I need to calculate a percentage difference of a B-V colour index between its estimated and actual value. So I tried doing this by difference between values/actual value x 100. However as B-V values can be on either side of zero this did not give representative answers.

So if anyone knows a way of calculating percentages of values close to zero or on either side of zero their help would be appreciated.



$B-V$ corresponds to the base 10 logarithm of a flux ratio.

$$B-V = -2.5 \log \left(\frac{f_B}{f_V}\right)$$

So trying to guess what you are trying to calculate, it is the percentage change in the blue to visible flux ratio?

In which case the percentage change is $$ p = \frac{ 10^{-(B-V)_2/2.5} - 10^{-(B-V)_1/2.5}}{10^{-(B-V)_1/2.5}}\times 100$$

A percentage change can of course be negative.


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