The thermodynamic square is mostly used to compute the derivative of any thermodynamic potential of interest. Suppose for example one desires to compute the derivative of the internal energy . The following procedure should be considered:
# Place oneself in the thermodynamic potential of interest, namely (, , , ). In our example, that would be .
# The two opposite corners of the potential of interest represent the coefficients of the overall result. If the coefficient lies on the left hand side of the square, a negative sign should be added. In our example, an intermediate result would be .
# In the opposite corner of each coefficient, you will find the associated differential. In our example, the opposite corner to  would be  (volume) and the opposite corner for  would be  (entropy). In our example, an interim result would be: . Notice that the sign convention will affect only the coefficients, not the differentials.
# Finally, always add , where  denotes the chemical potential. Therefore, we would have: .
The Gibbs–Duhem equation can be derived by using this technique. Notice though that the final addition of the differential of the chemical potential has to be generalized.