In the mathematical field of differential geometry, the Simons formula is a fundamental equation in the study of minimal submanifolds. It was discovered by James Simons in 1968. It can be viewed as a formula for the Laplacian of the second fundamental form of a Riemannian submanifold. It is often quoted and used in the less precise form of a formula or inequality for the Laplacian of the length of the second fundamental form.