This article goes into quite a bit of detail and determines how much power the Death Star would have had in order to destroy a planet.
So if we can’t use melting energy or vaporization energy, how do we determine the energy requirement to destroy a planet? The answer, in one word, is gravity. If you wish to destroy a planet, you must scatter its mass so quickly that the forces of gravity cannot reverse the expansion process. In other words, you must accelerate the planet’s entire mass to escape velocity. Another way of saying this is that you must bring the planet’s gravitational potential energy state up to zero. The concepts of gravititational potential energy and escape velocity are both discussed in the science page. Using those concepts, the energy requirement for blasting a planet apart can be calculated.