Z-score to Percentile Rank Formula?

[The Head]

I was wondering, is there a formula that converts a given z-score to its respective percentile rank? I know I can look up the conversion in a table, but I have a lot of data, and would rather just program a formula into Excel. Obviously, there is some sort of way that whoever created the table made the table, and I'm hoping I can use such a formula.

Thank you!

 

[DrDu]

look up NORMDIST and INVNORM

 

[The Head]

Thanks! That obviously works, but I would hate to use something without knowing how it actually works. Do you know the corresponding formula or procedure to actually calculate it by hand, if it were necessary?

 

[DrDu]

You have to numerically calculate the integral over a gaussian function. This integral is called error function (erf). There are some routines out there for the calculation. You might have a look at Abramovitz, Stegun, Handbook of mathematical functions.