As suggested above, one needs to know the standard deviation and mean before one can estimate the uncertainty, confidence, or statistical power for a given sample size. One also usually assumes a normal (Gaussian distribution), but this then leads to the requirement of testing normality after the experiment and if the data is not normally distributed, then one needs an alternate approach to estimating uncertainties and confidence levels.
I am sort of assuming by statistical power, you mean the number given the symbol pi in this discussion:
See the interpretation section.Every experimental design has this same sort of chicken and egg problem. You don't know the mean or standard deviation before the experiment is performed; therefore, you don't know a priori what the sample size needs to be.
The way to address this paradox is to estimate the mean and standard deviation that are likely from past studies that are as close as possible to the current study. Past experience tells me I need to weigh and measure 100 fish to reduce the uncertainty in the relative condition factor below 1%. This works most of the time, because the standard deviation tends to be about the same regardless of if I'm measuring rainbow trout in Colorado or black drum in Louisiana. However, some species can have a bimodal distribution with males and females having significantly different means or infected and healthy fish having significantly different means. This would require a different experimental design.
Experience has also taught me that I need about 10 shots to measure a bullet's ballistic coefficient to 1%, but that plastic tipped bullets tend to have smaller standard deviations than hollow point match bullets, so the same level of uncertainty requires more samples of hollow point match bullets. Most physical systems have smaller variation than biological systems, so it is common for biological systems to require a lot more samples for a given level of accuracy.
Statistical power comes in when comparing two samples, because it is related to the confidence that the two samples (treatment and non-treatment, or male and female, etc.) are significantly different. (Here, I mean significant in the statistical sense.) The closer the two means (of the different sample groups), the smaller the standard deviation needs to be to say whether or not the means or significantly different for a given sample size.