The paper introduces a new cosmological diagnostic pair, the Statefinder $\{r, s\}$, which is a geometrical tool for characterizing dark energy in a model-independent manner. The Statefinder parameters are dimensionless and derived from the scale factor of the universe and its time derivatives. The parameter $r$ is the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter $H$ and the deceleration parameter $q$, while $s$ is a linear combination of $q$ and $r$ that does not depend on the dark energy density. The Statefinder pair is algebraically related to the equation of state of dark energy and its first time derivative. The authors demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy, including cosmological constants, quiescence models, and kinescence models. They also show that the mean Statefinder pair can be determined with high accuracy from future SNAP-type satellite missions, which are expected to observe a large number of type Ia supernovae up to a redshift of around 2. The results indicate that the Statefinder pair can distinguish between various models of dark energy, including inverse power-law quintessence and the DGP brane cosmological model.The paper introduces a new cosmological diagnostic pair, the Statefinder $\{r, s\}$, which is a geometrical tool for characterizing dark energy in a model-independent manner. The Statefinder parameters are dimensionless and derived from the scale factor of the universe and its time derivatives. The parameter $r$ is the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter $H$ and the deceleration parameter $q$, while $s$ is a linear combination of $q$ and $r$ that does not depend on the dark energy density. The Statefinder pair is algebraically related to the equation of state of dark energy and its first time derivative. The authors demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy, including cosmological constants, quiescence models, and kinescence models. They also show that the mean Statefinder pair can be determined with high accuracy from future SNAP-type satellite missions, which are expected to observe a large number of type Ia supernovae up to a redshift of around 2. The results indicate that the Statefinder pair can distinguish between various models of dark energy, including inverse power-law quintessence and the DGP brane cosmological model.