Einstein Equation

E = mc^2

  • E is Energy.
  • m is mass.
  • c is the speed of light and it must be in units that match your choices for E and m.
  • Let energy be in Joules
    • J = N m
    • N = \dfrac {kg \: m} {s^2}
  • Let m be in kg.
  • let the speed of light be in m/s.

For Energy J = N m = \dfrac {kg \:m} {s^2} m = \dfrac {kg \: m^2} {s^2}

For mass times speed of light squared, the multiplication of the units gives: kg \dfrac {m^2} {s^2}

The two are equal.