<p>I found :</p>

<p><span class="math-container">$$B-V = -2.5 \log_{10} \left(\frac{f_B}{f_V}\right)$$</span></p>

<p>From <a href="https://astronomy.stackexchange.com/questions/14059/how-to-calculate-b-v-colour-index-value-percentage-difference/14062#14062">this</a> question. It works for my purposes.</p>

<p>Those are magnitudes on the left. Five magnitudes are a factor of 100, so 2.5 magnitudes are a factor of 10. So if <span class="math-container">$f_B/f_V =$</span> 100 (i.e. 10<span class="math-container">$^2$</span>) then <span class="math-container">$B-V =$</span>5. </p>

CC BY-SA 4.0
2019-11-23T18:35:42.590Z
This is from the standard relationship between flux and magnitude e.g. https://en.m.wikipedia.org/wiki/Apparent_magnitude (Note: $f_B$ here is *flux* in the Bessell/Johnson B filter, not frequency)
astrosnapper
CC BY-SA 4.0
2019-11-24T12:04:19.633Z
I made a small edit and noted that that's base-10 log. Feel free to edit further if this helps, or roll back if it doesn't. In a few days if nobody leaves an answer you find more helpful, you can also accept your own answer.
uhoh
CC BY-SA 4.0
2019-11-23T14:43:43.910Z
2019-11-24T12:03:26.640Z
2019-11-24T12:03:26.640Z
A.D
<p>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...</p>

<luminosity>
Formula to calculate B-V index?
A.D
# Formula to calculate B-V index?

(Asked by: username_0 on 2019-11-23)

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...

**Tags:** luminosity

---

## 1 answers

### Answer by username_0 on 2019-11-23. Score: 2 | Accepted answer

I found :

$$B-V = -2.5 \log\_{10} \left(\frac{f\_B}{f\_V}\right)$$

From [this](https://astronomy.stackexchange.com/questions/14059/how-to-calculate-b-v-colour-index-value-percentage-difference/14062#14062) question. It works for my purposes.

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.

> **Comments:**
> **username_1**: This is from the standard relationship between flux and magnitude e.g. https://en.m.wikipedia.org/wiki/Apparent_magnitude (Note: $f_B$ here is *flux* in the Bessell/Johnson B filter, not frequency)  
> **username_2**: I made a small edit and noted that that's base-10 log. Feel free to edit further if this helps, or roll back if it doesn't. In a few days if nobody leaves an answer you find more helpful, you can also accept your own answer.  

---

