  The nonextensive nature of black holes is one of the most intriguing
discoveries. In fact, the black hole entropy is a nonextensive quantity that
scales by its surface area at the event horizon. In our work, we extend the
thermodynamic phase space of black holes by treating the nonextensive parameter
of the R\'enyi entropy as the thermodynamic variable. Using Euler's theorem for
a homogeneous function of the black holes' mass, the compatible Smarr formula
and the first law of black hole thermodynamics can be obtained. It is also
demonstrated that, by keeping the same form of the black hole mass, the R\'enyi
temperature is straightforwardly defined as proposed in the literature. Since
many different types of black holes can indeed be successfully treated with
such a procedure, our consideration is fairly general. It is worthwhile to
argue that the black hole thermodynamics in R\'enyi statistics is rooted from
the relation among geometric quantities in the same way as the standard
approach corresponding to the Gibbs-Boltzmann statistics. Even though our
results are based on classical gravity, they may pave the way to derive the
R\'enyi temperature using the notion of quantum field in curved spacetime.
