# Power, root-power, and field quantities

A **power quantity** is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity, and luminous intensity.^{[1]} Energy quantities may also be labelled as power quantities in this context.^{[2]}

A **root-power quantity** is a quantity such as voltage, current, sound pressure, electric field strength, speed, or charge density, the square of which, in linear systems, is proportional to power.^{[3]} The term *root-power quantity* refers to the square root that relates these quantities to power. The term was introduced in ISO 80000-1 § Annex C; it replaces and deprecates the term **field quantity**.

## Implications[edit]

It is essential to know which category a measurement belongs to when using decibels (dB) for comparing the levels of such quantities. A change of one bel in the level corresponds to a 10× change in *power*, so when comparing power quantities *x* and *y*, the difference is defined to be 10×log_{10}(*y*/*x*) decibel. With root-power quantities, however the difference is defined as 20×log_{10}(*y*/*x*) dB.^{[3]}

In the analysis of signals and systems using sinusoids, field quantities and root-power quantities may be complex-valued.^{[4]}^{[5]}^{[6]}^{[disputed – discuss]}

## "Root-power quantity" vs. "field quantity"[edit]

In justifying the deprecation of the term "field quantity" and instead using "root-power quantity" in the context of levels, ISO 80000 draws attention to the conflicting use of the former term to mean a quantity that depends on the position,^{[7]} which in physics is called a *field*. Such a field is often called a *field quantity* in the literature, but is called a *field* here for clarity. Several types of field (such as the electromagnetic field) meet the definition of a root-power quantity, whereas others (such as the Poynting vector and temperature) do not. Conversely, not every root-power quantity is a field (such as the voltage on a loudspeaker).

## See also[edit]

- Level (logarithmic quantity)
- Fresnel reflection field and power equations
- Sound level, defined for each of several quantities associated with sound

## References[edit]

**^**Ainslie, Michael A. (Winter 2015). "A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound" (PDF).*Acoustics Today*.**11**(1): 12–19.**^**ISO 80000:1-2009 § C.3- ^
^{a}^{b}Brian C.J. Moore (1995).*Hearing*. Academic Press. p. 11. ISBN 978-0-08-053386-5. **^**ISO 80000-1:2009 § C.2**^**ISO 80000-3:2006 § 0.5**^**IEC 60027-3:2002**^**ISO 80000-1:2009 § C.2