The energy stored ($U$) in a capacitor is given by the formula $U = \frac{1}{2}CV^2$. For a parallel plate capacitor, the capacitance is $C = \frac{\varepsilon_0 A}{d}$ and the potential difference is related to the electric field by $V = Ed$.

Substituting these values into the energy equation: $U = \frac{1}{2} \left( \frac{\varepsilon_0 A}{d} \right) (Ed)^2$ $U = \frac{1}{2} \left( \frac{\varepsilon_0 A}{d} \right) (E^2 d^2)$ $U = \frac{1}{2} \varepsilon_0 E^2 (Ad)$

Alternatively, the energy density (energy per unit volume) is $u = \frac{1}{2}\varepsilon_0 E^2$. The total energy is the product of energy density and the volume of the space between the plates ($Volume = A \times d$). Thus, $U = u \times Volume = \frac{1}{2}\varepsilon_0 E^2 Ad$.