Magnet field and temperature calculator
What a gaussmeter reads above a magnet — anywhere above it, not just on the axis — and what happens to that reading as the magnet gets hot. The load line and the demagnetization curve move together, and when they cross below the knee, part of the loss never comes back.
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The magnet
Pick a shape and type its size. Everything else on the page follows from this.
- Total |B| at the probe
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- On the pole face, same offset
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- Pull force on steel
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- Permeance coefficient
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Demagnetization curve
Field against temperature
Field map
What this is doing
The load line
A magnet sitting on its own in air is working against its own stray field. The geometry sets how hard: the permeance coefficient Pc = (1−N)/N, where N is the volume-averaged demagnetizing factor, computed here from the shape rather than read off a chart. A cube comes out at exactly Pc = 2. Thin and wide means a low Pc and an operating point far down the curve; long and thin means a high one.
The knee
Heat a magnet and its remanence drifts down a little while its coercivity falls a lot. The curve pulls in toward the origin, the load line stays where it is, and at some temperature the crossing slips past the knee. Above that point the magnet does not return to where it started when it cools — it recoils along a lower line, and the gap is the irreversible loss. Push the slider up and back down to watch it happen.
The field at a distance
Closed-form solutions for a uniformly polarized disc, ring and block, off the axis as well as on it. A block works out in logs and arctangents over the eight corners of the surface-charge model; a cylinder needs elliptic integrals, one per pole face; a ring is the outer cylinder less the inner one. The polarization used is the one at the operating point, not the catalog remanence, so these numbers sit a percent or two below the calculators that assume Br everywhere. Move the probe out past the rim, or onto the axis of a ring, and the headline reading goes negative: that is return flux, and it points back into the magnet.
What it is not
A uniform-magnetization model, so it says nothing about corners, edge softening or a partly magnetized part. Pull force assumes flush contact with no air gap, paint or surface finish, against steel that saturates at 1.2 T — both at the interface and, usually the binding one, in the plate's own cross-section as the flux turns and runs sideways out from under the magnet. For anything being designed rather than sketched, measure the part. Nor does it pick a grade for you: the grade finder does that, from the limits on a drawing.
Where the numbers come from
134 grades read straight off Arnold's published demagnetization curves — the curve paths themselves, not the tables — then cross-checked against the Br and Hcj printed on the same page. Remanence, coercivity and knee shape all come from the curves where the curves show them. Temperature behavior is fitted through whatever each sheet supports: two or more points give the quadratic these properties can follow, a single quoted coefficient range gives a straight line, and the line above the charts tells you which it did for the grade you picked.
Worth knowing before you trust the fourth digit. Every neo and grain boundary diffused curve set turned out to be the room-temperature curve scaled linearly, with a quadratic term under 0.14% of the linear one, so those sheets carry nothing their tables do not. Only the SmCo grades bend, and only the ones whose coercivity is low enough to cross zero inside the plot — on the rest it runs off the left edge at every temperature drawn, and both the coercivity and the knee are then extrapolations, which the grade's own line says. The drawn knees are idealized throughout: they imply an energy product a few percent above what the same page prints.