Calculator Input
Enter geometry, material, leakage, fringing, and operating point values. Lengths use millimeters. Areas use square millimeters.
Formula Used
The calculator combines geometry based permeance, field based coefficient checks, and a simple linear magnet operating estimate.
| Purpose | Formula | Meaning |
|---|---|---|
| Magnet permeance | Pm = μ0 × μr × Am / Lm | Internal magnet path permeance. |
| Air gap permeance | Pg = μ0 × Ag × fringing / Lg | Useful air path before leakage correction. |
| Effective gap permeance | Pe = Pg × leakage factor | Gap path after leakage adjustment. |
| Series permeance | Ps = 1 / (1/Pm + 1/Pe) | Equivalent magnetic path permeance. |
| Geometry coefficient | Pc = (Lm/Lg) × (Ag_eff/Am) × leakage / μr | Dimensionless load line estimate. |
| Field coefficient | Pc = Bd / (μ0 × |H|) | Measured operating point comparison. |
| Estimated operating density | B = Br × Pc / (Pc + μr) | Approximate recoil line operating density. |
How to Use This Calculator
- Enter magnet length and area in millimeters and square millimeters.
- Enter the effective air gap length and projected air gap area.
- Set leakage below 1 when flux misses the useful gap.
- Set fringing above 1 when flux spreads at the gap edge.
- Add measured Bd and H values when you want a field based check.
- Press calculate. Results appear above the form.
- Use CSV for spreadsheet work. Use PDF for a quick report copy.
Example Data Table
| Case | Lm mm | Am mm² | Lg mm | Ag mm² | μr | Leakage | Fringing | Expected Pc |
|---|---|---|---|---|---|---|---|---|
| Compact sensor magnet | 8 | 80 | 2.5 | 70 | 1.05 | 0.82 | 1.10 | 2.41 |
| Holding magnet gap | 15 | 180 | 3 | 160 | 1.06 | 0.90 | 1.15 | 4.34 |
| Wide gap actuator | 20 | 240 | 6 | 210 | 1.08 | 0.78 | 1.18 | 2.66 |
| High leakage layout | 10 | 150 | 5 | 110 | 1.07 | 0.55 | 1.08 | 0.82 |
Permeance Coefficient Guide
What the Coefficient Shows
The permeance coefficient describes the magnetic load seen by a permanent magnet. It links the magnet shape, air gap, leakage, and operating field. A higher value usually means the magnet works at a stronger flux density. A lower value means the magnet faces stronger demagnetizing stress. This is important in motors, sensors, actuators, magnetic couplings, and holding fixtures.
Why Geometry Matters
Magnetic circuits are controlled by length and area. A longer magnet can support a stronger load line. A shorter air gap also improves the coefficient. Larger effective gap area can raise useful permeance, but leakage can remove part of that gain. Fringing can increase the apparent gap area near edges. The calculator includes both effects so the estimate is more practical.
Using Operating Point Data
Measured flux density and demagnetizing field give a second coefficient check. This is useful when test data or simulation output is available. If the field based value is close to the geometry value, the magnetic model is consistent. If the values differ strongly, review the assumed gap, leakage factor, material grade, and field units.
Reading the Results
The geometry coefficient is best for early design. The field coefficient is best for validation. Magnet permeance and gap permeance show which section limits the magnetic path. Series permeance gives the combined path. The estimated operating flux density uses a linear recoil approximation. It is helpful for quick comparisons, not final certification.
Design Notes
Always allow margin for heat, tolerances, coating thickness, and assembly gaps. Temperature derating reduces the available remanence. High demagnetizing field can push the magnet near its coercive limit. Use the safety ratio as a warning indicator. For final products, compare this result with finite element analysis and supplier magnet curves.
FAQs
1. What is a permeance coefficient?
It is a dimensionless load line measure for a magnet. It compares flux density with demagnetizing field and helps estimate the magnet operating point.
2. Is a higher coefficient always better?
Not always. A higher coefficient often improves flux density, but design goals, cost, size, saturation, and gap shape still matter.
3. What units should I enter?
Enter lengths in millimeters, areas in square millimeters, flux density in tesla, and demagnetizing field or coercive force in kA/m.
4. What does the leakage factor mean?
It represents the useful portion of flux that crosses the intended air gap. Lower values mean more flux escapes through unwanted paths.
5. What does the fringing factor mean?
It increases effective gap area when flux spreads near the air gap edges. It is usually slightly above one.
6. Why compare geometry and field coefficients?
The comparison checks consistency. A large mismatch may point to wrong dimensions, unit errors, saturation, heavy leakage, or unrealistic material assumptions.
7. Can this replace magnetic simulation?
No. It is a fast engineering estimate. Complex shapes, saturation, nonlinear materials, and nearby steel parts should be checked by simulation or testing.
8. What is a safe coefficient range?
There is no universal range. Many designs aim above one, but safe operation depends on magnet grade, temperature, coercivity, and load conditions.