PSD to SPL Conversion

Hi everybody,

I want to convert some data from PSD, with unity [dB/Hz], for SPL, with unity [dB].

Let us say that my frequency vector is 'f = [500 525 575 675 825]', in [Hz], and my spectrum vector is = [80 79 78 77 76 75].

I know that 'SPL = 10*log10((p^2)/(p_{ref}^2))', with 'p' and 'p_{ref}' in [Pa] (Pascal).

To evaluate my PSD data I've done 'PSD = 10*log10(pi/(p_ref^2))', with 'pi' in [Pa^2/Hz] (data from my cross-spectrum matrix).

So how do I convert 'p' into 'pi' in a way to have my results in SPL? I know that it is not so simple as 'pi = p*deltaf', with 'deltaf' being the difference between neighbour frequencies (I've tried it and the results do not make any sense).

I appreciate if anybody could help.

Thanks!