energy density comparison between inductors and capacitors
Every inductor has a rated current, every capacitor a rated voltage. And of course their rated inductance or capacitance. And they come in a defined package where you can calculate the volume.

With capacitors you have to be careful though. Ceramic capacitors with some dielectrics will change their rated capacitance based on the voltage they are charged, so it's not quite as simple.

As an example, let's take a look at this inductor:


10 µH
5 A
6.65 x 6.45 x 5.8 mm³ = 248.8 mm³


Neglecting the resistance of the inductor:

energy stored: \$E_{ind} = \frac{1}{2} L I^2 = \frac{1}{2} 10~\text{µH} (5~\text{A})^2 = 0.125~\text{mJ}\$

Energy density: \$0.125~\text{mJ} / 248.8~\text{mm}^3 = 0.5~~\text{µJ}/~\text{mm}^3\$

And for a capacitor let's take one of this series:


47 µF
25 V
5.8 x 5.2 x 5.2 mm³ = 156.8 mm³


Again neglecting parasitics:

Energy stored: \$E_{cap} = \frac{1}{2} C U^2 = \frac{1}{2} 47~\text{µF} (25~\text{V})^2 = 14.7~\text{mJ}\$

Energy density: \$14.7~\text{mJ} / 156.8~\text{mm}^3 = 93.8~~\text{µJ}/~\text{mm}^3\$

So for these two the numbers of the study seem to hold up. I neglected the loss of parasitics, you can model these as well and get smaller numbers.