This is the question asked by millions of website owners and webmasters. There is no defined calculation to tell you the exact time duration about SEO rankings. Sometimes a site will be on 1st page for couple of days and will be thrown away to 10-20 pages back.

Things to remember while optimizing a site:

1. Avoid finding back-links of competitors and submitting them. Sometimes you never get back-linked from the site(s) you have submitted.
2. Stop changing contents by useless keyword analytical tools. Just concentrate on your content changes strictly on Google guidelines. Google webmaster control panel is the best seo tool than others.
3. Promote your site in Genuine way by Google guidelines accepted SEO Software tools like SEO Software Submitter.
4. You can see the ranking results in couple of months. Your site might be somewhere in between 10-20 pages depending on the keyword competition.
5. Regular promotion (article marketing, PR releases, PAD submission, RSS submission,etc) from SEO Software Submitter will move your site to unshakable position in 1st page of Google within 6-12 months.

Good luck for your SEO success !