I had a piece of armor that when unequipped said its armor rating was about 65, then when I equipped it, its rating changed to 72. Also my overall armor rating jumped 100 pts when equipping. Has anyone else had this?

1- are you wearing other pieces of apparel that affect your armor rating?
2- have you taken any weapon perks that cause increases to armor rating?
3- have you taken a potion or cast a spell or received a blessing that raises your armor rating?
4- have you looked at the "active effects" section in the magic menu?

I have other armor on but their equipped status wasnt changing, just the single piece.
I have the Heavy Armor juggernaut perk, but shouldnt that be calculated into the stats before I equip it?
No potion, spell
No effects

No, its only calculated when the items are worn.

Then thats just bad design, but it still doesnt explain where the extra 30pts of overall armor came from

Has your heavy armor skill increased a few levels Since you last looked ?

Your Armor rating increases with your Heavy Armor skill.

And the heavy armor Juggernaut perk, that is the one that's gives a 25%bonus when wearing all heavy armor right? That one only takes effect when all items are worn.

Now the one at the very bottom which increases AR by 20% for each point invested, that you will see withou equipping the item.

I found out whats happening: Lotharofthehillpeople was right, your skill is only calculated once you equip it but also theres a hidden stat which gives +40 for having a chest piece on and +20 for every other piece equipped. idk why they have to make the system so confusing, whats display should be how much youd get when you put it on.