The lowest estimated number is three million, and the highest even reaches one hundred million.
The currently most accepted figure comes from Professor Camilo Mora at the University of Hawaii at Manoa:
8.7 million, not including viruses.
He arrived at this number by analyzing the trends in taxonomic hierarchies—that is, those domain, phylum, class, order, family, genus, species numbers you learn in biology textbooks (org/content/113/21/5970)
For example, one phylum might have 10 classes = 100 orders = 1,000 families = 10,000 genera = 100,000 species, and the numbers for different taxa tend to show similar trends, with higher-level groupings being relatively stable compared to species.
So, after a series of simulations, you can come up with a more reliable estimate of the total number of species.
This paper by Professor Camilo Mora is one of the most cited statistical documents in the world, so it's pretty authoritative.
8.7 million versus 2 million.
