I decided to run some tests on an actual chip connected to the bench power supply.
Code:
#Picaxe 08M2
#Terminal 4800
Symbol SAMPLES = 128
Symbol Nref = w0
Symbol total = w1
Symbol average = w2
Symbol counter = w3
Do
total = 0
For counter = 1 To SAMPLES
CalibAdc10 nref
total = total + nref
Next
average = total / SAMPLES
SerTxd( #average, " " )
Pause 1000
Loop
This gave the following results and what "K" would be to determine the supply voltage from the actual reading using "Vpsu=K/Nref" ...
Code:
Vpsu Nref K
5.5 191 1050.5
5.0 211 1055.0
4.5 234 1053.0
4.0 263 1052.0
3.5 301 1053.5
3.0 351 1053.0
2.5 421 1052.5
What a single "K" value should be is rather hard to say, and probably depends upon which range one wanted to have least errors for.
Ignoring above 5V, the K*50 to maximise PICAXE maths resolution for this case would be between 52600 and 52750, 52675 being halfway between the two, somewhat higher than the 52378 the perfect world value would be.
Using 52675 gives an excellent match for the voltage points measured, across the entire 2.5V to 5.5V range.
Using the perfect world 52378 gave results which were 2 or 4 units out (20mv/40mV) against using 52675 so it doesn't seem it really makes much difference what "K" is used nor whether calibrated or not, but it does point to calibration being necessary if hoping to achieve best accuracy.