According to a study by a group of Italian researchers, published in the journal Current Biology, dogs also convey anxiety and potential danger when wagging their tails.
Researchers found that dogs tend to move their tails more to the right or left depending on how happy or anxious they feel. Other dogs recognize and interpret the different tail wags.
Researchers showed 43 dogs of various breeds video of other dogs wagging their tails or sitting still and documented their reactions on camera.
When dogs saw another dog wagging to the left, their heart rates picked up and they appeared anxious. But when the dog in the video wagged to the right, the viewing dog remained relaxed.
Researchers found a clear pattern that is they believe is tied to the brain's hemispheres.
"The direction of tail wagging does in fact matter, and it matters in a way that matches hemispheric activation," said co-author Giorgio Vallortigara of the Center for Mind/Brain Sciences of the University of Trento.
The right hemisphere, activated when wagging left, is associated with negative approaches and responses including anxiety and flight from danger.
A wag to the right, on the other paw, suggests that the dog's left brain has been activated, more closely related to positive responses and social approachability, according to study authors.
The change is sometimes too subtle for humans to detect, but dogs know the difference.
The finding that dogs are "sensitive" to the tail expressions of other dogs "supports the hypothesis of a link between brain asymmetry and social behavior and may prove useful to canine animal welfare theory and practice," according to the authors.
But Vallortigara doesn't think that the dogs necessarily intend to communicate those emotions to other dogs. Rather, the bias in tail wagging is likely the automatic byproduct of corresponding brain activation, that other dogs may then recognize.
The authors add that dogs' asymmetrical bias could prove useful for veterinarians and dog owners.
"It could be that left/right directions of approach could be effectively used by vets during visits of the animals or that dummies could be used to exploit asymmetries of emotional responses," Vallortigara says.