# Formula to calculate B-V index? [duplicate]

Is there a formlua or equation to calculate a star's B-V index based on it's observed frequencies in the B and V spectrums ? I have unfortunately not been able to find anything...

$$B-V = -2.5 \log_{10} \left(\frac{f_B}{f_V}\right)$$
Those are magnitudes on the left. Five magnitudes are a factor of 100, so 2.5 magnitudes are a factor of 10. So if $$f_B/f_V =$$ 100 (i.e. 10$$^2$$) then $$B-V =$$5.
• This is from the standard relationship between flux and magnitude e.g. en.m.wikipedia.org/wiki/Apparent_magnitude (Note: $f_B$ here is flux in the Bessell/Johnson B filter, not frequency) – astrosnapper Nov 23 '19 at 18:35