Energy Density of Electric and Magnetic Fields
Calculate the energy stored per unit volume in vacuum electric and magnetic fields, with live unit conversion and a transparent contribution breakdown.
Field strengths
Required, non-negative magnitude. V/m and N/C are equivalent in SI.
Required, non-negative magnetic flux density magnitude.
Energy density
375.807 J/m³
u = ½ε₀E² + B²/(2μ₀), using 2022 CODATA vacuum constants.
Contribution breakdown
| Component | Energy density (J/m³) | Share of total |
|---|---|---|
| Electric field | 17.7084 | 4.71% |
| Magnetic field | 358.099 | 95.29% |
| Total | 375.807 | 100.00% |
The two contributions add exactly to the displayed total before presentation rounding.
Where is the field energy concentrated?
The contribution chart needs two non-zero finite components. The table remains the authoritative numeric breakdown.
At the demonstration values, the magnetic term provides 95.29% of the total field energy density.
How to use the energy density of fields calculator
What this calculator does. This calculator estimates the energy stored per unit volume in an electric field and a magnetic field in vacuum. It evaluates the standard relation u = ½ε₀E² + B²/(2μ₀) and reports the result in joules per cubic meter (J/m³). It is useful for comparing field-energy scales, checking electromagnetism exercises, and examining how strongly an electric or magnetic field contributes to a local energy-density estimate. It does not model material polarization, magnetic media, nonlinear constitutive behavior, spatially varying fields, losses, or a volume integral for total stored energy in a real device.
When to use it. Use it to check the local vacuum field energy around a capacitor or magnetic-field source, compare electric and magnetic terms in an electromagnetic example, verify unit conversions before a laboratory calculation, or explore the square-law sensitivity of field energy to changing field magnitude. For electromagnetic waves, remember that the electric and magnetic amplitudes are not generally independent; in a plane wave in vacuum they are linked. OpenStax explains the same field-energy decomposition in its section on energy carried by electromagnetic waves.
How to calculate. The calculator opens with a ready-to-use demonstration and an immediately available XLSX export. To replace it:
- Enter the Electric field strength as a non-negative decimal magnitude, then choose the Electric field unit. You may use V/m, kV/m, MV/m, N/C, kN/C, or MN/C; the calculator converts the live value when you change the unit.
- Enter Magnetic field (B) as a non-negative decimal magnitude, then choose the Magnetic field unit from T, mT, µT, nT, or G. Unit changes convert the current value rather than merely relabeling it.
- Read Energy density first, then use Electric contribution, Magnetic contribution, the contribution table, and the stacked comparison chart to see which term dominates. All of these views come from the same canonical calculation.
- Select Download Excel to export the current validated inputs and outputs to a real OOXML workbook. Reset clears the demonstration values and calculated state; after Reset, Download Excel is disabled until both required magnitudes form a complete valid input set again.
Input guide. Electric field strength is required and represents the magnitude of E. Enter an ordinary decimal number using a dot as the decimal separator; commas are accepted only as standard three-digit grouping separators, so 2,000 is valid but 1,5 is rejected as ambiguous. The startup example is 2000 kN/C, equivalent to 2.000 × 10⁶ V/m. Increasing E increases only the electric term, and because E is squared, doubling E quadruples that contribution. A common mistake is to enter a signed vector component; this calculator expects a magnitude, so negative values are rejected. Electric field unit is required and controls only representation and conversion; N/C and V/m are equivalent units for electric field strength.
Magnetic field (B) is required and represents magnetic flux density magnitude. The startup example is 0.03 T, which is also 30 mT or 300 G. Increasing B raises only the magnetic term, again with a square-law relationship. Magnetic field unit is required for representation; choose the unit that matches your source data and let the calculator convert the live magnitude. Do not confuse magnetic flux density B, measured in teslas, with magnetic field strength H, measured in amperes per meter. NIST's Guide to SI derived quantities and units lists tesla for magnetic flux density, volt per meter for electric field strength, and joule per cubic meter for energy density.
Output guide. Energy density is the sum of the two field contributions and is an exact identity within this vacuum model, displayed in J/m³. A zero result means both input magnitudes are zero. Electric contribution is ½ε₀E²; Magnetic contribution is B²/(2μ₀). The Contribution breakdown table reports Component, Energy density (J/m³), and Share of total. Share is a comparison percentage, not an additional energy quantity. The chart uses the same two non-zero contributions as a 100% stacked comparison; if only one contribution is positive, the chart is replaced by a compact message rather than drawing a misleading one-part graphic. High or low contributions simply reflect the squared input magnitudes and the vacuum constants, not a safety threshold or engineering recommendation.
Worked example. With the startup values E = 2000 kN/C = 2.000 × 10⁶ V/m and B = 0.03 T, the electric term is ½ × 8.8541878188 × 10⁻¹² × (2.000 × 10⁶)² = 17.7083756376 J/m³. The magnetic term is (0.03)² ÷ (2 × 1.25663706127 × 10⁻⁶) = 358.098622004 J/m³. Adding them gives 375.806997642 J/m³, displayed as 375.807 J/m³. The table therefore shows about 4.71% electric and 95.29% magnetic contribution.
Learn more. The constants used here follow the 2022 CODATA recommendations; NIST publishes the 2022 CODATA recommended constants, including vacuum permittivity and vacuum magnetic permeability. For current unit-system definitions and prefix conventions, the BIPM publishes the International System of Units (SI) Brochure.
How the model works
The electric and magnetic terms are additive because each describes energy per unit volume associated with its field component. In vacuum, the model uses ε₀ = 8.8541878188 × 10⁻¹² F/m and μ₀ = 1.25663706127 × 10⁻⁶ H/m. Both terms are proportional to the square of field magnitude, so relative changes can matter more than their absolute-looking numbers suggest: a 10% increase in one field magnitude produces a 21% increase in that field's energy-density term, assuming the other input stays fixed.