Human participants judged the pungency of various concentrations of carbon dioxide presented to one nostril, the other nostril, or both (dichorhinic stimulation). Perceived magnitude grew sharply with concentration over the range explored. The combinatorial rule of bilateral integration followed the Pythagorean theorem: the effective mass in a bilateral stimulus equalled the square root of the sum of squares of the mass entering each nostril. This simple rule implies a possible mutual inhibitory interaction between the two nostrils, but it also implies partial spatial summation of the sensory impact of bilaterally presented concentrations. When persons inhale a relatively strong irritant, such as the higher concentrations used here, they will exhibit a very brief reflex interruption of inhalation. An experiment on the threshold for the reflex implied that it too followed the Pythagorean rule of integration. This occurred for both males and females, though females displayed a lower threshold for the reflex, whether evoked unilaterally or bilaterally. This reflex may hold promise as an objective indicator of functional status of the nasal common chemical sense.