TeXcount counts the number of words in LaTeX document. How to setup is here though TeXLive might install it. Simple command just to count the total number of words is
texcount input.tex
The result is:
FILE: input.tex
Words in text: 4415
Words in headers: 52
Words in float captions: 75
Number of headers: 16
Number of floats: 6
Number of math inlines: 3
Number of math displayed: 0
