Imagine a tiny particle jiggling in a fluid, but also drifting slowly downstream. Its position over time is a mix of random zigzags and a steady push. In the world of stochastic calculus, this is an Ito process. The Ito formula is the tool that lets us describe how functions of such processes evolve—it is the stochastic version of the chain rule, but with a surprising extra term that captures the roughness of Brownian motion.