Eulerian turbulence observations, made in the surface layer under unstable conditions (z/L > 0), by a sonic anemometer were used to estimate the Lagrangian structure function constant C(0). Two methods were considered. The first one makes use of a relationship, widely used in the Lagrangian stochastic dispersion models, relating C(0) to the turbulent kinetic energy dissipation rate epsilon, wind velocity variance and Lagrangian decorrelation time. The second one employs a novel equation, connecting C(0) to the constant of the second-order Eulerian structure function. Before estimating C(0), the measurements were processed in order to discard non-stationary cases at least to a first approximation and cases in which local isotropy could not be assumed. The dissipation epsilon was estimated either from the best fit of the energy spectrum in the inertial subrange or from the best fit of the third-order longitudinal Eulerian structure function. The first method was preferred and applied to the subsequent part of the analysis. Both methods predict the partitioning of C(0) in different spatial components as a consequence of the directional dependence of the Eulerian correlation functions due to the isotropy. The C(0) values computed by both methods are presented and discussed. In conclusion, both methods provide realistic estimates of C(0) that compare well with previous estimations reported in the literature, even if a preference is to be attributed to the second method.