I am looking for a formula to convert a z-score into the percentile or confidence interval.

for example a z-score of 1 would give 68%, a z-score of 2 would give 95%

what is the formula/equation for this?

I do not want to use an online z-score to percentile calculator, and I do not want to use a table or graph. I want to use a formula to convert my z-score to a percentile.