Item Rank

Basic Info

The item rank defines the power or quality of an equipment item or weapon in comparison to other equipment or weapons. It is displayed in the item tooltip in the bottom right of the screen when 'looking' at an item.
The item rank determines what player level is required to gain the full amount of an item's vocation-specific Strength, Dexterity or Intelligence stat, both from the property and their associated attributes (Vast Grip, Dexterity and Intelligence respectively).
The level requirement to gain full stats from an item is usually 80% of the item rank rounded to the closest 5, or otherwise can be used to full potential even at a lower level if you have completed the quest or faction associated with the item (Hover your mouse over the item rank number on wiki pages to see what the required level or other requirements are.).
That being said, you can get some amount of the item's stat even if your level is lower than the item's required level. Take a look at the formula below to calculate for a specific case.
For example, the Umbral Plate Armor has an item rank of 400, meaning that the player level required to get the full stats from it is 320. This means that if you are below level 320 you will not get the full amount of dexterity it offers through its 'Dexterity' property and 'Dexterity' attribute while wearing it.
In comparison, the Chaos Sword has an item rank of 520, but only requires you to be a knight and to have completed the White Light Faction to be able to gain the full stat bonuses from it.

Stat Formula

This formula is used to calculate the multiplier which defines how much of an item's stat you would get depending on your level and the item's required level if you are below the requirement.
The multiplier is applied separately to the item's Str/Dex/Int originating from a property and the Str/Dex/Int originating from an attribute.

 reqLevel = 80% of item rank rounded to closest 5 (if no overriding quest requirement on item)

 multiplier = (playerLevel - reqLevel * 0.25) / (reqLevel * 0.75)

 propertyBonus = multiplier * propertyStat > rounded down
 attributeBonus = multiplier * attributeStat > rounded down
 
 totalBonus = propertyBonus + attributeBonus

Taking for example a level 40 archer and a Demonbone Helmet (Item rank 80 = reqLevel 65) which gives 3 Dexterity as a property and 3 as an attribute (if enchanted with Dexterity) for a total of 6:

 multiplier = (40 - 65 * 0.25) / (65 * 0.75) = 0.487179..

 propertyBonus = 0.487179 * 3 = 1.461537 rounded down to 1
 attributeBonus = 0.487179 * 3 = 1.461537 rounded down to 1
 
 totalBonus = 1 + 1 = 2

Thus, a level 40 archer would gain a total of 2 dexterity (out of 6 possible) while wearing a demonbone helmet, 1 from the property and 1 from the attribute (if enchanted with Dexterity).