The magnet constant (specified as the voltage constant $K_e$ or torque constant $K_t$ in permanent magnet motors) is the fixed physical ratio that defines exactly how much back-EMF voltage a motor generates per unit of rotational speed, or how much torque it produces per amp of current. While physics textbooks use the term "magnetic constant" to describe vacuum permeability ($\mu_0 = 4\pi \times 10^{-7}$ T·m/A), on the electronics workbench, we care about the permanent magnet flux linkage inside the BLDC, stepper, and DC motors we use to move things. This constant is the fundamental DNA of your motor; it dictates the hard ceiling on your RPM for a given battery voltage and the exact current draw required to push a mechanical load.
Think of the magnet constant like a fixed gear ratio in a transmission. You cannot change it via software or by tweaking your ESC (Electronic Speed Controller), and it strictly governs the trade-off between your voltage "fuel" (speed) and current "muscle" (torque). If you mismatch this constant to your power supply, you will either stall out under load or burn up your driver board trying to force current through a motor that is already back-EMF limited.
What the Magnet Constant Actually Changes in Your Circuit
In a real motor drive circuit, the magnet constant directly dictates two critical operating parameters: your bus voltage headroom and your $I^2R$ thermal losses.
As a permanent magnet motor spins, it acts as a generator, producing a reverse voltage called back-EMF. The rate at which this voltage climbs is defined by $K_e$. When the back-EMF equals your supply voltage, the motor can spin no faster, regardless of how much current your ESC can supply. Conversely, the torque constant ($K_t$) tells you exactly how many amps your H-bridge or stepper driver must source to achieve a target mechanical force. Because copper windings have resistance, pushing more amps generates heat proportional to the square of the current ($I^2R$).
Worked Numeric Example: Sizing a 24V BLDC Drive
Let’s run the numbers on a practical build. You are designing a 24V DC conveyor belt drive using a brushless motor. The motor datasheet lists a magnet voltage constant $K_e = 4.2$ V/kRPM (volts per 1000 RPM) and a torque constant $K_t = 0.28$ Nm/A.
1. Calculating Maximum Theoretical Speed:
Your power supply is 24V. The motor generates 4.2V of back-EMF for every 1000 RPM.
Max RPM = Supply Voltage / $K_e$
Max RPM = 24V / 4.2 V/kRPM = 5,714 RPM.
Reality check: Under load, you need voltage headroom to push current through the winding resistance. Your practical unloaded max speed will be closer to 5,400 RPM, and loaded speed will drop further.
2. Calculating Current Draw Under Load:
The conveyor requires 1.2 Nm of continuous torque to move the belt.
Required Current = Target Torque / $K_t$
Required Current = 1.2 Nm / 0.28 Nm/A = 4.28 Amps.
3. Sizing the ESC and Wire:
You must select an ESC rated for at least 1.5x the continuous current to handle startup spikes and thermal derating.
4.28A × 1.5 = 6.42A.
Decision: Buy a 10A or 15A BLDC ESC. Using 18 AWG silicone wire for the phase leads will keep voltage drop negligible at this current level.
Where You Meet This in Practice
You will run into the magnet constant whenever you are matching a motor to a power system. Here is where it bites DIYers who ignore the datasheet:
- Drone and RC Builds: Pilots look at the $K_v$ rating (which is just the inverse of $K_e$). If you put a high $K_v$ (low $K_e$) motor on a heavy quadcopter and try to push it with a 6S (22.2V) battery, the motor will demand massive current to produce the necessary torque, instantly overheating the ESC or causing a LiPo voltage sag brownout.
- CNC Router Z-Axes: Stepper motors need high holding torque to fight gravity. If you choose a stepper with a low $K_t$, your driver (like a TMC2209) will have to push maximum rated current just to hold the carriage still, leading to skipped steps and melted driver chips.
- E-Bike Hub Motors: Direct-drive hub motors have very low $K_e$ (high torque constant) to get a heavy bike moving from a stop without a gearbox. If you try to use an e-bike hub motor as a high-speed spindle for a DIY CNC, it will top out at 300 RPM because the back-EMF hits your 48V battery limit almost immediately.
Common Confusions: Magnet Constant vs. Kv vs. Pole Pairs
The terminology in motor datasheets is notoriously messy. Here is how to cut through the noise:
$K_e$ vs. $K_v$: The hobby RC world uses $K_v$ (RPM per Volt), while industrial engineering uses $K_e$ (Volts per rad/s or Volts per kRPM). They are mathematical inverses. A motor with a $K_v$ of 1000 RPM/V has a much lower magnet constant (and less torque per amp) than a motor with a $K_v$ of 200 RPM/V.
Magnet Constant vs. Pole Pairs: The physical strength of the neodymium magnets and the number of magnetic pole pairs on the rotor dictate the magnet constant. Adding more pole pairs increases the $K_t$ (more torque per amp) but also increases the $K_e$ (lower top speed for a given voltage). You cannot change pole pairs without buying a different motor rotor.
Magnet Constant vs. Inductance: Beginners often confuse the magnet constant with the winding inductance ($mH$). Inductance dictates how fast the current can ramp up (affecting high-speed torque), while the magnet constant dictates the steady-state speed and torque limits. (Source: Electronics Tutorials)
Decision Tree: Picking the Right Magnet Constant for Your Build
Stop guessing based on physical motor size. Use this decision matrix to select the correct magnet constant for your specific voltage and mechanical requirements.
| Application Profile | Required Magnet Constant Trait | Target $K_t$ / $K_e$ Range | Typical Hobby/RC Equivalent |
|---|---|---|---|
| High Speed, Low Torque (Spindles, Drone Props, Cooling Fans) | Low $K_t$, High $K_e$ | $K_t < 0.05$ Nm/A | High $K_v$ (>1500 RPM/V) |
| Balanced Speed & Torque (3D Printer Extruders, Conveyor Belts) | Medium $K_t$, Medium $K_e$ | $K_t$ 0.10 - 0.25 Nm/A | Medium $K_v$ (400 - 900 RPM/V) |
| High Torque, Low Speed (CNC Z-Axis, Robot Arms, E-Bike Direct Drive) | High $K_t$, Low $K_e$ | $K_t > 0.30$ Nm/A | Low $K_v$ (<200 RPM/V) |
Frequently Asked Questions
Can I change a motor's magnet constant by wiring it in Star vs. Delta?
Yes. In a 3-phase BLDC motor, wiring the stator in Delta rather than Star (Wye) will reduce the effective $K_e$ by a factor of $\sqrt{3}$ (about 1.732), allowing the motor to spin 73% faster on the same voltage, but it will require 73% more current to produce the same torque.
Does the magnet constant degrade over time?
Only if you overheat the motor. Neodymium (NdFeB) magnets begin to suffer irreversible demagnetization if they exceed their maximum operating temperature (usually 80°C to 150°C depending on the grade, like N42 vs N42SH). If you bake the rotor, the physical magnetic flux drops, permanently lowering your $K_t$ and $K_e$.
Why do stepper datasheets list holding torque instead of $K_t$?
Holding torque is the peak static torque at the rated current. To find the dynamic $K_t$ of a stepper, divide the datasheet's holding torque (in Nm) by the rated phase current (in Amps). For example, a stepper with 1.2 Nm holding torque at 2.0A has a $K_t$ of roughly 0.60 Nm/A. (Source: Oriental Motor)
Ultimately, the magnet constant is not just a theoretical physics footnote; it is the primary sizing metric for your entire electrical drive system. Calculate your required torque and max speed first, use $K_t$ and $K_e$ to find the motor that natively matches those physical demands, and then size your ESC and battery to support the resulting current and voltage. Defaulting to a high-torque, low-$K_e$ motor like the LDO-57STH56-2804A for heavy mechanical loads will save you from the inevitable thermal shutdowns that plague builds designed purely on physical motor dimensions.
