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An ordinary capacitor stores energy by separating charge across a dielectric: $E=C{V}^2/2$ and $Q=CV$. Electronic charge redistribution is rapid, giving high specific power, but the dielectric breakdown field and modest capacitance limit specific energy. Series resistance limits pulse power and produces heating; a large nominal capacitance does not remove those losses.

A supercapacitor has a much larger interfacial area and nanometre-scale charge separation. An electric double-layer capacitor stores charge without a bulk redox transformation; pseudocapacitance adds sufficiently fast surface or near-surface redox storage. ion motion in pores, electrolyte stability and series resistance constrain its response. Its specific energy usually exceeds an ordinary capacitor's while high specific power and cycling durability remain possible.

An electric battery stores chemical free energy through coupled electrode oxidation-reduction reactions. It can store substantial energy per mass, but charge transfer, ionic transport, diffusion and heat removal constrain rapid discharge. The terminal voltage and accessible capacity depend on discharge rate and state of charge. Accordingly the plotted order follows the storage and transport mechanisms; it is not a claim that every battery has less power than every supercapacitor.

Specific energy is usable energy divided by device mass, commonly $\mathrm{Wh}\mathrm{k}{\mathrm{g}}^{-1}$; specific power is deliverable power divided by mass, commonly $\mathrm{W}\mathrm{k}{\mathrm{g}}^{-1}$. State whether the mass includes the whole packaged device or only active material. Volumetric energy density uses volume instead.

A conventional capacitor separates charge across a dielectric and stores $U=C{V}^2/2$, enabling rapid charge/discharge but relatively little energy. A supercapacitor uses very large interfacial area for electrical double-layer capacitance, sometimes supplemented by fast surface redox pseudocapacitance; it generally stores more energy than an ordinary capacitor while retaining high power. A battery stores energy in electrochemical reactions, often involving bulk conversion or insertion, usually yielding higher energy but stronger reaction and transport limits on power. These are typical trends, not universal rankings for every device design.

Define mass-specific differential capacitance, or specific capacitance, byState whether $m$ is one electrode's active mass, both electrodes' active mass or the entire device mass; these conventions are not interchangeable. An average capacitance inferred from a finite voltage interval is $\Delta Q/(m\Delta V)$ and need not equal the local derivative.

A nearly ideal double-layer supercapacitor has an approximately flat capacitance over its stable operating window, so stored charge rises nearly linearly with potential. Real electrodes need not be flat: dilute-electrolyte double-layer models can give a minimum near the potential of zero charge, while concentrated electrolytes, finite ion size and pore confinement can produce bell-shaped or double-peaked curves. Pseudocapacitance can add broad potential-dependent contributions near a redox transition. The sketch above therefore labels several possible behaviours instead of asserting a universal monotonic trend. Constant-potential simulations have directly found transitions between double-peaked and bell-shaped differential-capacitance curves as interfacial interactions change.^[ref]

A conventional capacitor stores separated electronic charge across a dielectric, with capacitance set approximately by $C=\epsilon A/d$. An electric double-layer capacitor stores charge at the interface between a porous electronic conductor and an ionic electrolyte. Electrolyte counterions screen charge on the electrode over a very small interfacial separation, and a porous electrode provides a large accessible area. The separator prevents an electronic short while permitting ionic transport; the two electrode interfaces form series capacitances.

Pseudocapacitance is charge storage by fast, reversible Faradaic processes that give a capacitor-like relation between stored charge and potential over a useful range. Examples include surface redox and suitably rapid insertion processes. It is distinct from purely electrostatic double-layer charging. Merely observing a redox peak does not establish pseudocapacitive behaviour: a slow two-phase battery reaction can remain battery-like even when its electrode is nanostructured.

Porous carbon emphasizes power and cycle life. Activated carbon, graphene-derived structures and nanotubes can provide high accessible area, electronic conduction and relatively reversible double-layer charging. Cost and stability can be favourable. However, inaccessible micropores, tortuous ionic paths, poor packing density and surface functional groups can reduce useful rate performance or volumetric energy density. Area measured by gas adsorption is not automatically accessible to electrolyte ions.

Metal oxides can add substantial redox charge storage. A suitable oxide offers high pseudocapacitance, but its electronic conductivity, ion-transport distance and electrochemical stability can limit power. Some high-performing compositions are expensive or contain scarce elements. Structural changes and dissolution can shorten life. Conductive composites and thin active layers help, but adding inactive support dilutes device-level energy storage.

Conducting polymers combine redox activity with electronic conduction and flexible processing. Their oxidation state and counterion population change during charging. Repeated ion and solvent uptake causes swelling and shrinkage, which can crack or delaminate an electrode and shorten cycle life. Conductivity is also state-dependent, and potential windows are constrained by overoxidation or reduction. A practical comparison must include both electrodes, electrolyte, packaging and the usable voltage: $E\simeq C{V}^2/2$ makes voltage stability as important as a large gravimetric capacitance.

An electrochemical capacitor storing charge through high-area electric double layers, pseudocapacitance, or a combination. Its device energy depends on usable voltage, inactive mass and rate capability as well as electrode capacitance.