As correctly noted by Thorsal, the durability of an 'Unbreaking' item is not fixed, but depends on chance.
More specifically, the number of uses you will get out of a given tool will follow a binomial distribution. This is the same statistical law that predicts things like "how many heads will I get out of 100 coin tosses?"
Consider that a diamond pickaxe normally has durability of 1,536 uses. If you plot the binomial probability density function (PDF) for 1,536 'successes' with a 'success rate' of P = 1/2 = 0.5 (Unbreaking 1), P = 1/3 = 0.333 (Unbreaking II), and P = 1/4 = 0.25 (Unbreaking III) you get the following graph:
This shows that an Unbreaking III Diamond Pick will last, on average, about 6,144 uses (four times as long as a normal Diamond Pick.) However there is also a chance it will break after only 6,000 uses. Similarly, there is a chance it will last for 6,500 uses.
However there is basically no chance it will last longer than 7,000 uses, or less than 5,000 uses.
Pretty sure that's Armor Staus HUD (non-english site), also found on the Minecraft Forum, which provides a heads-up display for both armor and tools with durability (by adding a swing counter).
If by chance it's not the exact mod you have, ASH does the exact same thing that it does.
Best Answer
Try pressing the F3 + H when you aren't looking in your inventory. If it works, the game should tell you in the chat that it's enabled. Then, when you open your inventory and look at a tool, it should show the durability with it.