For power/sample size analysis, you have to fix either one or the other: You're generally interested in determining the sample size to achieve a given power, or you want to know the power of a test given a certain sample size. In both cases, the type I risk ($\alpha$) is also fixed at a given value (typically, 5%), and we can accommodate group imbalance, dropouts, etc.
Given the way statistical test of null hypothesis are framed (definition of a null hypothesis, $H_0$, and the alternative, $H_1$, yielding the acceptance and rejection regions), the calculator is asking you the expected correlation, $\rho$, under the alternative.
Now, be aware that computing power "after the fact" (so-called post-hoc power analysis) is clearly not a definitive solution if you are working with a planned design.