If the spectral flux density is denoted fν, the monochromatic AB magnitude is: or, with fν still in janskys, The exact definition is stated relative to the cgs units of erg s−1 cm−2 Hz−1: Inverting this leads to the true definition of the numerical value "3631 Jy" often cited: Actual measurements are always made across some continuous range of wavelengths.
The bandpass AB magnitude is defined so that the zero point corresponds to a bandpass-averaged spectral flux density of about 3631 Jy: where e(ν) is the "equal-energy" filter response function and the (hν)−1 term assumes that the detector is a photon-counting device such as a CCD or photomultiplier.
The STMAG system is similarly defined, but for constant flux per unit wavelength interval instead.
[3] This must not be confused with absolute magnitude in the sense of the apparent brightness of an object if seen from a distance of 10 parsecs.
However, because all magnitude systems involve integration of some assumed source spectrum over some assumed passband, such conversions are not necessarily trivial to calculate, and precise conversions depend on the actual bandpass of the observations in question.