Joules are an expression of energy with the base units (kilograms_meters^2)/seconds^2. In modern physics, the mass of an object is also a measure of the energy contained in the object. Albert Einstein proposed that mass and energy are related by the equation "E = m_c^2," where "E" is the object's energy in joules, "m" is the object's mass and "c" is the speed of light. This equation, called the mass-energy equivalence formula, is used to convert between energy and mass.
Set up the mass-energy equivalence equation. Set your amount of joules equal to mass multiplied by the speed of light, which is 3_10^8 meters per second. As an example, if you have 5 joules of energy, the equation "E = m_c^2" is set equal to "5 = m * (3*10^8)^2"
Solve for "m" in the energy equation by dividing both sides of the equation by (3_10^8)^2. Using the same example, "m" is equal to 5.556_10^-17 kilograms.
Convert "m" to grams. There are 1,000 grams in every kilogram, so you can convert 5.556_10^-17 kilograms to grams by multiplying by 1,000. The resulting answer is 5.556_10^-14 grams.