Enter any two of the quantities below to solve for the remaining values using the magnetic energy density relation .
Tune the coil current to keep magnetic energy density inside its safe window as flux gusts buffet the field.
Magnetic fields store energy just as electric fields do. In free space the energy density is , where is field strength and is the permeability of free space. Multiply the density by volume to obtain total stored energy, .
The energy stored in transformer cores, inductors, and superconducting magnets determines how they behave during switching or quenches. In plasma physics and astrophysics, magnetic pressure influences the dynamics of charged particles and stabilizes fusion devices. Because energy density scales with , doubling the field quadruples stored energy; the calculator makes that nonlinear growth obvious with a single entry.
| Magnetic field (T) | Energy density (J/m³) | Equivalent pressure (Pa) |
|---|---|---|
| 0.01 | 0.00004 | 0.00004 |
| 0.10 | 0.004 | 0.004 |
| 1.0 | 0.40 | 0.40 |
| 5.0 | 10.0 | 10.0 |
| 10.0 | 40.0 | 40.0 |
Even a seemingly modest 5 T field stores the same energy per cubic meter as a 10 kPa pressure difference. That comparison helps mechanical engineers visualize the forces superconducting coils must withstand.
Provide any two inputs—such as field and volume—to determine the remaining quantities. The tool validates that enough data is supplied and computes the missing numbers instantly in your browser. If you only know total energy and coil volume, leave the field blank and the script will back-calculate for you.
In materials with relative permeability , replace with . High-permeability cores concentrate flux and increase stored energy, but they eventually saturate. Use the calculator to estimate energy at different values and compare the results to the material’s saturation limit to avoid overheating or acoustic noise.
Students can explore how energy grows with , while professionals can estimate energy in coils, magnetic traps, or astrophysical plasmas. Because everything runs locally, the calculator doubles as a quick field-theory reference and a safe way to check lab designs or lab reports before running costly simulations.
The formula assumes uniform fields and ignores edge effects. Complex geometries may require finite-element analysis. Resistive losses and dynamic effects (such as eddy currents) are also excluded. Treat the results as a first-order approximation, then refine with a detailed magnetic model or empirical measurements.
