# Difference between theoretical equations and empirical equations

Some equations are theoretical in the sense that they are derived from an underlying theory. Other equations are empirical in the sense that they were selected only because they fit experimental data and without a theoretical justification.

If we look at an equation can we identify whether it is a theoretical equation or an empirical equation just by looking at the equation?

• I honestly have no idea what you want to know, exactly. Could you perhaps expand on your question? – Martin Ueding Apr 23 '16 at 10:01
• Hi Sonu. I've edited your question to make it clearer what you are asking. If I have misunderstood you please feel free to undo my edit. – John Rennie Apr 23 '16 at 10:44

We can look at the constants included within an equation to get an idea of whether it was theoretically derived, or an empirical result. If we have fundamental constants, such as $\hbar, \epsilon_0, e, c,$ etc, then it was probably theoretically derived. An empirical law would have an arbitrary constant which was measured by experiment.
An interesting example would be the Stefan-Boltzmann law. $$P = \sigma T^4$$
This was originally derived experimentally, with $\sigma$ being denoted as the Stefan-Boltzmann constant, which was measured experimentally - thus it was an empirical law.
However, after Planck published his law, it was possible to see that the Stefan-Boltzmann constant could be expressed in terms of fundamental constants $$\sigma = \frac{2 \pi^5 k_B^4}{15 c^2 h^3}$$ Turning this empirical equation into a theoretical one.