The banks don't come up with a credit score, the banks order your credit through the various credit bureaus (Equifax, TransUnion, Experian) which provide them your credit scores. The reason you can't figure it out on your own is because the algorithm to calculate your credit score is proprietary to each credit bureau , i.e. a "trade secret". There are thousands of factors that go into calculating a credit score, and each credit bureau has a different way of analyzing that information to come up with it's on credit score. This is also why if your credit history is the exact same on all 3 credit bureaus, you will still get 3 different credit scores. So you can get your credit scores by applying for credit (mortgage, auto loan, credit card, etc.) or you can go to the various online websites to get them there - but since everyone wants to know their credit score, and they are willing to pay to find out, that is why you are being charged, as it's coveted information.
If you are just starting to learn about what credit scores are, I have found that the http://www.myfico.com/crediteducation/creditscores.aspx website is an invaluable tool as it explains everything in an easy to understand manner.
Shane Milne | Lending in all 50 states | NMLS #81195