Magnetic Permeability
Calculate magnetic permeability (μ), relative permeability (μᵣ), and magnetic susceptibility (χ) for any material using μ₀ constant. Free calculator with 14 material presets from vacuum to mu-metal and interactive charts.
About This Calculator
The Magnetic Permeability Calculator helps you determine the magnetic properties of any material by computing its absolute permeability (μ), relative permeability (μᵣ), and magnetic susceptibility (χ). This tool is essential for students, physicists, electrical engineers, and materials scientists working with electromagnetism, transformer design, magnetic shielding, and inductor core selection.
The calculator uses the vacuum permeability constant μ₀ = 4π × 10⁻⁷ H/m as the reference. For a selected material with known relative permeability μᵣ, the absolute permeability is calculated as μ = μ₀ × μᵣ, and the magnetic susceptibility as χ = μᵣ − 1. Materials are classified as diamagnetic (μᵣ < 1), paramagnetic (μᵣ > 1), or ferromagnetic (μᵣ ≫ 1) based on their relative permeability.
Key Concepts
Diamagnetic materials like copper, silver, and water have relative permeability slightly less than 1 (χ negative). They create an induced magnetic field opposing the external field, resulting in a weak repulsive force. This property is used in magnetic levitation and MRI shielding.
Paramagnetic materials like aluminum and platinum have relative permeability slightly greater than 1 (χ positive but small). They are weakly attracted to magnetic fields and do not retain magnetization once the external field is removed.
Ferromagnetic materials like iron, nickel, cobalt, and mu-metal have relative permeability much greater than 1 (χ large and positive). They exhibit strong attraction to magnetic fields, can retain permanent magnetization, and are used in electromagnets, transformers, inductors, and magnetic recording media.
Frequently Asked Questions
What is magnetic permeability?
Magnetic permeability (μ) measures how easily a material can support the formation of a magnetic field within itself. It is defined as the ratio of magnetic flux density (B) to magnetic field strength (H), given by μ = B/H. The vacuum permeability μ₀ = 4π × 10⁻⁷ H/m serves as the reference value.
What is the difference between permeability and relative permeability?
Absolute permeability (μ) is the material's actual permeability measured in henrys per meter (H/m). Relative permeability (μᵣ) is the ratio of the material's permeability to vacuum permeability: μᵣ = μ/μ₀. For example, iron has μᵣ ≈ 5000, meaning it conducts magnetic field 5000 times better than vacuum.
What are diamagnetic, paramagnetic, and ferromagnetic materials?
Diamagnetic materials (μᵣ < 1, e.g., copper, silver, water) create an opposing magnetic field and are weakly repelled by magnets. Paramagnetic materials (μᵣ > 1, e.g., aluminum, platinum) are weakly attracted. Ferromagnetic materials (μᵣ ≫ 1, e.g., iron, nickel, cobalt) are strongly attracted and can retain magnetization, making them ideal for permanent magnets and transformer cores.
How is magnetic susceptibility related to permeability?
Magnetic susceptibility (χ) and relative permeability (μᵣ) are related by χ = μᵣ − 1. Susceptibility measures how much a material becomes magnetized in an applied field. For diamagnetic materials χ is negative (∼−10⁻⁵), for paramagnetic χ is positive (∼10⁻⁵ to 10⁻³), and for ferromagnetic χ can reach 10⁵ or higher.
Is this calculator free to use?
Yes, this magnetic permeability calculator is completely free to use with no registration, login, or hidden charges. You can calculate permeability, relative permeability, and susceptibility for any material instantly.
Can I share my magnetic permeability calculation results?
Yes, the URL automatically saves your selected material and input values so you can bookmark or share the exact calculation with others. Simply copy the URL from your browser address bar.
What materials are included in this calculator?
The calculator includes presets for vacuum, air, water, copper, silver, lead, aluminum, platinum, cobalt, nickel, pure iron, silicon steel, mu-metal, and MnZn ferrite. You can also enter a custom relative permeability value for any other material.
How accurate are the magnetic permeability calculations?
The calculations use the exact vacuum permeability constant μ₀ = 4π × 10⁻⁷ H/m and the precise material relative permeability values. Results are displayed with high precision — permeability in scientific notation, relative permeability to 8 decimal places, and susceptibility in scientific notation.