I always assumed this speed was calculated taking available runway length into account, and if you try to stop after V1 you are in serious danger of over-running the runway and going off the end. Hence the need to fly with a failure after V1.
However, I was talking to a couple of retired Big Aeroplane driver mates the other day and they told me this was not the case! V1 is calculated for weight and other factors, but runway length isn't one of them.
SSD
I somewhat doubt they meant that and I wonder if there's been a misunderstanding.
On one airline I know of on the line the V1 (amongst other things) is calculated by entering weight and other factors, as you put it, into either a computer program or by reference to a (thick) book which contains a page for every single runway on the network. If you're using the computer you enter the runway identifier and entry point,
not the length into the "computer", if using the book you use the page appropriate to runway and entry point. In neither case do you as the pilot, actually enter the numeric runway length in feet or metres, since the "computer"/book has that inormation so it is a value most assuredly involved in determining the value of V1.
I suspect that is what your Big Aeroplane pilots were driving at ( at least I hope that was what they meant, otherwise
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