Relation between output and dB

[Migaspin]

I've been developing a project with help of this library. It consists in an arduino board capable of identifying sound pollution. The code I'm using was found in here and was adapted to my needs. The code is the following:

#include <arduinoFFT.h>
 
#define SAMPLES 128             //Must be a power of 2
#define SAMPLING_FREQUENCY 10000 //Hz, must be less than 10000 due to ADC
 
arduinoFFT FFT = arduinoFFT();
 
unsigned int sampling_period_us;
unsigned long microseconds;
 
double vReal[SAMPLES];
double vImag[SAMPLES];
 
void setup() {
    Serial.begin(115200);
 
    sampling_period_us = round(1000000*(1.0/SAMPLING_FREQUENCY));
}
 
void loop() {
   
    /*SAMPLING*/
    for(int i=0; i<SAMPLES; i++)
    {
        microseconds = micros();    //Overflows after around 70 minutes!
     
        vReal[i] = analogRead(36);
        vImag[i] = 0;
     
        while(micros() < (microseconds + sampling_period_us)){
        }
    }
 
    /*FFT*/
    FFT.Windowing(vReal, SAMPLES, FFT_WIN_TYP_HAMMING, FFT_FORWARD);
    FFT.Compute(vReal, vImag, SAMPLES, FFT_FORWARD);
    FFT.ComplexToMagnitude(vReal, vImag, SAMPLES);
    double peak = FFT.MajorPeak(vReal, SAMPLES, SAMPLING_FREQUENCY);
 
    /*PRINT RESULTS*/
    //Serial.println(peak);     //Print out what frequency is the most dominant.
 
    for(int i=0; i<(SAMPLES/2); i++)
    {
        /*View all these three lines in serial terminal to see which frequencies has which amplitudes*/
         
        //Serial.print((i * 1.0 * SAMPLING_FREQUENCY) / SAMPLES, 1);
        //Serial.print(" ");
        Serial.println(vReal[i], 1);    //View only this line in serial plotter to visualize the bins
    }
 
    delay(1000);  //Repeat the process every second OR:
    //while(1);       //Run code once
}

I've been trying for a while now to figure out a relation between the values provided by the program and a decibel value.

Any ideas?

[HorstBaerbel]

If you want to get real-world dB values this is not so easy, as you have to take into account the non-linearity of your microphone (see this).
In general you can convert complex values to dB using: magnitude_dB = 20 * log10(magnitude_complex).