The three flavor neutrino oscillation probabilities in matter are tedious to calculate analytically, and one usually resorts to numerical calculations using a computer. While this serves the purpose of obtaining the requisite probabilities, the computer program is essentially a black box and it is often difficult to discern the physics behind its output. To this end, an approximate analytical formula for the probabilities could fill the gap and provide us with not only a better understanding of the physics, but also a means of performing back-of-the-envelope calculations to estimate the parameters required for long-baseline neutrino oscillation experiments. In this talk, I present an approximation which was derived using the Jacobi method, first discussed by Carl Gustav Jacob Jacobi in 1846. It is surprisingly simple while at the same time amazingly accurate. I will also show several applications of the approximation to demonstrate its utility.