Estimate μr for cores, alloys, and composites. Switch methods: μ, B/H, or susceptibility inputs quickly. Validate units, export reports, and document your calculations easily.
Relative permeability is a dimensionless measure that compares a material’s magnetic response to vacuum. The relationships below assume a linear region of the B–H curve.
| Scenario | B (T) | H (A/m) | μ = B/H (H/m) | μr = μ/μ₀ | χm = μr − 1 |
|---|---|---|---|---|---|
| Soft magnetic core (linear region) | 0.25 | 1500 | 1.666666666667e-4 | 132.629 | 131.629 |
| Near-vacuum reference | 0.001256637 | 1000 | 1.256637e-6 | 1.000 | 0.000 |
| Paramagnetic example | — | — | — | 1.002 | 0.002 |
Relative permeability (μr) tells you how strongly a material supports magnetic flux compared with vacuum. A μr of 1 means “vacuum-like.” Values above 1 indicate enhanced magnetization, often used to guide flux in cores.
Vacuum permeability μ₀ is approximately 1.256637061×10⁻⁶ H/m. This calculator uses that value by default, but also allows a custom μ₀ for sensitivity checks or aligned reference datasets.
You can compute μr from absolute permeability μ, from measured B and H using μ = B/H in a linear region, or from magnetic susceptibility using μr = 1 + χm. These routes cover datasheets, lab measurements, and models.
Orders of magnitude matter when selecting a material. The table below gives realistic, approximate ranges. Always verify with the operating frequency, temperature, and bias field used in your design.
| Material class | Typical μr range | Notes |
|---|---|---|
| Vacuum / air | ≈ 1.000000 | Reference baseline for comparisons. |
| Paramagnetic | 1.000001 – 1.01 | Slight enhancement; often near unity. |
| Diamagnetic | 0.999999 – 1.000000 | Slight reduction; still close to unity. |
| Ferrites (power cores) | 200 – 5000 | Frequency-dependent; lower losses at high frequency. |
| Soft iron / steels | 200 – 6000+ | Strongly nonlinear; saturates with bias. |
Many magnetic materials have a B–H curve where μ changes with field strength. When using B and H, choose a point in the near-linear region. Near saturation, μr drops, so a single-number μr can mislead.
For laboratory data, ensure B is in tesla and H is in A/m, and confirm the test frequency and waveform. Datasheets may list initial permeability, maximum permeability, or effective permeability based on geometry and gaps.
Higher μr can reduce magnetizing current in inductors and improve flux confinement in transformers, but it can also increase sensitivity to bias, temperature, and tolerances. In gapped cores, the effective μr is dominated by the air gap, not the raw material.
Use the computed χm to cross-check plausibility: χm = μr − 1. If you expect a near-unity material, μr should be very close to 1. For high-permeability cores, confirm you are not using saturated B–H points.
Not always. Many materials are nonlinear, so μr varies with field strength, frequency, and temperature. Use B and H from a defined operating point for the most meaningful μr value.
Use it when you measured flux density and field strength at the same point and conditions. It is best in a near-linear region of the B–H curve to avoid saturation effects.
μ is absolute permeability in H/m. μr is dimensionless and equals μ divided by μ₀. μr lets you compare materials without carrying units.
An air gap greatly reduces the effective permeability of a magnetic path. Even if a core has high μr, the gap often dominates reluctance and stabilizes inductance versus bias.
Susceptibility χm links material magnetization to field strength in linear models. Reporting χm helps validate results and supports workflows that start from χm instead of μ or B–H data.
Yes. Diamagnetic materials have μr slightly below 1. The difference is usually tiny, so measurements require careful instrumentation and consistent units.
Use the value matching your conditions: frequency, temperature, and bias. For core design, “initial” or “effective” permeability is often more relevant than a peak value.