# How to convert frequency into db

I have made an Arduino circuit which outputs in terms of frequency(hz) and I need output in terms of db as well

So is there any formula which can I apply to convert frequency hertz to db or is there any reference link to understand the conversion process.

Any help will be highly appreciated

• Sad to see both answers reversed the required capitalization of "dB" – Chris Stratton Dec 12 '15 at 4:11
• My answer was written on my tablet that capitalises the first letter of a sentence for you automatically. Too much haastle to change it for just one symbol... however the question doesn't have any capitalization, correct or otherwise ;) – Majenko Dec 12 '15 at 11:18

dB is volume (sound pressure), frequency is pitch. The two are entirely different concepts and can't be converted. A bit like you can't convert the roundness of a doughnut into blue. Roundness and blueness (it has blueberries in it by the way) are two different properties of the doughnut.

dB it self just express in a logarithmic scale a ratio between two values and it self is unit independent (because is a ratio). Just because the most common uses of dB scales are linked to intensity or power doesn't necessarily mean that can't be used to represent other ratios of different types of quantities. Or at least I couldn't find any definition that restricts the use of dB in such cases. The formulas to express such ratio are present here you just have to figured it out what is really your ratio.

So, for example, if you have some kind of sensor that somehow the output is a frequency, let's say something like

``````f(x) = ax + f0  [Hz]
``````

There is no reason why you can't express this function in a logarithmic ratio scale using dB something like, related to f0 or f(x=0)

``````L(x) = 10*Log10*(f(x)/f0) [dB]
``````

which would give you the represented dB output of your equation with respect to x.

But since we are in arduino stackexchange and talking about sensor, the common use of dB in electronics is the representation of power ratio or (the more common) a frequency response of a circuit(or system) that is represented by a Bode Plot, so I advise you to really take a good look at both links and try to figure what you really are asked to represent.

• Great answer! Not many would have thought about the real definition of dB. – Rob Dec 12 '15 at 20:50

Decibels (Db) are calculated using amplitudes and by definition decibels are the measurement of sound intensity or power level of electrical signal by comparing it with a given level on a logarithmic scale, which is independent of frequency.

You can measure the decibels though if you know the amplitude of your source which i'm guessing is ~5v .