If you absolutely want to test whether your data's histogram has a good fit to a normal distribution then you need to apply what is known as a GoodnessOfFit test.
For a normal distribution you use what is known as a ShapiroWilk test which will give you a statistics which tells you how 'well' the 'fit' is.
But again I want to give a note of caution to take in what the above posters have said: you need to understand your data not only from a probabilistic or histogram point of view, but more importantly from a process point of view.
Understanding the underlying process and the effect that it has on describing the final distribution is going to be a lot more useful than just trying to fit things to distributions especially if you are looking at something from the point of view of the process as opposed to using results for statistical purposes like say testing whether the errors of a regression are normally distributed.
