🧲 Magnetic Permeability Calculator
Calculate magnetic permeability and relative permeability
Magnetizing field strength in Amperes per meter
Resulting magnetic flux density
How to Use This Calculator
Enter Magnetic Field Strength (H)
Input the magnetic field strength (magnetizing field) in Amperes per meter (A/m). This is the H field that produces the magnetic flux density.
Enter Magnetic Flux Density (B)
Input the resulting magnetic flux density in Tesla. This is the B field that results from applying the H field to the material.
Calculate
Click the "Calculate Permeability" button to get both absolute permeability (μ) in H/m and relative permeability (μr) relative to free space.
Formula
μ = B / H
μr = μ / μ₀
Where:
- μ = Absolute Permeability (Henries per meter, H/m)
- B = Magnetic Flux Density (Tesla, T)
- H = Magnetic Field Strength (Amperes per meter, A/m)
- μr = Relative Permeability (dimensionless)
- μ₀ = Permeability of Free Space = 4π × 10⁻⁷ H/m
Example Calculation:
For a material with H = 1000 A/m, B = 0.001 T:
μ = 0.001 / 1000 = 1×10⁻⁶ H/m
μr = (1×10⁻⁶) / (4π×10⁻⁷) = 0.796
Note: Relative permeability indicates how much better a material conducts magnetic flux compared to vacuum. μr = 1 for vacuum/air, >1 for paramagnetic materials, >>1 for ferromagnetic materials (iron, nickel, cobalt).
About Magnetic Permeability Calculator
The Magnetic Permeability Calculator determines the ability of a material to support the formation of magnetic fields. Permeability (μ) relates the magnetic flux density (B) to the magnetic field strength (H). Relative permeability (μr) compares a material's permeability to that of free space, indicating how effectively the material concentrates magnetic flux.
When to Use This Calculator
- Material Characterization: Determine permeability of magnetic materials
- Electromagnet Design: Calculate permeability for core materials
- Transformer Design: Select appropriate core materials based on permeability
- Physics Education: Understand magnetic properties of materials
- Magnetic Circuit Analysis: Analyze magnetic circuits with different materials
Why Use Our Calculator?
- ✅ Quick Calculation: Instantly determine permeability from B and H measurements
- ✅ Relative Permeability: Also calculates μr for easy comparison
- ✅ Material Analysis: Essential for understanding magnetic material properties
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Learn about magnetic materials and their properties
Common Applications
Transformer Core Selection: Calculate permeability to select appropriate core materials for transformers. High-permeability materials (ferromagnetic) concentrate magnetic flux, reducing transformer size and losses. Iron cores have μr of 100-5000, making them ideal for power transformers.
Electromagnet Design: Determine permeability of core materials to design efficient electromagnets. Ferromagnetic cores with high relative permeability (100-100,000) significantly increase magnetic field strength compared to air-core coils, enabling powerful electromagnets for industrial and scientific applications.
Magnetic Circuit Analysis: Use permeability values to analyze magnetic circuits, similar to electrical circuit analysis. Materials with different permeabilities affect flux paths and field distributions, important for designing motors, generators, and magnetic sensors.
Tips for Best Results
- Permeability can be nonlinear for ferromagnetic materials (depends on H)
- Use initial permeability (low H) for linear approximation
- Relative permeability μr = 1 for vacuum, air, and non-magnetic materials
- Ferromagnetic materials (iron, nickel, cobalt) have μr >> 1
- Superconductors have μr = 0 (perfect diamagnetism)
Frequently Asked Questions
What is magnetic permeability?
Magnetic permeability (μ) is a measure of a material's ability to support magnetic field formation. It's the ratio of magnetic flux density (B) to magnetic field strength (H): μ = B/H. Higher permeability means the material concentrates magnetic flux more effectively.
What is the difference between absolute and relative permeability?
Absolute permeability (μ) has units of H/m and describes the material's actual permeability. Relative permeability (μr) is dimensionless and compares the material's permeability to free space: μr = μ/μ₀. Relative permeability is more commonly used because it directly shows how many times better the material is than vacuum.
What are typical relative permeability values?
Vacuum/air: μr = 1 (reference). Paramagnetic materials (aluminum, platinum): μr ≈ 1.00001-1.01 (slightly > 1). Ferromagnetic materials: μr = 100-100,000 (iron: 200-5000, mu-metal: up to 100,000). Diamagnetic materials (copper, water): μr ≈ 0.99999 (slightly < 1).
Is permeability constant for all materials?
No. For non-magnetic materials (paramagnetic, diamagnetic), permeability is approximately constant. For ferromagnetic materials, permeability varies with magnetic field strength H and can be nonlinear. Initial permeability (at low H) is often specified, but permeability decreases as the material saturates.
How does permeability relate to magnetic susceptibility?
Permeability and magnetic susceptibility (χ) are related: μ = μ₀(1 + χ), so μr = 1 + χ. Susceptibility measures how much a material becomes magnetized in response to an applied field. Paramagnetic materials have positive χ, diamagnetic have negative χ, ferromagnetic have large positive χ.
Why is high permeability important in transformers?
High-permeability cores concentrate magnetic flux, allowing transformers to operate with fewer turns, smaller size, and lower losses. This improves efficiency and reduces material costs. Ferromagnetic cores with μr > 1000 enable compact, efficient power transformers and inductors.