The outer diameter of the connector is about 1.37 inches. enters my Dyson hoses and dips to a depth of about 1/4 inch. This will hold it in place but not too tight so it can be easily removed. The inner diameter of the connector is about 1.24 inches and the overall diameter is 2.5 inches, so they are not as big as a store vacuum. The quality is just great. The bristles are very soft, just what I wanted. As I use them to vacuum my piano which has a very thin high gloss finish. At around $3.25 each, this is a steal. And delivered phenomenally quickly. I am planning to buy another set for my second home. They're so cheap I just leave one on each floor. Save me the trouble of going up and down stairs. As other reviewers have pointed out, the bristles suck into the center and block the flow path. This is not a problem for fine dust particles, but clumps of dust collect on the bristles and you have to remove the brush from time to time and vacuum it with a hose. I suspect that picking up bulkier things like pet hair can get really annoying. But I have another brush for this application.