Energy Density of Electric and Magnetic Fields Calculator
Compute the electromagnetic energy stored per unit volume in an electric field E (in V/m) and/or a magnetic field B (in Tesla). Enter either or both field strengths to see the electric energy density, magnetic energy density, and total — using SI constants ε₀ and μ₀.
V/m
T
Combined electric + magnetic field energy stored per cubic metre
39.7892
J/m³Electric (uₑ = ε₀E²/2)
0%
Magnetic (u_B = B²/2μ₀)
100%
- 1
Electric energy density
ε₀ × 10,000² ÷ 2 = 0.000443ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. - 2
Magnetic energy density
0.01² ÷ (2 × μ₀) = 39.788736μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space. - 3
Total energy density
uₑ + u_B = 0.000443 + 39.788736 = 39.789178
How does this calculator work?
Electric fields store energy at uₑ = ε₀E²/2 J/m³ and magnetic fields at u_B = B²/(2μ₀) J/m³, using constants ε₀ = 8.854 × 10⁻¹² F/m and μ₀ = 4π × 10⁻⁷ H/m. Enter E (V/m) and/or B (T) to see each contribution and the combined electromagnetic energy density.
Formula
How this is calculated
An electric field of strength E stores energy at a density uₑ = ε₀E²/2 per cubic metre, where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. Similarly, a magnetic field of flux density B stores u_B = B²/(2μ₀) per cubic metre, where μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space. These two expressions come directly from the energy stored in capacitors (½CV²) and inductors (½LI²) extended to continuous field distributions.
When both fields coexist — as in an electromagnetic wave — the total energy density is the sum u = uₑ + u_B. In a plane electromagnetic wave in vacuum, the electric and magnetic contributions are always equal, which is why the total is often written u = ε₀E². At radio-wave amplitudes (E ≈ 1 V/m) the density is of order 10⁻¹¹ J/m³; at lightning-stroke fields (E ≈ 10⁶ V/m) it reaches tens of J/m³.
This calculator assumes field values in vacuum (or approximately in air, where the constants differ by less than 0.1%). Inside a dielectric or magnetic material, the formulas gain relative permittivity εᵣ and permeability μᵣ factors respectively, which are not modelled here.
Frequently asked questions
Electric field energy density is the energy stored per cubic metre in an electric field: uₑ = ε₀E²/2, where ε₀ ≈ 8.854 × 10⁻¹² F/m. For a field of 10⁴ V/m (typical near a charged object), this equals about 4.4 × 10⁻⁴ J/m³.
In a plane electromagnetic wave propagating in vacuum, the electric and magnetic energy densities are exactly equal at every instant: uₑ = u_B. This is because E and B are related by E = cB, and the constants work out so ε₀E² = B²/μ₀.
Energy density is measured in Joules per cubic metre (J/m³). This is equivalent to Pascal (Pa), the unit of pressure — electromagnetic radiation exerts radiation pressure equal to its energy density (for a perfect absorber).
TG we-Calculate Editorial Team. (2026). Energy Density of Electric and Magnetic Fields Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/energy-density-of-electric-and-magnetic-fields-calculator
TG we-Calculate Editorial Team. "Energy Density of Electric and Magnetic Fields Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/energy-density-of-electric-and-magnetic-fields-calculator.
TG we-Calculate Editorial Team, "Energy Density of Electric and Magnetic Fields Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/energy-density-of-electric-and-magnetic-fields-calculator
@misc{wecalculate_energy_density_of_electric_and_magnetic_fields_calculator, title = {Energy Density of Electric and Magnetic Fields Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/energy-density-of-electric-and-magnetic-fields-calculator}}, year = {2026}, note = {TG we-Calculate} }
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