Energy Density Of Electric and Magnetic Fields Calculator - Field Energy Per Volume

The energy density of electric and magnetic fields calculator finds how much electromagnetic energy is stored in each cubic metre of space. It sums the energy packed into the electric field, uE, and the energy packed into the magnetic field, uB, to give a single total energy density in joules per cubic metre (J/m3).

• • Capacitor and cavity design: Engineers estimate stored field energy before choosing insulation and spacing.
• • Electromagnetism coursework: Students check that uE and uB match in a travelling plane wave.
• • Radiation and antenna analysis: Researchers compare electric and magnetic energy near sources and in far fields.

Every electric field carries energy, and every magnetic field does too. The energy is spread through space rather than sitting at a point, so we describe it as a density: energy per unit volume. That is why the units are joules per cubic metre.

This calculator works for static fields, slowly varying fields, and electromagnetic waves. You enter the field strengths and, if the fields sit inside a material, the relative permittivity and permeability of that material.

Understanding field energy density helps explain why a capacitor stores energy in the gap between its plates and why the energy of a light wave is shared equally between its electric and magnetic parts.

The capacitor gap is where that field energy actually lives, which is why this result connects directly to the capacitor calculator, where the same electric-field energy appears as stored charge energy.

The calculator evaluates two separate energy-density terms and adds them. The electric term grows with the square of the electric field; the magnetic term grows with the square of the magnetic flux density.

• E: Electric field strength in V/m.
• B: Magnetic flux density in tesla.
• ε0: Vacuum permittivity, 8.8541878128e-12 F/m.
• μ0: Vacuum permeability, 4·π·1e-7 H/m.
• εr, μr: Relative permittivity and permeability of the medium (1 in vacuum).

In a vacuum the formula becomes u = (1/2) ε0 E2 + B2 / (2 μ0). The first term is the electric-field energy density and the second is the magnetic-field energy density. Each term has the same joules-per-cubic-metre unit, so they can be added directly.

Inside a material the field energy changes because the medium stores and returns energy differently. Multiplying the electric term by εr and the magnetic term denominator by μr captures that effect. A water-filled capacitor, for example, raises εr to about 80 and stores far more electric-field energy for the same E.

This energy density of electric and magnetic fields calculator follows the standard electromagnetism result that the energy density is (1/2)(E·D + B·H), which reduces to the formula shown above. Worked examples below show the numbers for common cases.

According to Wikipedia — Energy density, the electromagnetic energy density in vacuum is u = (1/2) ε0 E² + B²/(2 μ0)

If you start from a charge rather than a field, first find E with the point-charge relation using the electric field of a point charge calculator, then return here.

Three ideas help you read the outputs: what 'density' means here, why the two terms are symmetric, and how a material changes the balance.

The electric-field energy density is always non-negative because it depends on E squared. The same is true for the magnetic term and B squared, so the total can never go negative.

These relationships are confirmed by standard references: the electric and magnetic field energy densities are uE = (1/2) ε0 E2 and uB = B2/(2 μ0) in vacuum.

When you compute magnetic energy using an inductor, you are really summing this same magnetic energy density over the coil's volume, so the inductor energy calculator expresses the same physics through current and inductance.

Enter your field values and medium constants, then read the three results. No unit conversion is needed beyond the labels shown.

1. 1 Enter the electric field E: Type the magnitude of E in volts per metre. Use 0 if you only have a magnetic field.
2. 2 Enter the magnetic flux density B: Type B in tesla. For a plane wave in vacuum, set B = E / 299792458.
3. 3 Set the medium constants: Leave εr and μr at 1 for vacuum or air, or enter the material's relative permittivity and permeability.
4. 4 Read the densities: The primary result is the total energy density; the electric and magnetic contributions are listed beneath it.

For a radio wave with E = 300 V/m in vacuum, enter E = 300 and B = 1.00069e-6 T. The calculator returns uE ≈ uB ≈ 4.0e-7 J/m3, so u ≈ 8.0e-7 J/m3, confirming the equal split of a plane wave.

Gauss's law links a known charge distribution to the electric field used in the energy-density formula, so the Gauss's law calculator is the natural first step from charge to field.

A dedicated tool removes arithmetic mistakes and makes the electric and magnetic contributions visible side by side.

• • Clear split of field energy: See how much of the total comes from E versus B without hand-squaring constants.
• • Material-aware results: Include εr and μr so the answer reflects a dielectric or ferromagnet, not just a vacuum.
• • Plane-wave check: Verify uE = uB for a travelling wave, a common exam and design sanity check.

Knowing the separate uE and uB values helps when one field dominates, such as near a charged plate (electric) versus inside a solenoid (magnetic).

The magnetic force on a moving charge depends on B, and that force is sustained by the magnetic-field energy density you compute here.

The Lorentz force calculator shows the mechanical side of the same field, making the link between stored magnetic energy and the push a moving charge feels.

Four inputs control the output. Their ranges and the medium properties have the largest effect.

• • The formula assumes linear, isotropic media; strongly nonlinear ferromagnets need a more elaborate treatment.
• • It gives energy density at a point from the local E and B; total energy still requires integrating over volume.

Permeability is not constant for all materials. Vacuum and air are 1, while iron can exceed several thousand, which is why the same B can mean very different stored energy.

Vacuum permeability μ0 and vacuum permittivity ε0 are fixed SI constants, so the only free choices in a vacuum are E and B themselves.

According to NIST CODATA — Vacuum permittivity and permeability, ε0 = 8.8541878128e-12 F/m and μ0 = 4π×1e-7 H/m are fixed SI constants

Permeability is not constant for all materials, which is why the magnetic permeability calculator is useful for finding the μr that changes the magnetic term here.