• (estimated more PR needed from links)
• (must be a number from 0 to 1)
• (must be a number)
Updated 1/16/09: PageRank Calculator was refined to be more accurate by adding in a logarithmic calculation as PageRank increases, more...

How the calculator works

General Overview
The calculator works based off the Google PageRank formula from the original paper on PageRank by Google founders Sergey Brin and Lawrence Page. That formula can be expressed by the following equation 1.

PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))

Using that formula and some calculus and algebra the formula was setup so that the it could be solved for the amount of PR needed from links to obtain a specific target PR for your site. Basically it calculates how much PR from inbound links is needed to obtain a specific PR for your page. So now we can calculate if we want a PR of X then how much PR will we need from links pointing to you.

With the PageRank number received from the calculation you can break that down to the number of links you'll need from with pages with a specific PR number. For your convenience we've calculated a few possible linking strategies under the total PR you'll need.

Damping Factor
The damping factor is a number used in the orginal PageRank formula that represents the probability that a Internet surfer randomly clicking on links will eventually stop clicking. And according to the original paper on PageRank by Google founders it's usually set to 0.85. We've left this as something you can change and fill in as the number might have changed since the original formulation of the PageRank formula which would create totally different results with our PR calculator.

Logarithmic Factor
The logarithmic factor is a number representing the amount of difficulty or extra PageRank needed as the number of PageRank increases. This number needs to be factored into the calculation because as you move up in PageRank the needed amount of PR between each step increases. For example you need more PR to go from PR2 to PR3 than you would to go from PR0 to PR1. It's commonly thought that this logarithmic factors could be 3, 6, or 8 but there seams to be more evidence that it's 6 4.

Average # of Links Per Page
The average number of links per page is the average number of links that pass PageRank on a page that is linking to you. Our number of 52 was taken form a news article from 2000 2. Although we have also found another more recent article stating that the number is now about 42. Even though the more recent study shows a lower number we've decided to use the 52 3 as the average because neither study is really that current and it would be better to error on the side of needing more links than less. But we've left that as something you can change for your calculation if you feel it should be a different number.

Current PR
This is the current PR of the page your looking to evaluate with the calculator. If you have no PR you'll want to set this to zero. You can also experiment with this by setting it to a fraction as the PR of your page is probably not exactly at a whole number.

PR You Want
This is the PR you want your web page to have. It's pretty simple and straight forward.

References
1 Sergey Brin and Lawrence Page (1998). "The anatomy of a large-scale hypertextual Web search engine". Proceedings of the seventh international conference on World Wide Web 7: 107-117 (Section 2.1.1 Description of PageRank Calculation).
2 Mark Ward (2000). "Web links that stick". BBC News Online.
3 Levering, R., and M. Cutler (2006). "The Portrait of a Common HTML Web Page". DocEng 2006 (Amsterdam, The Netherlands: October 10-13, 2006), 198-204.
4 Paul Postuma (2007). "Google PageRank demystified: How To increase your page's PageRank - Practical Tips". Ars Informatica 2007.

Update 1/16/09
After looking over the results of the calculator it became obvious that the answers we were getting back where not close enough to the real amount of PageRank you would need to get to your target PR. So after some investigating, more reading, digging around, and listening to other people's theories on the subject. The key factor that appeared to be missing is that PageRank is logarithmic.

Meaning you could express PageRank similar to climbing up stairs getting harder as you move up more stairs. Going from PR1 to PR2 takes X steps but as you now go from PR2 to PR3 it takes X steps plus X, then from PR3 to PR4 it takes X steps plus XX. So as the PR increase so does the number of steps added. Therefore the distance is farther between PR the higher the PageRank number. Now the next step was determining an amount to factor by - this amount is called the logarithmic factor.