Energy Density of Electric and Magnetic Fields Calculator
The energy stored per cubic metre in an electric or magnetic field — the physics behind capacitors, inductors and electromagnetic waves.
How much energy a field holds per cubic metre.
How the energy density of electric and magnetic fields calculator works
An electric field stores ½ε₀E² per cubic metre; a magnetic field stores B²/2µ₀. Both are energy densities, and adding them gives the total in an electromagnetic wave.
The comparison is instructive. A strong laboratory magnetic field of 10 T stores about 40 MJ/m³; an electric field at air's breakdown limit of 3 MV/m stores only 40 J/m³ — a million times less. That is why energy storage uses magnetic fields and superconducting magnets, not electrostatics.
Formula: uE = ½ε₀E²; uB = B²/2µ₀
Worked examples
| Inputs | Energy density | Note |
|---|---|---|
| A 1 tesla magnetic field | 397,887.357513 J/m³ | 398 kJ/m³ |
| Air at its breakdown field | 39.843845 J/m³ | only 39.8 J/m³ |
| An MRI magnet at 3 T | 3,580,986.217618 J/m³ | 3.6 MJ/m³ |
FAQFrequently asked questions
Where is the energy in a capacitor actually stored?
In the electric field between the plates, at ½ε₀E² per cubic metre. The ½CV² formula is that density integrated over the volume.
Why do magnetic fields store so much more?
Because air breaks down at about 3 MV/m, capping electric storage at roughly 40 J/m³, while a 10 T magnet reaches 40 MJ/m³ — a million times more.
Is energy density the same as pressure?
Numerically yes, and physically too: a magnetic field of energy density u exerts a pressure u on whatever confines it. At 10 T that is 40 MPa.
What about an electromagnetic wave?
The two contributions are equal in a vacuum wave, and their sum divided by c gives the momentum density.
Why are superconducting magnets so heavily built?
Because the magnetic pressure is real and enormous. An MRI magnet must physically resist megapascals of outward force.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.