An expression that allows the determination of the Lagrangian Kolmogorov structure function constant from the knowledge of the constant associated to the second order Eulerian velocity structure function and the  numerical coefficient relating the Eulerian spectra constant to the Lagrangian one, is suggested. Experimental data from both wind tunnel and atmospheric boundary layer observation were used to determine . The study agrees with the universal nature of the Eulerian  constant for fully developed turbulence. The analysis leads to an estimate of , in agreement with previous studies. This estimated value has been employed in a Lagrangian stochastic dispersion model to simulate the observed concentration obtained from classical diffusion experiments.