What is the equation for converting electric into electrical energy?
If it is already electrical energy, there is no need to convert something. It isn't quite clear what you want to convert.
Electricity does not occur in natural state. It has to be generated by converting one form of energy into electric energy. The electric energy of any machine can be calculated by subtracting the all losses occurring in a machine (electrical, mechanical and magnetic) from total input power or energy.
Each type of energy conversion should be investigated separately. The example you mention - converting radio waves to electrical energy - works as follows: The electromagnetic wave (the radio wave) arrives at an antenna as an alternating electrical and magnetic field - so this will quite naturally induce an electrical current (alternating current).
The details really depend on the electric appliance. Some common examples include: Converting electrical energy to heat, in a resistance. This may happen in a heater, for example. Using an electric motor to move things - for example in a fan, a mixer, and other appliances that involve movement. Other types of appliances generate light by exciting atoms (as in a fluorescent light bulb or a LED), or sound, as in speakers.