I ask about the correlation between the sample size, the power of the study and r (correlation coefficient, and if there are any direct online calculator of these three variables.
Yes, there are very good resources available online to assist with planning a study so as to have sufficient statistical power to detect some specific target effect size (or larger): in your case, a correlation. The g*power program (available for windows or mac OS) is freely available: http://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html
Depending on your statistical analysis, you can follow references for sample size, which are recommendations.
example is Hair et al (2010), where they recommend a data set of approximately 200 as larger sample sizes can have deviations and/or errors that leads to biased interpretation of the results.
Very elaborated comment David Morse , and thank you very much indeed for sharing the link of G*Power software. The G*Power software is an effective tool that can be used to compute statistical analyses for many different tests.