Use: enter a certain value in the input box, then click "Calculate" to obtain a specified value.

where F(z) is the cumulative function of standard normal function, i.e., the area of the red part.

Conversely,

one sided

two sided

where alpha is level of significance, i.e, the total area of the red part in one-sided or two-sided

The critical z-value is the critical point of standard normal function.

One-sided: Pr(Z>z) = α

Two-sided: Pr(-z<Z) + Pr(Z>z) = α, the outpur shown is the positive critical z-value, as the function is symmetric, another is the negative z-value, i.e., +z and -z

Reference: DistCalc (http://teachme.tuwien.ac.at/simulations/)