How is the dose of local anaesthesia in dentistry is calculated for a patient?

Adult patients.... Adult patients who have good overall heath, we typically use the least amount of the appropriate anesthetic agent that prevents patient perceived dental treatment created pain. Articaine or mepivicaine work well for infiltrations & Lidocaine for blocks. These provide long enough effect for most general dental procedures. Often less than 1 cartridge is all that is needed, when precisely placed.
Clinically. Ususlly it is based on the response - level of numbness- achieved after administering a "normal" generally accepted dose. This is typically 1.8 cc's of the anesthetic (one "carpule"). With septocaine, i often do not use even 1 carpule to start. Much depends on the area -- upper teeth are easier to numb with less.Also depends on the anesthetic used and the length and type of procedure.
See below. The maximum dose of local anesthetic would be calculated on a per kilogram basis for each local anesthetic used. However, since this would involve huge amounts of la to get to this maximum dose it is not usually needed.
Every. Every anesthetic has different maximum doses. The minimum needed to get a patient numb is typically used.
Patient weight . Every local anesthesia given is a very individual thing and each anesthesia depends on the patient to whom it is given. The doses of local anesthesia given by dentists are calculated according to the patient weight, age and state of health. However, as anesthesia are injected, the dose of each is adjusted as necessary, according to the effects produced.
Start with minimum. Any trained and experienced dentist is well aware of the minimum amount of local anesthetic necessary for each individual procedure. We start with that, and use more only if necessary. We rarely even get close to maximum dosages. Local anesthetics are "local" and therefore dosages are not as sensitive as "systemic" medications. Local anesthetics are sometimes not necessary if using "sweet air".