  A simple formula is derived for the Ricci scalar curvature of any smooth
level set ${\psi(x_0,x_1,...,x_n)=C}$ embedded in the Euclidean space $ \mathbb
R^{n+1}$, in terms of the gradient $ \nabla\psi$ and the Laplacian $
\Delta\psi$. Some applications are given to the geometry of low-dimensional
$p$-harmonic functions and high-dimensional harmonic functions.
