Before we understand how to convert z score to percentile we should understand what the terms z score and percentile mean.
In the standard normal distribution the value taken by the variable is called the z score and the are under the graph of the distribution before that value is called the percentile. For example for the z score 1.65 the percentile is 95% because the area under the curve behind that z value is 0.95 as shown in the image below.
The standard normal distribution is symmetric about zero and the total area under the curve is 1. Hence given the z score zero the percentile is 50% because half of the area under the curve lies behind zero.
Now that we have understood what the terms mean let us try to see how we can calculate the percentile given the z score. The way it is usually done is by referring to the comprehensive left hand z score table as in the below image. Simply find the z score you want and look for the corresponding value in the table. For example in the table below for the z score 1.65 the corresponding percentile is 0.95 or 95%.