If something is demonstrable, it can be shown or proved. A demonstrable fact is not only a feeling, a rumour, or a hope — you can point to evidence, a test, a number, or a clear example. Scientists talk about demonstrable results; lawyers talk about demonstrable harm. Though actually, “able to be shown” is not the same as “already shown.” Demonstrable means the proof is possible; demonstrated means someone has already done the showing. It is a formal adjective, at home in academic writing, reports, and serious argument. In casual speech people usually say “you can prove it” or “it’s clear.”