Question

How many lines of text is displayed in output in the web browser?

Answer 1

Indeed there is. It is called wc, originally for word count, I believe, but it can do lines, words, characters, bytes (and with some implementations, the length in bytes of the longest line or the display width of the widest one). The -l option tells it to count lines (in effect, it counts the newline characters, so only properly delimited lines):

wc -l mytextfile
Or to only output the number of lines:

wc -l < mytextfile
(beware that some implementations insert blanks before that number).