What is the effect of armor rating on received damage?

Solution 1:

If Tamara 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 displayed armor rating that is useful when wearing four pieces of armor. 667 is the maximum displayed armor rating that is useful when wearing 0 pieces of armor.

Solution 2:

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...