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There actually may be several reasons he did not tell you how much you needed.
When a contractor gives a FREE estimate they usually figure that a certain amount of estimates will end up as jobs and the time spent on the estimate is compensated by the installation. If he doesn't get the job, it really is a FREE estimate. It's getting more and more common for people to get a FREE estimate and then hire someone else to do the job based on those estimates.
By not giving you the estimate of how much you will need he increased the odds that he will be doing the installation.
There is also another consideration. If you have someone else install your stairs or you install them yourself based on the first guy's estimate who's responsible if it comes up short? I have the same problem in the wood flooring business.
It looks like the carpetman has you squared away on figuring out how much you need yourself.