Calculate magnetic reluctance with R = l/(μA) from path length, area and a typical core material, or solve for length, area or permeability.
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Reluctance Formula
mathcalR = (l) / (μ A) l = mathcalRμ A A = (l) / (mathcalRμ) μ = (l) / (mathcalRA)
- ℜ = reluctance, in ampere-turns per weber or A/Wb
- l = magnetic path length
- μ = absolute permeability of the material
- A = cross-sectional area of the magnetic path
The calculation assumes a uniform magnetic path, constant cross-sectional area, and constant permeability. Use absolute permeability in H/m, H/ft, or H/in, not relative permeability by itself.
Useful Tables
Common unit conversions used for reluctance calculations:
| Quantity | Input unit | SI conversion |
|---|---|---|
| Length | 1 ft | 0.3048 m |
| Length | 1 in | 0.0254 m |
| Area | 1 ft² | 0.09290304 m² |
| Area | 1 in² | 0.00064516 m² |
Typical permeability reference values:
| Material | Typical relative permeability, μr | Absolute permeability note |
|---|---|---|
| Air or vacuum | About 1 | μ ≈ 1.256637 × 10-6 H/m |
| Aluminum | About 1 | Nearly the same as air |
| Electrical steel | Hundreds to thousands | Depends strongly on grade and flux density |
| Ferrite core | Tens to thousands | Use the datasheet value when available |
Reluctance Calculation Notes
If you only know relative permeability, convert it first:
μ = μᵣ μ₀
Use μ0 ≈ 1.25663706127 × 10-6 H/m (2022 CODATA). A larger magnetic path length increases reluctance. A larger area or higher permeability lowers reluctance.
