An equivalent statement of the Dulong–Petit law in modern terms is that, regardless of the nature of the substance, the specific heat capacity c of a solid element (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole). Thus, the heat capacity per mole of many elements is 3R.
The initial form of the Dulong–Petit law was:
where K is a constant which we know today is about 3R.
In modern terms the mass m of the sample divided by molar mass M gives the number of moles n.
Therefore, using uppercase C for the full heat capacity (in joule per kelvin), we have:
or
Therefore, the heat capacity of most solid crystalline substances is 3R per mole of substance.
Dulong and Petit did not state their law in terms of the gas constant R (which was not then known). Instead, they measured the values of heat capacities (per weight) of substances and found them smaller for substances of greater atomic weight as inferred by Dalton and other early atomists. Dulong and Petit then found that when multiplied by these atomic weights, the value for the heat capacity per mole was nearly constant, and equal to a value which was later recognized to be 3R.
In other modern terminology, the dimensionless heat capacity C/(nR) is equal to 3. 
The law can also be written as a function of the total number of atoms N in the sample: 
where k is Boltzmann constant.