Since this has been marked as a duplicate, I want to clarify that it's not about critical values of one- vs two-tailed tests, but the calculation of the p-Value in this case. I get that in a two-tailed test, you look at both sides of the distribution and therefore you split alpha in half and you need a more extreme test statistic to get a significant result (at the same alpha level).
In my understanding, the p-value is the probability to get this or a more extreme test statistics if the H0 is true. This is easily calculated for a one-tailed test: I just calculate the integral right of the empirical test statistic
For a normal distribution, a z-Value of 1.645 gives me a p-Value of ~0.05. But if I do the same procedure with a two-tailed test, SPSS/Excel doubles the p-value. I get that you now look on the other side of the distribution as well, and therefore I think it's the integral of z(test statistic) + z(-test statistic), but why? I did not get the result -1.645, so I don't understand why I should add the 2.5% of the other side.