It’s a pity that neither the Combat Calculator program nor JO’s combat calculation properly distinguish between spells on the one hand, and combat artifacts and/or NPC on the other, when assaulting a popcenter that has a defending army.
It is my believe and experience, but not confirmed in the rulebook as far as I know, that whereas an offensive spell is only applicable in the army vs. army encounter, the combat artifact is used in that AND in the assault against the popcenter (the same is true if you have say a dragon in your army). Unfortunately the combat calculators are too primitive to take this into account.
What I do is tell the combat calculator to only look at the army vs. army, then take what it tells me is my army strength, subtract the value of my combat artifact(s), multiply by my losses, and then add back in my combat artifacts and compare with the popcenter defense which is easily calculated if the combat calculator your use doesn’t supply it.
So, suppose you have a +2000 combat artifact and are assaulting a major town/fort with a defending army. You program in NOT to assault the popcenter and learn that your losses will be 17% against the army, and that your total army strength is 18000. Take away the combat artifact leaves 16000, times 0.83 = 13280 which is your army strength after the battle not including the artifact; add back in the +2000 to get 15280 and you know you can take the major town/fort if the loyalty is 15280/8500 = 1.819 so say less than 82% loyalty.