The energy (measured in Joules) stored in a capacitor is equal to the work done to charge it. Consider a capacitance C, holding a charge +q on one plate and -q on the other. Moving a small element of charge from one plate to the other against the potential difference V = q/C requires the work :
where
We can find the energy stored in a capacitance by integrating this equation. Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:
Combining this with the above equation for the capacitance of a flat-plate capacitor, we get:
where