quantity††	\( q \)	\( \displaystyle \frac{Q}{m} \)	\( \mathrm{Q} \;\mathrm{M}^{-1} \)
entitic quantity	\( Q_N \)	\( \displaystyle \frac{Q}{N} \)	\( \mathrm{Q} \)
pquantity	\( \mathrm{p} Q \)	\( \displaystyle -\mathrm{lg} \left( \frac{Q}{[Q]} \right) \)	\( \mathrm{1} \)
volumic quantity†††	\( Q_V \)	\( \displaystyle \frac{Q}{V \;} \)	\( \mathrm{Q} \;\mathrm{L}^{-3} \)
areic quantity†‡	\( Q_A \)	\( \displaystyle \frac{Q}{A \;} \)	\( \mathrm{Q} \;\mathrm{L}^{-2} \)
lineic quantity‡	\( Q_l \)	\( \displaystyle \frac{Q}{l} \)	\( \mathrm{Q} \;\mathrm{L}^{-1} \)
quantity fraction	\( Q_i \)	\( \displaystyle \frac{Q_i}{Q_i + \sum_{j \neq i} Q_j} \)	\( \mathrm{1} \)
frequency spectral quantity	\( Q_\nu \)	\( \displaystyle \frac{Q}{\nu} \)	\( \mathrm{Q} \;\mathrm{T} \)
wavenumber spectral quantity	\( Q_\tilde{\nu} \)	\( \displaystyle \frac{Q}{\tilde{\nu}} \)	\( \mathrm{Q} \;\mathrm{L} \)
wavelength spectral quantity	\( Q_\lambda \)	\( \displaystyle \frac{Q}{\lambda} \)	\( \mathrm{Q} \;\mathrm{L}^{-1} \)
moment of vector quantity	\( \mathbf{M} \)	\( r \times \mathbf{Q} \)	\( \mathrm{Q} \;\mathrm{L} \)

The new terms volumic quantity, areic quantity, and lineic quantity are systematic and avoid the ambiguities associated to the old terms.

Many references, including early IUPAP/IUPAC recommendations, confound the flow of a quantity with the flow per unit area –i.e., with the areic flow–. Recent IUPAP/IUPAC recommendations 1 propose the term flux for the flow and the term flux density for the areic flow. However, their recent recommendation is ambiguous, because by density they really mean surface density i.e., flow per area instead per volume. Moreover, to increase the confusion, many older references use the terms flux and flux density as if they were synonyms. We prefer the more systematic and unambiguous terminology presented above. Notice that the rate of any extensive quantity can be transformed into a flux by multiplying it by the unit vector in the direction of the flow; for instance, the flux of mass \( \dot{\mathbf{m}} = (\mathrm{d}\mathbf{m}/\mathrm{d}t) = (\mathrm{d}m/\mathrm{d}t) \mathbf{e} \), where \( \mathbf{e} \) is the unit vector.