It takes dividing by the speed of light squared and I defy anyone to explain the logic of that.
Simple, mass is in kilograms, velocities are in meters per second, and units of energy are in joules, which are in units of kg*m2
, so multiplying the square of the speed of light by mass directly gives an energy measurement.
Using this, you can even backtrack and calculate how much mass was converted to energy in, for example, the Hiroshima bomb. It released about 63 teraJoules of energy, which is 6.3x1013
. The speed of light is approximately 3x108
m/s (which is close enough to 2.99792458x108
and much easier to multiply). Squaring that gives 9x1016
, by which we can divide the energy figure above so the m2
will cancel and leave only kg.
And it leaves 0.0007 kg, or 0.7 grams
of mass completely converted into energy. That's all it takes to flatten a city.