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I'm playing a level 10 blade singer wizard with one level into barbarian for unarmored defense. I have a +5 Dex modifier, a +5 Int modifier, and a +4 Con modifier. I also have a staff of power that gives +2 to AC.

My total AC would be 4+5+10=19 from Unarmored Defense, +2 from the staff of power, and +5 from the Blade Singer arcane tradition, for a total of 19+2+5= 26 AC. Is my math correct?

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Your math is correct.

Initially your unarmored defense is 10 + Dex + Con. The Staff of Power has a constant effect, so that boosts your AC by +2.

Your normal AC is therefore = 10 + 5 (Dex) + 4 (Con) + 2 = 21 AC.

During a Bladesong, which lasts 1 minute, you add +5 (Int) to your AC, for a total of 21 + 5 = 26 AC!

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Your unarmoured defence AC when Bladesong isn't active is: 10 + 4 Con + 5 Dex + 2 Magic Item = 21 AC

With Bladesong active you gain +5 Int to your AC which makes it 26 AC. Keep in mind that if you use your Staff of Power to make an attack with both hands, your Bladesong will end early!

You must have rolled very well for your stats considering you have 20 Dex, 18 Con, 20 Int.

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