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Each armor piece has a certain armor rating, I get that higher values are better, but what does the armor rating affect exactly?

By how much does a higher armor rating reduce damage? And I assume that only works against physical damage, and does not affect magic at all?

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Armor rating does not affect magic damage. –  Raven Dreamer Nov 13 '11 at 16:18
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2 Answers 2

If Tom Wijsman's formula is correct, hp can be factored out of the formula. Also, there's a 12/100 factor I saw from uesp.

resulting damage = damage * (1 - armorfactor)
armorfactor = 0.12 * (hidden armor + displayed armor) / 100
hidden armor = 100

Which gives these values.

50 armor -> 18% reduction -> 82% damage taken
150 armor -> 30% reduction -> 70% damage taken
317 armor -> 50% reduction -> 50% damage taken
442 armor -> 65% reduction -> 35% damage taken
567 armor -> 80% reduction -> 20% damage taken

The hidden armor in the formula is when wearing four pieces of armor (chest, head, hand, legs). If you are wearing robes or hood, or are missing feet or hands, then hidden armor is less than 100 and you get less reduction. This reduction in reduction is not reflected in the displayed armor rating.

Finally, damage reduction is capped 80%, so 567 is the maximum total armor rating that is useful.

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Additionally, there's a cap at 80% damage reduction. What this means is that a full suit of Hide will cap you out with appropriate perks and smithing. –  LessPop_MoreFizz Nov 19 '11 at 2:30
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It's rumored that the formula is like:

resulting damage = damage / (hp + (hp * armor / 100)) * hp

In which way 100 damage to 100 HP and 50 Armor results in 66.66 damage.
This is similar to like it was back in Morrowind...

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This is weird, if your health starts out at 50 and you have 100 armor rating, does that mean you can take 100 damage? How does the game keep track of how much damage your armor has absorbed so when you end up at 25 health, you can only take 50 more damage before dying? –  z ' Nov 14 '11 at 4:19
    
I was just using 50hp as an example number –  z ' Nov 14 '11 at 4:22
    
That was a bad example, I've propagated the formula to rather show the resulting damage. We still need confirmation on this though, but that requires studying of the damage in the game and comparing it to the formula. I might look into that when I get to play Skyrim again... –  Tom Wijsman Nov 14 '11 at 4:27
    
that makes more sense now –  z ' Nov 14 '11 at 16:39
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