Energy Density of Fields Calculator

Electric and magnetic fields store energy throughout the volume they occupy. Energy density measures that stored energy per unit volume and is expressed in joules per cubic meter. This calculator evaluates the electric contribution, the magnetic contribution, and their sum for linear, isotropic media. It is useful for studying capacitors, inductors, solenoids, transmission lines, electromagnetic waves, insulation systems, and many other devices in which field energy is distributed through space rather than concentrated at a single point. Electric-field energy density equals one half times absolute permittivity times electric field strength squared. Absolute permittivity is vacuum permittivity multiplied by the medium's relative dielectric constant. The calculator uses vacuum permittivity of approximately 8.8541878128 × 10^-12 farads per meter. A larger relative permittivity stores more electric energy at the same specified electric field. In practical capacitor problems, however, voltage, free charge, and geometry may determine how the field changes when a dielectric is introduced, so the correct comparison depends on what is held constant. Magnetic-field energy density expressed in terms of magnetic flux density B equals B squared divided by twice the absolute permeability. Absolute permeability is vacuum permeability multiplied by relative magnetic permeability, and vacuum permeability is approximately 1.25663706212 × 10^-6 henries per meter. Because this input is B in teslas, increasing permeability while holding B fixed reduces the computed density. If a problem instead holds magnetic field intensity H fixed, the equivalent expression is one half times permeability times H squared. The formulas assume a linear material whose permittivity and permeability do not vary with field strength, direction, frequency, temperature, or position. Ferromagnetic cores can be nonlinear, hysteretic, and frequency dependent, while dielectric materials can exhibit loss and dispersion. The tool therefore provides an ideal local energy-density estimate rather than a complete finite-element or loss analysis. Enter RMS or peak fields consistently when analyzing time-varying signals. For sinusoidal waves, instantaneous density varies during a cycle, and time-average calculations require the appropriate RMS convention. The separate outputs help identify whether electric or magnetic storage dominates and support quick checks of electromagnetic designs and physics exercises.