Star Magnitude Comparison Calculator

The magnitude system is logarithmic and inverted, so comparing two objects means converting a difference of magnitudes into a ratio of fluxes. The defining constant is Pogson ratio, the fifth root of 100, which equals 2.5119: five magnitudes correspond to exactly a factor of 100 in brightness. The comparison therefore reduces to ratio = 10^((m2 - m1)/2.5), and the star with the smaller or more negative value is always the brighter one. A difference of 0.75 magnitude is a factor of 2, one magnitude is 2.512, and 2.5 magnitudes is exactly 10. Combining two sources runs the arithmetic backwards: convert each magnitude to a relative flux with 10^(-m/2.5), add the fluxes, then take -2.5 log10 of the sum. Two equally bright stars combine to 0.753 magnitude brighter than either alone, which is why unresolved binaries look brighter than their components. Useful anchors span about 58 magnitudes: the Sun at -26.74, the full Moon at -12.7, Venus near -4.6 at maximum, Sirius at -1.46, Vega at +0.03, the naked-eye limit near +6.0, and the faintest Hubble detections beyond +31. The critical caveat is that a magnitude is meaningless without a passband. Values usually refer to Johnson V unless stated, and the same star has different B, V and R magnitudes - their differences form the color index that measures temperature. Atmospheric extinction of roughly 0.2 magnitude per airmass in V at sea level means an object low in the sky measures fainter than its catalogued value, and variable stars such as Algol shift by about 1.3 magnitudes on a 2.87-day cycle.

The scale is one of the oldest quantitative systems still in scientific use. Hipparchus of Nicaea compiled a star catalogue in the second century BC that sorted naked-eye stars into six ranks, the first being brightest and the sixth barely visible. Ptolemy carried the scheme into the Almagest around 150 AD, and it passed essentially unchanged through Islamic and European astronomy for roughly 1,700 years. The telescope broke its boundaries - Galileo saw stars fainter than sixth rank in 1610 - but the classes stayed qualitative and inconsistent between observers. John Herschel established in the 1830s that a first-magnitude star is about a hundred times brighter than a sixth-magnitude one, supplying the empirical basis for a definition. Norman Robert Pogson, then working at the Radcliffe Observatory in Oxford, proposed in 1856 that the ratio be fixed at exactly 100^(1/5) per magnitude step, deliberately preserving the classical numbers while making them precise; the astronomical community adopted it, and the constant carries his name. Edward Pickering large-scale photometry at Harvard from the 1880s produced the first consistent catalogues on that footing. Joel Stebbins pioneered photoelectric photometry from around 1907, replacing eye estimates with instrumental precision, Harold Johnson and William Morgan defined the standard UBV passband system in 1953, and John Oke and James Gunn introduced the AB magnitude system in 1983, tying magnitudes directly to physical flux density rather than to a reference star.