Permeability Converter
Convert a magnetic permeability value between H/m, N/A², G·cm/Oe, and μ₀ using the calculator’s stated factors. Enter a value, then choose the From unit and To unit; see the notes below before using the μ₀ or G·cm/Oe results.
Convert Magnetic Permeability Between Units
Magnetic Permeability Conversion Formula
Where:
- \(v\) — the entered Permeability value.
- \(F_{\mathrm{from}}\) and \(F_{\mathrm{to}}\) — the factors assigned to the selected units by this calculator.
- \(\mu_0\) — the reference vacuum permeability used in the calculation.
This formula describes the calculator’s implemented arithmetic. Its factors for μ₀ and G·cm/Oe do not give reliable physical permeability conversions; see the limitations below.
Magnetic Permeability – Calculation Example
Example: use the default Permeability value of 0.0000012566, with H/m as the From unit and μ₀ as the To unit.
\[0.0000012566\times\frac{1}{1/\mu_0}=0.0000012566\times(4\pi\times10^{-7})\approx1.57909\times10^{-12}\]
Result: the calculator displays 0 μ₀ because it rounds the calculated number to 10 decimal places. This is not the physically correct value relative to vacuum: \(0.0000012566\ \mathrm{H/m}\div\mu_0\approx0.9999705\).
How to use the calculator
- Enter a nonnegative number in Permeability value. Interpret it in the unit you will select next.
- Choose the value’s current unit in From unit.
- Choose the requested unit in To unit.
- Read Converted Permeability, including its unit label. For dependable unit equivalence, use H/m and N/A²; check the limitations before relying on either other option.
H/m and N/A² are equivalent SI expressions, so converting between them leaves the numerical value unchanged. For example, 0.0000012566 H/m equals 0.0000012566 N/A². Selecting the same From unit and To unit also leaves the entered number unchanged.
What magnetic permeability means
Magnetic permeability, usually written \(\mu\), relates magnetic flux density \(B\) to magnetic field strength \(H\). In a linear, isotropic material, \(B=\mu H\). Permeability indicates how strongly a material responds to an applied magnetic field under those conditions. It is used when analyzing magnetic circuits, inductors, transformers, and other electromagnetic systems.
Absolute permeability has SI units of henries per meter (H/m), which are equivalent to newtons per ampere squared (N/A²). Relative permeability, \(\mu_r\), is different: it is the dimensionless ratio \(\mu/\mu_0\). A result of approximately 1 for \(\mu_r\) means the material’s permeability is approximately the reference vacuum value. The reference used here is \(\mu_0=4\pi\times10^{-7}\ \mathrm{H/m}\).
Permeability is not interchangeable with magnetic flux or magnetic flux density. If you need those quantities rather than a permeability unit change, use the Magnetic Flux Converter or Magnetic Flux Density Converter. The Magnetomotive Force Converter covers another quantity used in magnetic-circuit calculations.
Assumptions and important limitations
The μ₀ option is implemented in the wrong direction for a physical relative-permeability conversion. To find a dimensionless value relative to vacuum from an H/m value, divide by \(\mu_0\): \(\mu_r=\mu/\mu_0\). To convert that dimensionless value back to H/m, multiply by \(\mu_0\). The calculator does the reverse in these two cases. Its default H/m-to-μ₀ result also rounds a very small calculated number to zero; zero should not be interpreted as zero physical permeability.
Do not treat the G·cm/Oe option as a verified permeability-unit conversion. The calculator assigns it the numerical factor \(10^{-3}/\mu_0\), but G·cm/Oe is not directly interchangeable with H/m through that factor as a general physical unit conversion. Check the definitions, unit convention, and source of any value taken from older magnetic-material data before comparing it with SI permeability.
The relation \(B=\mu H\) with one fixed \(\mu\) assumes an appropriate linear-material model. Permeability can vary with field strength, frequency, temperature, and measurement direction; ferromagnetic materials may also show hysteresis. A unit conversion does not account for those effects. When working with alternating fields, keep the measurement frequency alongside the permeability value; the Frequency Converter can help standardize that separate quantity.
Frequently Asked Questions
How can I calculate permeability from measured B and H?
For a material that behaves linearly over the measured range, divide magnetic flux density by magnetic field strength: \(\mu=B/H\). Use \(B\) in tesla and \(H\) in amperes per meter to obtain \(\mu\) in H/m. If the measurements include an offset or the material is nonlinear, the slope \(\Delta B/\Delta H\) may be more useful than a single ratio. State the field range used.
What is a typical magnetic permeability value?
Vacuum permeability is approximately \(1.2566\times10^{-6}\ \mathrm{H/m}\), and air is very close to that value. Many nonmagnetic materials are also close, while ferromagnetic materials can have relative permeabilities of hundreds or thousands—or values outside that range. There is no universal “good” value: the relevant permeability depends on the material, operating field, frequency, and application.
How do I enter a value given in µH/m or mH/m?
Convert the prefix before entering the value as H/m. One microhenry per meter is \(10^{-6}\ \mathrm{H/m}\), and one millihenry per meter is \(10^{-3}\ \mathrm{H/m}\). For example, \(2.5\ \mathrm{\mu H/m}=2.5\times10^{-6}\ \mathrm{H/m}\). Keep the “per meter” part unchanged; a value given simply in henries describes a different quantity.
What is the difference between permeability and magnetic susceptibility?
Magnetic susceptibility \(\chi_m\) describes how much magnetization a material develops in response to a field. For a linear, isotropic material in SI units, \(\mu_r=1+\chi_m\) and \(\mu=\mu_0(1+\chi_m)\). Both \(\chi_m\) and relative permeability are dimensionless, whereas absolute permeability is measured in H/m. These simple relations may not describe a nonlinear or direction-dependent material with one fixed number.
Why is AC permeability sometimes given as a complex number?
In alternating fields, a material’s response can lag behind the applied field. Complex permeability represents both the response and that phase difference; its imaginary component is associated with magnetic losses under the stated sign convention. It also depends on frequency. This converter accepts a single nonnegative real number, so it cannot convert a complete complex permeability value or account for its frequency dependence.
Can magnetic permeability be negative?
Ordinary static materials generally have positive permeability, but an effective negative permeability can arise in certain engineered materials over a limited frequency range. Such a value needs its frequency and measurement convention to be meaningful; it should not be treated as an ordinary static material property. This calculator does not accept negative inputs and is not suitable for analyzing those cases.
Why does G·cm/Oe need more context than G/Oe?
The extra centimeter matters: \(\mathrm{G\cdot cm/Oe}\) and \(\mathrm{G/Oe}\) are not the same unit expression. In older magnetic data, a length factor may come from a particular specimen geometry, measurement method, or reported quantity. Find the source’s definition and any geometry factors before interpreting the number as permeability. The calculator’s G·cm/Oe option does not resolve that ambiguity.
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