ALL the calculations? That would take someone years... entire series of textbooks are devoted to the topic of lasers.
Even the simplest equations involving lasers are of a second-year university level, so unless you are at this level, introducing and explaining any equation is most likely a futile exercise.
A basic conceptual illustration of how lasers work should not be beyond a high-school student. Check out the Mk gave you and if there is something that needs further explaining, we should be able to help.