Permeance coefficient calculator
permeance coefficient Pc for an NdFeB magnet
The permeance coefficient tells you where on the demagnetisation curve a free-standing magnet actually operates. It depends only on the shape of the body and on the ratio of its dimensions along the direction of magnetisation - not on the material grade. Pick a shape and enter the dimensions in millimetres.
We have no formula for Pc for a ring or a sphere from a verified source, so we do not calculate this shape. The closed formula covers a cylinder and a block with a square cross-section.
We have no formula for Pc for a ring or a sphere from a verified source, so we do not calculate this shape. The closed formula covers a cylinder and a block with a square cross-section.
| Permeance coefficient Pc: | — |
|---|---|
| Coefficient on the intrinsic curve Pci: | — |
| Ratio of magnetisation length to transverse dimension: | — |
| Formula used: | — |
The calculator returns the permeance coefficient that follows from the geometry of the magnet. It does not locate the knee of the demagnetisation curve - that needs a full B-H curve for the given grade and temperature, which we do not publish because we have not measured it.
Permeance coefficient - what this number means and why it matters
What the permeance coefficient is
The permeance coefficient, written as Pc, is the slope of the load line in the second quadrant of the hysteresis loop. The point where that line crosses the demagnetisation curve is the operating point of the magnet - it defines the flux density the magnet actually holds once it has been magnetised and taken off the magnetiser. For a free-standing magnet of simple geometry, Pc follows purely from the shape of the body and from the ratio of its dimensions along the direction of magnetisation. The material grade has no bearing on it: the very same block made in N38 and in N50 has an identical permeance coefficient. Absolute size does not matter either - scaling every dimension by the same factor leaves Pc untouched, because the volume changes while the ratio of length to cross-section does not.
What this calculator does not do
The calculator gives the permeance coefficient that follows from the geometry of the magnet. It does not indicate where the knee of the demagnetisation curve lies - that requires the full B-H curve for a given grade and temperature, which we do not publish because we have not measured it. This means the calculator will not tell you whether a given magnet will demagnetise at 80 degrees Celsius, nor by how much its flux density will drop after heating. Pc alone establishes only where the load line sits in the second quadrant - not where it intersects the curve of the material. Settling that question calls for demagnetisation curves measured for a specific grade at a specific temperature, and for complex geometries also for finite element analysis. Treat the result as a comparative guide between shapes, not as a guarantee of how the magnet will behave in service.
Same volume, an elevenfold difference
This is best illustrated by two blocks of exactly the same volume, 200 mm³. The first measures 20 × 10 × 1 mm and is magnetised through its 1 mm thickness - its permeance coefficient is roughly 0.13. The second measures 10 × 5 × 4 mm and is magnetised through its 4 mm thickness - its permeance coefficient is roughly 1.49. The same amount of material, the same grade, the same mass, yet Pc differs by a factor of eleven. The first block operates at a far less favourable point and is markedly more exposed to loss of properties at elevated temperature or in the presence of an external field. That is the whole purpose of this calculator: to show that the operating point of a magnet is set by its geometry, not merely by how much material went into it and which grade appears in the designation.
See also
- magnetic moment calculator - magnetic moment of the body in A·m²
- magnetic force and flux density calculator - flux density at a distance from the surface
- SI unit calculator - conversion of magnetic units