Magnetic Reluctance
S = l / (µ0 · µr · A)
Quick answer
This calculator solves S = l / (µ0 × µr × A) for Reluctance. With Path Length 10 mm, Relative Permeability 0.5, Cross Section Area 10 cm², the result is 15.92 MA·t/Wb. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Reluctance is the magnetic-circuit analogue of resistance: it is the opposition a magnetic path presents to flux. A longer path raises reluctance while a larger cross-section or a higher-permeability material lowers it. High-permeability cores have very low reluctance, which is why they concentrate flux so effectively. An air gap, with µr = 1, adds large reluctance.
Variables
- S — Reluctance (ampere-turns/weber)
- l — Magnetic path length (m)
- µr — Relative permeability of the material
- A — Cross-sectional area (m²)
- µ0 = 4π×10⁻⁷ H/m —
Practical Notes
Reluctances in series add like resistors; a small air gap dominates the total reluctance of an otherwise high-µ core, which is how gapped inductors store energy and resist saturation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| S | Reluctance | A·t/Wb | A·t/Wb, kA·t/Wb, MA·t/Wb |
| l | Path Length | mm | mm, cm, m, km |
| mur | Relative Permeability | — | — |
| A | Cross Section Area | cm² | mm², cm², m² |
Step by step
- 1. What you know: Path Length 10 mm, Relative Permeability 0.5, Cross Section Area 10 cm²
- 2. The relation: S = l / (µ0 × µr × A)
- 3. Substitute: l = 10 mm, mur = 0.5, A = 10 cm²
- 4. Result: Reluctance = 15.92 MA·t/Wb
Worked examples
Minimum range
Given: Path Length 0.1 mm, Relative Permeability 0.025, Cross Section Area 10 mm²
Result: Reluctance = 318.3 MA·t/Wb
Low range
Given: Path Length 1 mm, Relative Permeability 0.25, Cross Section Area 1 cm²
Result: Reluctance = 31.83 MA·t/Wb
Typical
Given: Path Length 10 mm, Relative Permeability 0.5, Cross Section Area 10 cm²
Result: Reluctance = 15.92 MA·t/Wb
High range
Given: Path Length 10 cm, Relative Permeability 0.8, Cross Section Area 100 cm²
Result: Reluctance = 9.947 MA·t/Wb
Maximum range
Given: Path Length 1 m, Relative Permeability 8, Cross Section Area 0.1 m²
Result: Reluctance = 0.9947 MA·t/Wb
Solving for each variable
Solve for Reluctance
Path Length 0.1 mm, Relative Permeability 0.025, Cross Section Area 10 mm² → 318.3 MA·t/Wb
Solve for Path Length
Reluctance 10 kA·t/Wb, Relative Permeability 0.025, Cross Section Area 10 mm² → 3.14 × 10⁻⁶ mm
Solve for Relative Permeability
Reluctance 10 kA·t/Wb, Path Length 0.1 mm, Cross Section Area 10 mm² → 795.8
Solve for Cross Section Area
Reluctance 10 kA·t/Wb, Path Length 0.1 mm, Relative Permeability 0.025 → 0.3183 m²
How Reluctance changes with Path Length
| Path Length (input) | Reluctance (result) |
|---|---|
| 1 mm | 1.592 MA·t/Wb |
| 2.5 mm | 3.979 MA·t/Wb |
| 5 mm | 7.958 MA·t/Wb |
| 7.5 mm | 11.94 MA·t/Wb |
| 10 mm | 15.92 MA·t/Wb |
| 15 mm | 23.87 MA·t/Wb |
| 2 cm | 31.83 MA·t/Wb |
| 4 cm | 63.66 MA·t/Wb |
| 7 cm | 111.4 MA·t/Wb |
| 10 cm | 159.2 MA·t/Wb |
The same result in other units
| Unit | Value |
|---|---|
| kA·t/Wb | 15920 |
| MA·t/Wb | 15.92 |
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<p><a href="https://vbatpower.com/formulas/magnetic-reluctance/">Magnetic Reluctance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Magnetic Reluctance?
Use S = l / (µ0 × µr × A). With Path Length 10 mm, Relative Permeability 0.5, Cross Section Area 10 cm², Reluctance works out to 15.92 MA·t/Wb.
What is the formula for Magnetic Reluctance?
The formula is S = l / (µ0 × µr × A). Reluctance is the magnetic-circuit analogue of resistance: it is the opposition a magnetic path presents to flux.
How do you find Path Length when you know the other values?
Rearrange for Path Length: with Reluctance 10 kA·t/Wb, Relative Permeability 0.025, Cross Section Area 10 mm², Path Length is 3.14 × 10⁻⁶ mm.
How do you find Relative Permeability when you know the other values?
Rearrange for Relative Permeability: with Reluctance 10 kA·t/Wb, Path Length 0.1 mm, Cross Section Area 10 mm², Relative Permeability is 795.8.
What units does Magnetic Reluctance use?
Reluctance is shown in kA·t/Wb, MA·t/Wb. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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