Calculator Inputs
Select a method and enter values. Units are converted internally before calculation.
Formula Used
- Field energy density: u = B² / (2μ), where μ = μ₀ μr.
- Total energy in volume: U = u · V.
- Inductor energy: U = ½ · L · I².
Choose the field model when B and region volume are known. Choose the inductor model when inductance and current are known.
How to Use This Calculator
- Select a method that matches your measurement setup.
- Enter values and select appropriate units for each input.
- Click Calculate to view energy values above the form.
- Use Download CSV to save a data row.
- Use Download PDF to export a printable report.
Example Data Table
| Method | B (T) | μr | V (m³) | L (H) | I (A) | Energy (J) |
|---|---|---|---|---|---|---|
| Field | 0.50 | 1.0 | 0.0020 | — | — | 199.47 |
| Field | 0.20 | 2000 | 0.00010 | — | — | 0.00080 |
| Inductor | — | — | — | 0.015 | 3.0 | 0.06750 |
| Inductor | — | — | — | 0.0022 | 1.2 | 0.00158 |
Examples are illustrative and assume ideal conditions.
Article: Understanding Energy in Magnetic Fields
1) Why magnetic energy matters
Magnetic energy describes how much work is stored in a field or coil. It affects inductors, transformers, solenoids, MRI magnets, and power electronics. Designers use energy values to estimate transient behavior, forces, heating risk, and the severity of arc events when current is interrupted.
2) Energy density model for a field region
For many practical regions, the calculator uses u = B²/(2μ), where u is in J/m³, B is magnetic flux density in tesla, and μ = μ₀ μr. The constant μ₀ is about 1.256637×10⁻⁶ H/m. Total energy becomes U = u·V for a known volume.
3) Practical unit conversions you can trust
The input panel converts common units to standard SI for accuracy. Tesla (T) is the base unit. Millitesla (mT) and microtesla (µT) are scaled by 10⁻³ and 10⁻⁶. Gauss (G) is also supported, where 1 G = 10⁻⁴ T. Volume accepts m³, liters, cm³, and mm³.
4) What permeability changes in the result
Relative permeability (μr) captures how strongly a material responds to magnetization. For the same B, higher μr increases μ, which reduces energy density u by the same factor. This explains why fields in high-μ cores can store less energy than the same flux density in air.
5) Inductor model and the I² scaling
When inductance and current are known, the calculator uses U = ½·L·I². Because energy scales with current squared, doubling current increases stored energy by four times. Inductance is converted from H, mH, µH, or nH into henry before evaluation.
6) Data examples for quick intuition
If B = 0.50 T in air (μr≈1), energy density is about 99,472 J/m³. For a 0.002 m³ region, this yields roughly 199 J, matching the example table. For an inductor with L = 15 mH at I = 3 A, the energy is 0.0675 J.
7) Using results for design checks
Use energy for sanity checks and comparisons: higher B quickly raises energy; larger volumes raise total energy linearly. For coils, compare energy to capacitor storage or mechanical constraints to anticipate surge behavior. Always validate core saturation and frequency effects separately.
8) Limits and engineering notes
These formulas assume quasi-static conditions and a reasonably uniform field. Real systems can include fringing, leakage, saturation, and temperature dependence of μr. If your geometry is complex, use this tool to estimate order-of-magnitude values, then refine with field simulation or measured inductance.
FAQs
1) Which method should I choose?
Use the field method when you know B, μr, and the region volume. Use the inductor method when you know inductance and current from measurements or a datasheet.
2) Why does higher μr reduce energy density for the same B?
Energy density is u = B²/(2μ). If μ increases (via higher μr) while B stays the same, u decreases in proportion. This is a property of how energy is expressed in terms of B.
3) Can I enter gauss for magnetic flux density?
Yes. The calculator converts gauss to tesla using 1 G = 10⁻⁴ T, then computes energy in SI units for consistency.
4) What does energy density mean physically?
Energy density is stored energy per unit volume (J/m³). Multiply it by the region volume to estimate total stored magnetic energy in that space.
5) Why does inductor energy scale with I²?
Inductor energy is U = ½·L·I². The squared term comes from integrating voltage-current power during current buildup. It is why small current changes can strongly affect energy.
6) Are the results valid at high frequency?
The formulas are best for quasi-static conditions. At high frequency, losses, skin effects, and frequency-dependent μr can change effective inductance and stored energy. Treat results as an estimate and verify with measurements.
7) What if my field is not uniform?
If B varies across the volume, the true energy is an integral over space. Use an average B for a rough estimate, or split the volume into zones and sum energies for improved accuracy.