Maximum Energy Product (BH)max: What the Number in a Magnet Grade Really Tells You

Introduction

A drawing calls out N52 because it is the strongest grade on the datasheet. The prototype works on the bench. Then the magnet goes into its housing, the assembly warms up, and the measured field comes in below spec, even though the material certificate says the magnet passed. The number behind "52" is the magnet's maximum energy product, and it is a real, measured property. But it describes one specific operating point, on a closed-circuit test sample, at room temperature. Knowing what (BH)max actually measures, and where your design sits relative to it, is the difference between a grade that delivers and a grade that only looks good on paper.

What is maximum energy product?

Maximum energy product, written (BH)max, is the largest value of B × H anywhere on a permanent magnet's demagnetization curve, and it measures how much magnetic energy the magnet can supply to the space around it per unit of its own volume.

A permanent magnet in use sits somewhere in the second quadrant of its hysteresis loop, the demagnetization curve. Each point on that curve is a possible operating state: a flux density inside the magnet, Bd, paired with an opposing field inside the magnet, Hd. Which point the magnet lands on depends on its own shape and on the magnetic circuit around it.

Multiply Bd by Hd at any point and you get the energy product for that state, which is the energy density the magnet can put into an external air gap. Graphically it is the area of a rectangle drawn from the origin to that point on the curve (the hatched area in Figure 1). Slide along the curve and the rectangle changes shape. At one point its area peaks. That peak is (BH)max.

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normal (B–H) and intrinsic (J–H) demagnetization curves

It is quoted in two unit systems. SI uses kilojoules per cubic metre (kJ/m³); North American and most Asian datasheets still use mega-gauss-oersteds (MGOe). The conversion is fixed: 1 MGOe ≈ 7.96 kJ/m³, so a 50 MGOe magnet is about 398 kJ/m³.

Why do engineers need (BH)max when they already have Br and Hc?

Remanence tells you how strong a magnet is with no load and coercivity tells you how hard it is to demagnetize, but only (BH)max tells you how much useful field a given volume of material can deliver across a gap.

The idea grew out of a practical problem. As motors, generators and loudspeakers spread in the late 19th and early 20th century, the only permanent magnets available were hardened steels, and getting a strong field out of them meant using a lot of steel. Equipment was heavy and expensive. The engineering question became: how small can the magnet be and still produce the field the device needs?

Remanence (Br) and coercivity (Hc) each answer half of that question. An electrical analogy helps here. Br behaves like a battery's open-circuit voltage, and Hc like its short-circuit current. Neither tells you how much power the battery can actually deliver to a load; that peaks somewhere in between. (BH)max is the magnet's equivalent of maximum deliverable power, and it gave designers a single figure to rank materials by and a target to design toward.

The analogy goes further than it first appears. For a magnet whose demagnetization curve is close to a straight line, as it is for sintered NdFeB, the peak falls at roughly half of Br, just as a linear source delivers maximum power at half its open-circuit voltage. That also sets a ceiling: an ideal straight-line magnet cannot exceed Br² / 4μ₀. Energy product is capped by remanence, which is why every jump in (BH)max in the history below came from a material with higher saturation magnetization.

Where on the curve does a magnet actually reach (BH)max?

A magnet only operates at (BH)max when its shape and the surrounding magnetic circuit place its working point there; for sintered NdFeB, that point sits at roughly half the remanence.

The working point is set by the load line, whose slope is the permeance coefficient (Pc). A long magnet in a closed steel circuit has a steep load line and works high on the curve, near Br. A thin, wide magnet in open air has a shallow load line and works low on the curve, closer to the knee where irreversible loss begins.

The hysteresigraph report in Figure 4 shows this on a real N52 sample: Br = 1.435 T, and the (BH)max point falls at Bd = 0.714 T, Hd = 552.9 kA/m. That is almost exactly half of Br, as the straight-line argument predicts.

This is what the concept was really for. Once (BH)max was defined, a designer had something concrete to optimize: choose the magnet's length and cross-section so the working point lands near the peak, and you get the required gap field from the least material. In practice many designs deliberately sit somewhat above the (BH)max point, trading a little material efficiency for margin against heat and opposing fields. But that is a choice made against the curve, not instead of it.

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How is maximum energy product measured?

(BH)max is measured on a closed-circuit hysteresigraph, which drives a sample from saturation through demagnetization, records B and H continuously, and reports the largest B × H product found.

The sample is clamped between the pole pieces of an electromagnet, fully magnetized, then subjected to a steadily increasing reverse field. Sensing coils record B and H through the whole second quadrant. Software multiplies the two at every point and picks out the maximum.

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Hysteresigraph test system and a measured demagnetization curve

The governing test methods are IEC 60404-5 and ASTM A977/A977M. Chinese suppliers test to GB/T 3217, which covers the same closed-circuit measurement; a certificate citing it is equivalent in method.

Two things about that test matter when you read a certificate. It is run on a closed circuit, so it reports the material's capability rather than the performance of your part in your assembly. And it is normally run at 20 °C. Both are reasons a magnet can pass inspection and still underperform in service.

How has (BH)max changed across magnet materials?

Each new permanent-magnet family has raised the ceiling on (BH)max, from under 1 MGOe for early magnet steels to over 50 MGOe for modern sintered NdFeB.

Material Introduced Typical (BH)max What it changed
Carbon and tungsten steels Early 1900s < 1 MGOe (< 8 kJ/m³) First practical permanent magnets; bulky
AlNiCo 1930s > 5 MGOe (> 40 kJ/m³) Made permanent magnets a routine engineering material
Ferrite (ceramic) 1950s 3–5 MGOe (24–40 kJ/m³) Low energy product, but very low cost and electrically insulating; still the volume leader
SmCo 1970s > 20 MGOe (> 159 kJ/m³) First rare-earth magnets; high-temperature performance
Sintered NdFeB 1980s > 50 MGOe (> 398 kJ/m³) Today's standard for high-performance magnets

Values are those given in the source article; kJ/m³ figures are direct unit conversions.

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(BH)max of permanent-magnet materials by year with the theoretical limit for NdFeB

The practical effect is easiest to see in volume. Figure 3 compares how much magnet it takes to produce 1,000 G (0.1 T) at 5 mm from the pole face. An N48 NdFeB disc does it with 0.22 cm³. Ceramic 8 ferrite needs 19.6 cm³, nearly 90 times as much. That ratio explains why small high-fidelity speakers and wireless earbuds use NdFeB: with ferrite, the magnet alone would be larger than the whole earbud.

What do NdFeB grade numbers like N35, N42 and N52 mean?

In sintered NdFeB, the number in the grade name is the nominal maximum energy product in MGOe, so N42 material is specified at roughly 40–43 MGOe.

Grade (BH)max range (MGOe) (BH)max range (kJ/m³)
N35 33–36 263–287
N42 40–43 318–342
N52 49–53 390–422

Ranges follow common industry convention for sintered NdFeB (the grade system of GB/T 13560 is the reference most Chinese producers use). Exact range limits vary between manufacturers. Always confirm against the supplier's own datasheet.

The letters after the number matter as much as the number. Suffixes such as M, H, SH, UH and EH denote progressively higher intrinsic coercivity (Hcj) classes, and Hcj is what lets a magnet survive heat and opposing fields without permanent loss. In standard sintered NdFeB, the very highest (BH)max grades are usually only available in the lower coercivity classes. You can see it in the Figure 4 sample: the N52 tested at Hcj = 18.48 kOe (1,471 kA/m), a value that works at room temperature but leaves limited margin once a motor heats up.

So a higher number does not mean a better magnet for your application. It means more energy per cubic centimetre at 20 °C, at the optimal working point.

How should you specify (BH)max on a drawing or RFQ?

Specify (BH)max as a minimum together with the temperature, intrinsic coercivity and working point your design depends on, rather than as a grade name alone.

Use this list before the drawing goes out:

  1. State the operating temperature range. (BH)max falls as the magnet warms. Because it scales roughly with Br², it drops about twice as fast as Br does. A grade that clears your requirement at 20 °C may not clear it at 120 °C.
  2. Pair the grade number with a coercivity class. Write N42SH, or give a minimum Hcj, not just N42. The suffix is what protects the magnet at temperature.
  3. Give the geometry and the circuit, not just the material. The supplier can only tell you where your working point sits, and how close it is to the knee, if they know the magnet's dimensions and what surrounds it.
  4. Don't buy the top grade by default. At an optimal working point, the volume needed for a given field scales roughly with 1/(BH)max. Moving from N48 to N52 therefore saves about 8 % in magnet volume, and the higher grade usually comes with lower Hcj. Often a mid-range grade with a better suffix is the stronger design.
  5. Ask for the full demagnetization curves at your worst-case temperature, not just a 20 °C certificate. A supplier who has actually characterized the material can send them, along with the squareness ratio (Hk/Hcj), measured to IEC 60404-5 or GB/T 3217. Those curves let you check the design yourself rather than taking the grade name on trust.

 

If your design needs more energy product than NdFeB can hold at temperature. For most room-to-moderate temperature applications, sintered NdFeB magnets in the right coercivity class remain the most volume-efficient choice.


Post time: Oct-07-2026