Mass is a basic quantity that doesn't have to be broken down; kilograms are generally the preferred unit. A joule is a newton-meter, and a newton is a kilogram-meter per second squared; so that means joules are (kg x m/s^2) x m = kg x m^2/s^2 = kg x (m/s)^2, which is mass (kg) times velocity (m/s) squared, with the velocity being the speed of light.

So a mass of 1 kg, if converted to energy, would come out to 1 kg x (3 x 10^8 m/s)^2 = 9 x 10^16 J.