FFT with windowing amplitude correction

I am trying to calculate the FFT of a pressure signal with the correct amplitude, as I want to calculate the resulting sound pressure level from the FFT.

Basically, I can calculate the FFT amplitude correctly when I don't use a window, but I want to use a Hanning window and I do not know how to normalize for the window power. In the code below, from this post https://www.mathworks.com/matlabcentral/answers/33653-psd-estimation-fft-vs-welch, the FFT is normalized by window power by taking FFT/(window'*window). However, the FFT is never normalized by dividing by the length Nx of the signal. But still, the correct PSD is found. From what I can understand, the result from pwelch should also be scaled before it can be used to obtain the correct sound pressure levels.

 Fs = 1024; 
 t  = (0:1/Fs:1-1/Fs).'; 
 x  = sin(2*pi*t*200);
 Nx = length(x);

 % Window data
 w = hanning(Nx);
 xw = x.*w; 

 % Calculate power
 nfft = Nx; 
 X = fft(xw,nfft);
 mx = abs(X).^2; 

 % Normalize by window power. Multiply by 2 (except DC & Nyquist) 
 % to calculate one-sided spectrum. Divide by Fs to calculate 
 % spectral  density.
 mx = mx/(w'*w); 
 NumUniquePts = nfft/2+1; 
 mx = mx(1:NumUniquePts);
 mx(2:end-1) = mx(2:end-1)*2;
 Pxx1 = mx/Fs;
 Fx1 = (0:NumUniquePts-1)*Fs/nfft; 

 [Pxx2,Fx2] = pwelch(x,w,0,nfft,Fs);

 plot(Fx1,10*log10(Pxx1),Fx2,10*log10(Pxx2),'r:');
 legend('PSD via FFT','PSD via pwelch')

If someone can please clarify exactly how to calculate a windowed FFT of which the amplitude is correctly scaled for signal length and window power, it would be greatly appreciated. Matlab's documentation is not very clear on the subject.

[Elliott Martinson]

you're normalizing after squaring.

should normalize BEFORE you square the fft results. Otherwise you could (i suppose) square the normalization factors as well, but that seems silly