A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB).
A field level (or root-power level) is a logarithmic quantity used to measure quantities of which the square is typically proportional to power (for instance, the square of Voltage is proportional to Power by the inverse of the conductor's Resistance), etc., with commonly used units neper (Np) or decibel (dB).
The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and its reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards.
The ISO standard defines each of the quantities power level and field level to be dimensionless, with 1 Np = 1. This is motivated by simplifying the expressions involved, as in systems of natural units.
Logarithmic ratio quantityEdit
Power and field quantities are part of a larger class, logarithmic ratio quantities.
ANSI/ASA S1.1-2013 defines a class of quantities it calls levels. It defines a level of a quantity Q, denoted LQ, as
r is the base of the logarithm;
Q is the quantity;
Q0 is the reference value of Q.
For the level of a root-power quantity, the base of the logarithm is r = e.
For the level of a power quantity, the base of the logarithm is r = e2.
Frequency level of a frequency f is the logarithm of a ratio of the frequency f to a reference frequency f0. The reference frequency is C0, four octaves below middle C. 
In electronics, the octave (oct) is used as a unit with logarithm base 2, and the decade (dec) is used as a unit with logarithm base 10: