It says in the perks description Protection spells are number of times stronger if you wear no amour dose this include boots and gauntlets? I'm wearing some enchanted steal boots and gauntlets at moment but with robes, would I have to take these items off for the perk to work?

Yup, boots and gauntlets count. If you want to take those perks and have them work you can't wear them. Alot of people hate this because they want to wear the dragon masks

You can test this yourself if you already took the perk by casting and checking active effects in both cases.

Ok thanks for your reply, I will have to not wear any amour at all then as Ive invested alot into this perk and alteration school dose this include leather bracer's and boots?

Any thing with an armor rating. BTW if you are on the PC i suggest getting the "extended mage armor duration" mod. This will about increase the duration of the casts 5X. it takes alot of the headache out of using that armor. SHAME on bethesda for making stock mage armor annoying as hell to keep active.

Yeah I know what you mean unfortunately im on 360 As I would love to try out some of the magic mods.