Formula: Capacitor Energy Capacitance Voltage
$$W_{\text e} ~=~ \frac{1}{2} \, C \, U^2$$
$$W_{\text e} ~=~ \frac{1}{2} \, C \, U^2$$
$$C ~=~ \frac{2 W_{\text e}}{U^2}$$
$$U ~=~ \sqrt{ \frac{2 W_{\text e}}{C} }$$
Electrical energy
$$ W_{\text e} $$ Unit $$ \mathrm{J} = \mathrm{Nm} = \frac{ \mathrm{kg} \, \mathrm{m^2} }{ \mathrm{s}^2 } $$
Energy stored, for example, in the electric field of a plate capacitor. The formula also applies to other charged bodies to which a capacitance \(C\) can be assigned.
Capacitance
$$ C $$ Unit $$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$
Capacitance is a measure of how well a body can store charge. For example, how well the plate capacitor can store charge on its plates.
Voltage
$$ U $$ Unit $$ \mathrm{V} = \frac{ \mathrm J }{ \mathrm C } = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A} \, \mathrm{s}^3 } $$
Voltage, for example, between the electrodes of a plate capacitor.