The new value. Equip the new item and then fill in the table with the values in your profile tab. You only have to fill in the values that changed, the calculator will use the current value if no other is specified. So I have looked around and I can't seem to find a DPS calculator that shows the stats stated in the title Primarily: Damage Per Time, Skill Damage which includes the Skills you actually use and not white damage.
Note that DPS has been switched to 'Burst DPS' which is essentially Unbuffed DPS * Elemental% * Elite% * Skills%. Skills% is the affix found in items (and not passives or skills used by heroes).Essentially the DPS calculator is the amount of damage if you were to hit an Elite with your Skill based affix with the assumption that the Skill only does 100% weapon damage and that the Skill is related with your best Element. What we have at the moment, is something that helps the player determine the relative value of a DPS affix in relation to another affix (ie. how good is a main stat vs CC vs CD vs Elemental vs Elite etc)
The primary principle to using the calculator remains the same below but has been updated with new Elemental%, Elite% and Skill% calculator options which is applied to the *Skill DPS ('Burst DPS')
- copied and stickied this thread into General Discussions as it's a rather useful function of the site that generally gets missed by people.
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(examples are old below (pre-expansion) but still applies with the latest expansion and patch version of Diablo 3)
A useful DPS and EHP calculator tool is now available in all character sheets where it is now possible to more clearly assess what stat to focus on to increase your overall unbuffed DPS or EHP (unbuffed meaning that we don't use chosen passives/skills or paragon points giving us a fair baseline to make a ladder in the site)
This is particularly useful to determine how much of a gain a certain stat is and then compare it to another, for instance :
Instead of 50% critical hit damage, you can get the same DPS increase from around 204 STR in the above example. The same principle applies to every stat in both calculators. 
So, 1% life is the same as approx 10 VIT above.
Here's another way to look at things for those who play HC in particular :