The conversion formula from a linear ratio r into dBFS units is the following: dBFS = 20 * log10(r). The value of r can be different things, but in my case, this is a RMS value divided by the maximum value.

However, the linear to dB conversion formula is dB = 10 * log10(v), so I do not understand why the same formula is not used for dBFS conversion. Why does the extra factor 2 is required in the dBFS formula? Is it some kind of convention we just need to accept or is there a more logical explanation?


1 Answer 1


However, the linear to dB conversion formula is dB = 10 * log10(v)

It is – for power-related units.

For amplitude units, it's $\text{dB} = 20\log_{10}(v)$. Simple as that!

(this serves the purpose that a modification of x dB of the amplitude changes the power by the same amount. Would both use 10·…, things would break. "I amplified my signal by 10 dB" means I scaled the amplitude by $10^{0.5}$, and it means I scaled the power by $10^1$. That's the same thing, because power goes quadratically with amplitude.)

  • $\begingroup$ I can't believe I had no clue about that -_- Thanks! $\endgroup$
    – Tey'
    Commented Jul 15, 2021 at 2:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.