# Energy Density of Electric and Magnetic Fields Calculator

URL: https://speedycalculator.com/calculators/physics/energy-density-of-electric-and-magnetic-fields/
Last updated: 2026-10-30

> The energy density calculator finds the energy stored per unit volume in an electric field, a magnetic field, or both, in a medium with given permittivity and permeability.

## Inputs

- Electric field E (V/m, kV/m, V/cm, MV/m, N/C)
- Magnetic field B (T, mT, µT, G, nT)
- Relative permittivity ε_r
- Relative permeability μ_r

## Results

- Electric energy density
- Magnetic energy density
- Total energy density

## Formula

```
u = ½·ε₀·ε_r·E² + B²/(2·μ₀·μ_r)
```

## Explanation

Fields store energy. A capacitor's energy is in the electric field between its plates; an inductor's in its magnetic field. In an electromagnetic wave the energy is shared equally between the two.

### How to use the Energy Density of Electric and Magnetic Fields Calculator

- **Electric field E**
- **Magnetic field B**
- **Relative permittivity ε_r**
- **Relative permeability μ_r**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the electric field and magnetic field and the medium properties.

### Inputs explained

FieldWhat to enterElectric field EUnits: V/m, kV/m, V/cm, MV/m, N/CMagnetic field BUnits: T, mT, µT, G, nTRelative permittivity ε_rA numberRelative permeability μ_rA number

### What each result means

- **Electric energy density** = 0.5×8.8541878128e-12×[Relative permittivity ε_r]×[Electric field E]^2
- **Magnetic energy density** = [Magnetic field B]^2÷(2×1.25663706212e-06×[Relative permeability μ_r])
- **Total energy density** = [Electric energy density] + [Magnetic energy density]

### Example values

How the main result changes when **Electric field E** changes and everything else stays at the example values above:

Electric field E (V/m)Total energy density (J/m³)500,000397,888.4643750,000397,889.84781,000,000397,891.78461,250,000397,894.27481,500,000397,897.31852,000,000397,905.0659

## Worked example

Inputs — Electric field E: 1,000,000 V/m; Magnetic field B: 1 T; Relative permittivity ε_r: 1; Relative permeability μ_r: 1.

Results — Electric energy density = 4.427094 J/m³; Magnetic energy density = 397,887.357513 J/m³; **Total energy density = 397,891.784607 J/m³**.

## Key terms

- **Energy density**: Energy per unit volume.

## FAQ

**Why do magnetic fields store so much energy?**
μ₀ is tiny, so even 1 T stores about 400 kJ/m³.

**What about an EM wave?**
Electric and magnetic energy densities are equal.

**Is energy density the same as pressure?**
They have the same units (J/m³ = Pa).

**How is energy stored in a capacitor?**
In the electric field between the plates.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)