Watching my resting dog breathe I noticed he inhaled slowly and exhaled without much apparent control, just relaxing and letting it all huff out, then pausing awhile before the next inhalation; I tried this, it feels good, so I keep doing it when I want to feel more calm.

From reading Breath, by James Nestor, I learned that a good target for calm-inducing breathing is about eleven seconds for an inhale/exhale pair, common with many religious activities like chants, etc. Breathing like my dog, I aim for five seconds in, ~three out (not counting, just letting it out), and as long a pause as feels right, sometimes pushing myself a little to extend.