Magnetic Permeability Calculator
Choose a solve mode, enter the known values, and this calculator instantly works out the remaining magnetic quantities: absolute permeability, relative permeability, magnetic susceptibility, flux density, field strength, and permeance. Switch between six modes to solve for whichever quantity you need. A reference table of common materials is included below.
Formula
Worked example
A silicon-steel core has B = 1.005 T and H = 1000 A/m. mu = 1.005 / 1000 = 1.005e-3 H/m. mu_r = 1.005e-3 / (4pi x 10^-7) = 799.5. chi = 799.5 - 1 = 798.5 (ferromagnetic). For a core with area 10 cm2 and path length 0.1 m: Lambda = (1.005e-3 x 0.001) / 0.1 = 1.005e-5 H.
What is magnetic permeability?
Magnetic permeability (symbol mu) measures how readily a material allows magnetic flux to pass through it. It is defined as the ratio of magnetic flux density (B, in tesla) to magnetic field intensity (H, in amperes per metre): mu = B / H. The unit is henry per metre (H/m). The permeability of free space, mu_0, equals 4pi x 10^-7 H/m (approximately 1.2566 x 10^-6 H/m) and serves as the reference value. Relative permeability mu_r = mu / mu_0 is a dimensionless number that compares a material directly to vacuum. Diamagnetic materials have mu_r slightly below 1, paramagnetic materials slightly above 1, and ferromagnetic materials many times above 1, ranging from a few hundred for soft iron to over one million for specialty alloys.
Magnetic susceptibility and how it relates to permeability
Magnetic susceptibility (chi) describes how much a material magnetises in response to an applied field. It is directly linked to relative permeability by the simple relationship chi = mu_r - 1. For diamagnetic materials chi is a small negative number (e.g. copper has chi = -6 x 10^-6). For paramagnetic materials chi is a small positive number (e.g. aluminum has chi = 2.1 x 10^-5). For ferromagnetic materials chi can reach tens of thousands, which is why they are so useful in inductors, transformers, and motors. This calculator works out chi whenever you provide a relative or absolute permeability.
Permeance and magnetic circuit design
Permeance (Lambda, measured in henries) is the magnetic analogue of electrical conductance and describes how easily a complete magnetic path - such as a transformer core - conducts flux. It is calculated as Lambda = (mu x A) / l, where A is the cross-sectional area of the core and l is the length of the magnetic path. Higher permeability, larger cross-section, or shorter path all increase permeance. The reciprocal of permeance is reluctance, which plays the same role in magnetic circuits that resistance plays in electrical circuits. Engineers use permeance to size cores, predict inductance, and control flux leakage in motors, inductors, and electromagnetic actuators.
Practical notes on permeability values
The relative permeability of ferromagnetic materials is not a fixed constant. It varies with applied field strength (reaching a peak and then dropping sharply above saturation), temperature (dropping to 1 at the Curie temperature), frequency (complex permeability in AC applications), and material processing (annealing, grain orientation, and alloying all affect mu_r). The values in the reference table above are low-field, room-temperature approximations useful for initial design. Always consult a manufacturer datasheet or a measured B-H curve for production calculations.
Relative permeability of common materials
| Material | mu_r (approx.) | Class | Typical use |
|---|---|---|---|
| Bismuth | 0.99983 | Diamagnetic | Shielding, Hall sensors |
| Copper | 0.999994 | Diamagnetic | Wiring, busbars |
| Water | 0.99999912 | Diamagnetic | Reference medium |
| Vacuum / Air | 1.0000000 | Non-magnetic | Reference baseline |
| Aluminum | 1.000021 | Paramagnetic | Structural, heat sinks |
| Platinum | 1.000265 | Paramagnetic | Precision instruments |
| Nickel | 100-600 | Ferromagnetic | Transformer cores, plating |
| Iron (pure) | 200-5000 | Ferromagnetic | Electromagnets, yokes |
| Silicon steel | 1000-10000 | Ferromagnetic | Power transformers, motors |
| Ferrite (Mn-Zn) | 750-15000 | Soft ferrite | Switching power supplies |
| Mu-metal | 20000-100000 | High-mu alloy | Magnetic shielding |
| Supermalloy | up to 1,000,000 | High-mu alloy | Precision sensors, relays |
Representative values at room temperature and low field strength. Ferromagnetic values vary with field strength, temperature, and material grade.
Frequently asked questions
What is the permeability of free space (mu_0)?
The permeability of free space, also called the magnetic constant or vacuum permeability, is mu_0 = 4pi x 10^-7 H/m = 1.25663706 x 10^-6 H/m. Since the 2019 revision of the SI, this is a defined constant (exact). It appears in the formula mu = mu_r x mu_0 and in the Biot-Savart law and Maxwell's equations.
What does relative permeability mean?
Relative permeability (mu_r) is the ratio of a material's permeability to that of free space. mu_r = 1 means the material behaves like vacuum. Values below 1 indicate diamagnetic materials that slightly oppose the field; values greater than 1 indicate paramagnetic or ferromagnetic materials that enhance the field. Ferromagnetic materials can have mu_r from a few hundred up to over one million.
How is magnetic permeability different from magnetic susceptibility?
They describe the same physical phenomenon from different angles. Permeability (mu or mu_r) describes how well a material conducts magnetic flux. Susceptibility (chi) describes how strongly the material magnetises in an applied field. They are related by chi = mu_r - 1. For diamagnetics chi is negative (small), for paramagnetics chi is a small positive number, and for ferromagnetics chi is large and positive.
Does permeability change with temperature?
Yes. For ferromagnetic materials, permeability typically increases as temperature rises up to the Curie temperature, then drops sharply to approximately 1 (the material becomes paramagnetic). For iron the Curie temperature is about 770 degrees C; for nickel it is about 358 degrees C. In precision applications, temperature-compensated core materials such as certain ferrite grades are chosen to minimise this variation.
What is the difference between absolute and relative permeability?
Absolute permeability (mu, in H/m) is the actual permeability of the material including the vacuum baseline. Relative permeability (mu_r, dimensionless) is mu divided by mu_0, expressing how much better the material is than free space at conducting magnetic flux. In most engineering formulas you use absolute permeability; relative permeability is more useful for quickly comparing materials or reading datasheet specifications.
What is permeance and how does it relate to inductance?
Permeance (Lambda = mu x A / l) measures how easily a complete magnetic circuit (core) passes flux. It equals the inductance of a single-turn coil wound on that core. For a coil with N turns, inductance L = N^2 x Lambda. Reluctance (R = 1 / Lambda) is the inverse: a high-reluctance path requires more magnetomotive force (ampere-turns) to drive the same flux.