Demagnetization & Permeance Coefficient Calculator
A grade's catalog maximum temperature assumes a specific test geometry. Your part is not that geometry. Enter the real dimensions, gap, temperature and any opposing field, and this tool returns the permeance coefficient, the operating point on the load line, the margin to the knee — and the maximum operating temperature your part can actually survive.
interactive — operating point & knee margin
The load line is set entirely by geometry. Temperature and applied field move the curve. Irreversible loss occurs when the operating point falls below the knee of the intrinsic curve — at that moment the magnet does not simply weaken, it permanently loses output and will not recover on cooling. Anything under about 15 % knee margin deserves a physical soak test before you commit to production.
why geometry decides the temperature limit
Every magnet demagnetizes itself. Free poles at each face generate an internal field pointing against the magnetization, and the shorter and wider the magnet is in the magnetized direction, the stronger that self-field becomes. The permeance coefficient is simply the slope of the resulting load line: high Pc means a stubby, well-supported operating point near remanence; low Pc means the magnet is already working close to the cliff before anything external happens.
This is why the catalog number misleads people. A published maximum operating temperature for sintered NdFeB is measured on a cylinder with a length-to-diameter ratio around 0.7 — a fairly generous geometry. Take the same grade, press it into a 1 mm-thick sensor disc 15 mm across, and the real limit can fall by fifty degrees or more. Nothing about the material changed; the load line did.
Ceramic and ferrite magnets have a positive coercivity temperature coefficient, so they get magnetically weaker as they get colder. A ferrite assembly that behaves perfectly on the bench can suffer permanent loss in a −40 °C cold-soak test. Select the ceramic grade in this tool and drop the temperature to see it happen.
method — how the estimate works
| step | what is computed |
|---|---|
| 1 — demagnetizing factor | For blocks, Aharoni's exact closed-form solution for a rectangular prism. Cylinders, rings and arcs are reduced to an equal-cross-section prism, a standard engineering substitution that stays within a few percent for practical aspect ratios. |
| 2 — permeance coefficient | Pc = (1 − N) / N for the free-standing case, or Pc = (l_m · A_g) / (l_g · A_m) scaled by a leakage factor when the magnet sits in a steel circuit. |
| 3 — curve at temperature | Remanence and intrinsic coercivity are shifted by their reversible temperature coefficients. The knee is placed at an adjustable fraction of Hcj. |
| 4 — operating point | The load line is intersected with the recoil line, including any external demagnetizing field, and the resulting field in the magnet is compared against the knee. |
| 5 — safe temperature limit | The whole calculation is swept across temperature to find the point where the operating field crosses the knee, in both directions — the upper limit for rare earths, the lower limit for ferrite. |
Two deliberate conservatisms are built in. The demagnetizing factor used is the magnetometric — volume-averaged — value rather than the mid-plane ballistic value that some suppliers quote, so the Pc reported here runs lower than a headline figure for the same part. And the knee is treated as a hard threshold rather than a gradual roll-off. Both bias the result toward caution, which is the correct direction for a risk tool.
Radially magnetized rings, multipole rings and Halbach arrays do not follow the simple open-circuit treatment above — their internal working point varies with angular position. For those, use the ring or arc entry as a rough first pass and bring us the drawing; radially oriented rings are what we build.
fixing a design that fails
| lever | effect | cost |
|---|---|---|
| increase thickness in the magnetized direction | raises Pc directly — usually the single most effective change | more material, more axial space |
| reduce face area at constant thickness | raises Pc; two smaller magnets often beat one wide one | assembly complexity |
| add a steel yoke or return path | can multiply Pc several times over — turns a marginal design safe | weight, cost, packaging |
| close the working air gap | raises Pc and raises useful field at the same time | tolerance and clearance pressure |
| move up a coercivity class — H, SH, UH, EH | shifts the knee out; the direct fix when geometry is fixed | higher price, usually lower remanence |
| switch to samarium cobalt | far flatter temperature behaviour, no cold-side trap | substantially higher cost, brittle |
| reduce the opposing field | shielding, distance, or a lower drive current | system-level change |
Trading remanence for coercivity is rarely a loss overall. A lower-Br, higher-coercivity grade that sits safely above the knee at temperature will out-perform a headline N52 that has already taken twenty percent irreversible loss in its first thermal cycle. Compare the classes on the neodymium grades chart, or work the geometry question from the other end with the magnet grade selector.
reference — the formulas used
| permeance coefficient — free standing | Pc = (1 − N) / NN = magnetometric demagnetizing factor along the magnetized axis |
| permeance coefficient — in circuit | Pc = (l_m · A_g) / (l_g · A_m · f_leak) |
| load line with applied field | B = −µ₀ · Pc · (H + H_a)H_a = external demagnetizing field |
| recoil line | B = Br(T) + µ₀ · µ_rec · H |
| operating point | |H_m| = ( Br(T) + µ₀ · Pc · H_a ) / ( µ₀ · (Pc + µ_rec) ) B_d = Br(T) − µ₀ · µ_rec · |H_m| |
| temperature shift | Br(T) = Br₂₀ · [1 + α · (T − 20)/100] Hcj(T) = Hcj₂₀ · [1 + β · (T − 20)/100] |
| knee & margin | Hk(T) = k_sq · Hcj(T) margin = ( Hk(T) − |H_m| ) / Hk(T) |
| prism demagnetizing factor | Aharoni's exact analytic solution for a rectangular prism, verified against the cube result N = 1/3 |
going deeper — load lines, recoil permeability and full magnetic-circuit design are treated in magnets 201 — advanced magnetics engineering, and the thermal behaviour on its own in magnets & temperature. Once the operating point is safe, size the working field with the pull force calculator or the magnetic coupling torque calculator.