A good definition of an active site in carbon is a site which can chemisorb oxygen. Those sites are around 0.5 - 2% of the total surface area.
The best method for its quantification is that of the breakthrough paper of Laine, Vastola and Walker Jr in 1963 (The Importance of Active Surface Area in the Carbon-Oxygen Reaction, J. Phys. Chem. Vol 67 2030-2034).
You can find all papers of PL Walker Jr in the website attached.
Also, see one of the last papers of professor Walker on the subject (link attached too) there, the concept of Active Surface Area (ASA) is well explained.