General expression for degrees of freedom is given by

where, Number of independent particles
Number of independent restriction
A monoatomic gas is free to move in any direction in space. So, it has 3 translational degrees of freedom.
In the case of diatomic gas molecules, it can also move freely in space, so translational degrees of freedom is 3.
A diatomic molecule can be considered two atoms connected with a bond, so it has two axes of rotation. One axis of rotation passes through the centre of any one atom, and the other passes through of the bond. But in this case, we will not consider the axis that passes along the bond through the centre of the two atoms, as in the bond length the centre of two atoms, so, for a diatomic gas, (translational) +2 rotational .
Law of equipartition energy Each molecules energy associated with each degree of freedom is .