How do I compute the financial advantages and disadvantages of taking Social Security as soon as I'm eligible?

I understand that the benefit increases the longer you wait to take it, up to a maximum, and I understand that whatever level you start taking it at is the one you stay with. I have also looked at the Social Security website, which tells me what factors to consider.

I’m not asking for advice or for factors to consider. What I want is just some help computing the numbers. If I start taking SS at age 62½ at a lower rate, rate A, that will amount to x dollars in, say, 2½ years. So how long would I have to receive the benefit at the higher rate B, at age 65, for the difference to equal the sum of what I got for those 2½ years? How long before the additional amount at rate B adds up to the x dollars I would have got at rate A for a period of time T? What I’m looking for here is the formula for calculating that.

Of course I don’t know how long I’m going to live (I didn’t opt to know my date of death), but I would still like to be able to judge whether I have a better chance of coming out ahead by taking the lower rate sooner or waiting for the higher rate.

When I try to think this one through and turn it into a formula, I get kind of muddled. I need one of you math guys to help me figure it out. Thanks.