The ratio between two quantities is called the constant of proportionality. If it is true that some quantity #x# changes as you change another quantity #y# then there is some constant of proportionality #k# which can be used to mathematically relate the two.

#x = ky#

If I know the value of #y#, I can calculate the value of #x#. If the value of #y# doubles, then I know that the value of #x# will also double.

This question is asked in the context of Stefan's Law where the two quantities being related are the total energy radiated per unit area (#j^*#) and the temperature (#T#). They don't relate directly the way the mathematical example above does. Instead, the total energy radiated varies as the fourth power of the temperature.

#j^* =sigma*T^4#

The constant of proportionality #sigma# is the value which relates the two. The value can be shown to derive from several other fundamental constants. It is related to the speed of light (#c#), Boltzmann's Constant (#k#), Planck's Constant (#h#), and #pi#.

#sigma = (2pi^5k^4)/(15c^2h^3) = 5.670 * 10^-8 (J)/(sm^2K^4)#