Energy can take on many different forms, but heat ranks as the most basic form, stored in microscopic motions of the atoms and molecules composing a material. The conduction and retention of heat, while each described mathematically with an equation, differ greatly.
People experience heat conductivity by touch. A piece of metal left in the cold feels much colder than a piece of wood at the same temperature, as heat moves through metal faster than wood, and always moves away from the warmer body. The heat conductivity equation, or Fourier's Law, calculates how heat moves. In simplest form, it says that heat flux is proportional to the negative temperature gradient.
The heat retention, or heat capacity, equation shows that the energy required to change a material's temperature is proportional to the product of the mass of the material and temperature difference.
Conductivity refers to the vector quantity of heat flux, while the heat retention equation provides a scalar value for how much energy must move to change a material's temperature.