What is the formula for conservation of mechanical energy?

There are many equations to solve for energy, depending on what form of energy your looking at. For kinetic energy, us KE = (1/2)mv2 where KE is kinetic energy, m is mass, and v is velocity. For potential energy used PE=mgh where PE is potential energy, m is mass, g is gravity, and h is height. Mechanical energy is PE + KE. There are also numerous equations for finding the amount of thermal energy.