What are common empirical formulas that can produce a rough estimate of project duration for waterfall methodology ( up to 20% fluctuation is acceptable). If it helps in narrowing down the answer, you can assume that following is more or less known :
Number of devs is known and fixed, most devs are above average in terms of know-how, however some learning about domain-specific issues might be required.
Known and fixed max. number of app users.
Technology stack to be used is reasonably diverse (up to 4 different languages and up to 6 various platforms).
Please feel free to provide estimate methods which cover a broader scope than the above points, they are just provided for basic guidance.
Do yourself a favor and pick up Steve McConnell's Software Estimation: Demystifying the Black Art. If you have access to past estimates and actuals this can greatly aid in producing a useful estimate. Otherwise I recommend this book and identifying a strategy from it most applicable to your situation.