Some years ago a class of new symplectic invariants was discovered, the so-called symplectic capacities. In this note we compute the Hofer-Zehnder-capacitycHZ, which is defined via periodic solutions of Hamiltonian differential equations, for two-dimensional, connected manifoldsM with an area element ω. It turns out thatcHZ(M,ω) is just the area |∫Mω|. Moreover, some examples illustrate the dynamics standing behind the definition ofcHZ. In the last part we treat the special case of the real plane where also another type of capacities exists, an example of which is Hofer's displacement energy.