Suppose \((M,g)\) denotes a Riemannian manifold, \(p\in M\), and \(\Pi\subseteq T_pM\) be a 2-dimensional subspace with the basis \(v,w\). Then
\[ \sec(v,w) = \frac{\Rm (v,w,v,w)}{\lvert v \wedge u \rvert^2} \]where
\[ \lvert v \wedge w\rvert^2 = \lvert v\rvert^2\lvert w\rvert^2 - \langle v, w\rangle^2. \]This can be deduced, by proving the identity in normal coordinates.