The following is from the Cornell Feline Health Center.
A cat’s respiratory rate can be a good indicator of the health of a number of organ systems, including the cardiovascular system and lungs. Monitoring resting respiratory rate can be a very useful and easily applied tool in maintaining your cat’s general health and well-being.
Respiratory rate is best obtained with your kitty sleeping. To perform this measurement, count the number of times that your cat’s chest rises and falls (while breathing in and breathing out, respectively) in 15 seconds, and multiply this number by 4 to determine the number of breaths/minute. Be careful not to count up (breathing in) as one and down (breathing out) as two. One breath is up AND down (breathing in AND out).
The normal respiratory rate for a cat should be below 35 breaths/minute. If you notice that your cat’s respiratory rate is greater than 35/minute, contact your veterinarian with this information for guidance.