Let $\pi \colon P \to M$ be a principal $G$-bundle. We define the connection 1-form $\omega \in \Omega^1(P, \mathfrak{g})$ associated to a connection on $P$. This is the principal bundle analogue of a covariant derivative operator $\nabla$ associated to a connection on a vector bundle, and is the most elegant way of describing connections on prinipal bundles.