Let X be the space of unimodular lattices in R^d. Let F: X/to R be the Siegel transform of a continuous compactly supported function f: R^d/to R. Siegel's formula says that the integral of f is the same as the integral of F. In this talk we show that the asymptotic average of F on certain normalized volume measure of the trajectory of a one-parameter diagonal flow also equals the integral of f. We will also give some applications of this result.