Reviewed by: JJ Ben-Joseph

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Electric fields, like magnetic fields, carry energy. When a capacitor is charged, work done by an external source is stored in the electric field between its plates. This stored energy per unit volume is called the electric energy density and is described by the expression $u=\frac{1}{2}\epsilon$₀E2, where $E$ is the electric field magnitude and $\epsilon \_0$ is the permittivity of free space. This calculator uses that relation to interconvert between field strength, energy density, total energy, and the volume over which the field extends.

Understanding electric energy density is essential for analyzing capacitors, transmission lines, and electromagnetic waves. In a parallel-plate capacitor with plate area $A$ and separation $d$, the energy density is uniform and the total energy equals the density times the volume $V=Ad$. In dielectric materials, the permittivity is $\epsilon =\epsilon$₀ε_r, enhancing the energy density by a factor of the relative permittivity $\epsilon$_r. Although our calculator uses the vacuum constant, results can be scaled for materials by multiplying the field or density appropriately.

The table below shows sample electric field values and their corresponding energy densities in vacuum.

Electric Field (V/m)	Energy Density (J/m³)
100	4.4×10−7
1,000	4.4×10−5
10,000	0.0044
100,000	0.44
1,000,000	44

Note how the energy density grows with the square of the field. Doubling $E$ increases the energy density by a factor of four. In high-voltage laboratories and power transmission systems, even modest volumes subjected to strong fields can store significant energy. This is why insulating materials and safety clearances are carefully engineered to prevent dielectric breakdown, which releases stored energy suddenly in the form of sparks or arcs.

The permittivity of free space has the value $\epsilon \_0=8.854187817\times {10}^{-} \mathrm{F/m}$. When fields exist inside materials, the permittivity changes and so does the energy density. For example, in glass with relative permittivity about 5, the same field stores five times more energy than in vacuum. Our calculator assumes vacuum, but simply replace $\epsilon$₀ with $\epsilon$ to generalize.

You can use the tool in several modes. Provide field strength and volume to compute both energy density and total energy. Supply energy density and volume to obtain total energy and field strength. If the total energy and volume are known, the calculator determines energy density first and then the field. Like our magnetic counterpart, the script works entirely client-side and checks that at least two values are given to avoid underdetermined situations. Results are displayed in volts per meter, joules per cubic meter, cubic meters, and joules respectively.

Electric energy density has broad applications. In waveguides and antenna theory, it contributes to the Poynting vector that describes energy flow. In high-energy physics, extremely strong fields near charged particles hint at the enormous energy densities present at subatomic scales. In everyday technology, understanding the energy stored in capacitors informs the design of flash photography, defibrillators, and power conditioning circuits.

As an example, consider a camera flash capacitor charged to produce an average field of 2 MV/m within a volume of 2×10⁻⁶ m³. Entering these values yields an energy density of 17.7 J/m³ and a total stored energy of approximately 0.035 J. This small but intense burst of energy is what powers a bright flash of light. Scaling up, a high-voltage laboratory capacitor bank with 1 MV/m over 1 m³ would store 4.4 MJ of energy, enough to cause severe damage if discharged improperly.

In more advanced treatments, electric energy density is part of the electromagnetic stress-energy tensor that couples fields to spacetime in general relativity. While such effects are minuscule under ordinary circumstances, they become significant in extreme environments such as near charged black holes or in the early universe where enormous fields may have influenced cosmic evolution. On a more practical level, researchers designing compact energy storage devices continually seek materials with high dielectric strength and large permittivity so that electric fields can store vast energy densities without breakdown. Exploring the simple formula implemented here is a first step toward understanding those cutting-edge technologies.

Try modifying the inputs to simulate different scenarios: how much energy is packed into the atmosphere during a thunderstorm when electric fields reach 3 MV/m over many cubic meters? How large must a laboratory capacitor be to store a joule of energy at a safe field strength? By playing with the numbers, you develop a tangible sense for the capabilities and limitations of electrostatic energy storage. This intuition is invaluable for electrical engineers, physicists, and hobbyists alike.

Comparing electric and magnetic energy densities offers a unified view of electromagnetism: in electromagnetic waves propagating through free space, the energy is shared equally between electric and magnetic fields. The calculator here can be paired with the magnetic version to explore this symmetry and to estimate how much energy travels in a light beam or radio transmission. Appreciating this balance deepens comprehension of Maxwell's equations and the conservation of electromagnetic energy.