Motor constants like the torque constant (Kt) and speed constant (Kv) are often misinterpreted, which can lead to suboptimal motor selection. They don't define a motor's power, but rather how a specific DC motor winding converts electrical energy into mechanical motion.
The torque constant (Kt) and speed constant (Kv) of a brushless DC motor are inversely proportional, describing two sides of the same electromechanical energy conversion process for a given motor winding.
A brushless DC motor datasheet lists several key parameters, including the torque constant (Kt), the speed constant (Kv), and the back-EMF constant (Ke). In OEM motor integration, these values are frequently misinterpreted. Kt describes how much torque is produced per ampere of current, while Kv describes the motor's speed relationship per volt. Neither constant, by itself, defines the maximum continuous torque, maximum safe speed, or overall thermal limits of the motor. Motor constants describe conversion ratios; the motor's operating limits describe how far those ratios can be safely utilized.
What Is the Torque Constant Kt in a Brushless DC Motor?
The torque constant (Kt) defines the amount of electromagnetic torque a motor produces for each ampere of current supplied to its windings, within the motor's linear operating region.
The relationship is generally expressed as:
T ≈ Kt × I
Where:
T= Electromagnetic TorqueKt= Torque ConstantI= Torque-Producing Current
The typical SI unit for Kt is N·m/A (newton-meters per ampere), though for miniature motors it is often expressed as mN·m/A (millinewton-meters per ampere). For example, if a motor has a Kt of 20 mN·m/A, then applying 1 ampere of current would produce approximately 20 mN·m of torque.
Key Engineering Insight: The numerical value of
Kton a datasheet can depend on the manufacturer's electrical conventions, including phase vs. line current definitions, peak vs. RMS values, and the commutation convention used.1 This is why simply comparing theKtvalue between two different manufacturers is not always a direct, one-to-one comparison.
A higher Kt value does not mean the motor can continuously produce more torque. The actual sustainable torque depends on the allowable continuous current, which is primarily a thermal limitation based on ambient temperature, cooling, duty cycle, and the motor's ability to dissipate heat. Kt tells you the torque per ampere—not the allowable amperes.
What Is the Speed Constant Kv?
The speed constant (Kv) describes the relationship between a motor's rotational speed and the back-EMF it generates, commonly expressed in units of rpm per volt.
The Kv constant is often used for a rough, idealized estimate of the no-load speed for a given supply voltage:
Speed (rpm) ≈ Kv (rpm/V) × Voltage (V)
For example, if a motor has a Kv of 1000 rpm/V, applying 12 volts might suggest an idealized no-load speed of around 12,000 rpm.
However, the actual operating speed will generally be lower than this simple calculation predicts. The moment a load is applied, the motor draws current, which causes a voltage drop (V = I × R) across the winding resistance. This reduces the effective voltage available to overcome back-EMF and produce motion. Therefore, Kv should be treated as a fundamental winding characteristic, not a performance guarantee under load. It indicates the speed-to-voltage relationship, not the maximum safe speed of the motor.
How Kt and Kv Are Related
If Kt and Kv both originate from the same motor winding, they must be related. They are, in fact, fundamentally linked and inversely proportional.
For the same motor and winding, Kt and Kv are inversely related when they are defined using consistent electrical and mechanical conventions.
For an ideal motor using a consistent set of SI units, the torque constant and back-EMF constant (Ke) are numerically equivalent:
Kt (N·m/A) = Ke (V/(rad/s))
When the speed constant is expressed in the common unit of rpm/V, the practical relationship becomes:
Kt (N·m/A) ≈ 9.549 / Kv (rpm/V)2
This simple formula reveals the critical trade-off in motor winding design:
- Higher Kv → Lower Kt
- Lower Kv → Higher Kt
Let's compare two motors based on this relationship:
- Motor A has a
Kvof1000 rpm/V. ItsKtis approximately9.55 mN·m/A. - Motor B has a
Kvof500 rpm/V. ItsKtis approximately19.1 mN·m/A.
Motor B produces roughly twice the torque per amp, but it also requires roughly twice the voltage to achieve the same speed relationship as Motor A. This shows how different windings allow for different strategies to meet a motion requirement.
Why Different Windings Change Both Kt and Kv
Changing the constants Kt and Kv is fundamentally a winding design decision, not a simple parameter tweak.
For a given motor platform, changing the number of winding turns is the primary factor that alters Kt and Kv. Wire diameter is then adjusted to manage resistance and thermal performance within the available space.
On the same mechanical motor platform, different windings create different motor "personalities" tailored to specific voltage and current supplies. For the same motor platform, increasing the number of turns generally increases torque per ampere and back-EMF per unit speed, resulting in a higher Kt and a lower Kv.
The wire diameter is adjusted to fit these turns into the winding area and to manage the resulting resistance and current density. A winding with fewer turns can use thicker wire, resulting in lower resistance3. This creates a trade-off between windings designed for high-current, low-voltage systems and those for low-current, high-voltage systems. This topic is explored further in our comparison of high torque BLDC motors vs high speed BLDC motors.
| Winding Characteristic | Higher-Kv Winding | Lower-Kv Winding |
|---|---|---|
| Number of Turns | Fewer | More |
| Wire Diameter | Typically thicker | Typically finer |
| Winding Resistance | Typically lower | Typically higher |
| Kv (rpm/V) | Higher | Lower |
| Kt (mN·m/A) | Lower | Higher |
| Current for Same Torque | Higher | Lower |
| Voltage for Same Speed | Lower | Higher |
Why High Kv Does Not Mean “Better High-Speed Performance”
A common pitfall in motor selection is specifying a "high-Kv motor" for a high-speed application, only to find the motor cannot perform reliably.
A high Kv only indicates a higher speed-to-voltage ratio; it does not mean the motor has a higher maximum safe operating speed.
The maximum usable speed of a motor system is generally constrained by several factors that are not determined by Kv alone:
- Mechanical Limits: Bearing speed ratings, rotor dynamic balance, and structural integrity.
- Thermal Limits: High speeds can increase iron losses and friction, generating excess heat.
- Driver Limits: The controller must be able to commutate the motor phases fast enough at high RPM.
- Voltage Limits: At high speeds, the back-EMF can approach the supply voltage, leaving insufficient voltage margin for control.
Consider two windings on the same motor platform. Winding A (high Kv, low Kt) requires more current for a given torque. Winding B (low Kv, high Kt) requires less current but more voltage for the same speed. Both windings are ultimately constrained by the thermal and mechanical capabilities of the same motor platform, although their resistance and loss distribution may differ. Kt and Kv only change how voltage and current are exchanged for speed and torque; they do not independently increase the motor's physical output capability4.
How to Use Kt and Kv for a Real Motor Selection
Kt and Kv are not selection criteria on their own but are engineering tools used to translate a mechanical requirement (torque and speed) into an electrical one (current and voltage).
Use Kt and Kv to translate torque and speed requirements into current and voltage estimates, then use the motor's operating limits to validate whether that operating point is sustainable.
A practical initial evaluation follows these steps:
Step 1: Check the Current Requirement
Start with the required torque. Using the motor's Kt, calculate the estimated current.
- Required Torque:
20 mN·m - Candidate Motor
Kt:10 mN·m/A - Estimated Current (
I ≈ T/Kt):20 / 10 = 2 A5
Next, check this current against the system's limits: Can the driver supply 2A continuously? Can the motor winding thermally sustain this current under the application's cooling conditions?
Step 2: Check the Voltage Requirement
Next, evaluate the speed requirement. Using Kv, estimate the back-EMF voltage.
- Required Speed:
10,000 rpm - Candidate Motor
Kv:1000 rpm/V - Estimated Back-EMF (
V_emf ≈ Speed/Kv):10,000 / 1000 = 10 V
This 10 V is the internal voltage (back-EMF) generated by the motor, not the required supply voltage. The bus voltage must be higher to provide a "voltage margin" that can push the required 2A of current through the winding's resistance (I×R drop) and the driver electronics.6
Step 3: Check Thermal and Mechanical Limits
Finally, even if the voltage and current estimates seem viable, check the motor's continuous operating limits, thermal assumptions, mechanical ratings, and absolute maximum limits.
- Thermal: Can the motor dissipate the heat from
I²Rlosses (and other losses) at 2A continuously within your device? - Mechanical: Can the motor's bearings and rotor structure safely handle 10,000 rpm for the required lifetime?
| Parameter | What It Tells You | What It Does NOT Tell You |
|---|---|---|
| Kt | Torque produced per ampere | Maximum continuous torque |
| Kv | Speed-per-volt relationship | Maximum safe RPM |
| Continuous Current | Thermally sustainable current | Short-term peak current |
| Peak Current | Short-term electrical limit | Continuous thermal performance |
What OEM Engineers Should Provide When Selecting Kt and Kv
To select the right motor winding, an engineer must describe the problem, not just propose a solution. "I need a high-Kv motor" is not a complete engineering requirement.
Instead of requesting a specific Kt or Kv, OEM engineers should provide the complete operating point and system constraints to the motor supplier.
A much more effective inquiry describes the application's reality. For example:
"Our system bus voltage is 24V, but it can drop to 22V under load. The motor must maintain 12,000 rpm while delivering a continuous torque of 15 mN·m. Our driver has a continuous current limit of 1.5A."
This information is sufficient for an initial evaluation of winding suitability, current demand, voltage margin, and thermal feasibility7.
Key parameters to provide for winding selection include:
- Electrical System: Minimum and maximum bus voltage, continuous/peak current limits from the driver.
- Operating Point: Target speed and the continuous/peak torque required at that speed.
- Dynamic Needs: Startup torque, acceleration requirements.
- Thermal Environment: Ambient temperature, cooling conditions, duty cycle.
- Physical Constraints: Maximum motor dimensions.
Conclusion
Kt and Kv are inversely related motor constants that describe how a specific BLDC winding converts current into torque and voltage into speed. Neither constant alone defines the motor's power or safe operating limits, so both must be evaluated together with winding resistance, available voltage and current, and the motor's thermal and mechanical constraints.
For OEM motor selection, the most useful approach is to define the complete operating requirements rather than specify a target Kt or Kv alone. Provide the bus-voltage range, required speed and torque, continuous and peak current limits, duty cycle, thermal conditions, and dimensional constraints so the winding can be matched to the application. Contact us at info@bodenmotion.com to discuss your requirements.
FAQ
Q1: What is the difference between Kt and Kv in a BLDC motor?
Kt (torque constant) specifies the torque produced per ampere of current (e.g., mN·m/A). Kv (speed constant) describes the motor's speed-to-voltage relationship, often used to estimate the back-EMF at a given speed (e.g., rpm/V).
Q2: How do you convert Kv to Kt?
When using consistent units (Kv in rpm/V and Kt in N·m/A), the approximate relationship for the same motor winding is Kt ≈ 9.549 / Kv. This shows they are inversely proportional.
Q3: Does a higher Kv mean a higher maximum motor speed?
Not necessarily. A higher Kv means more RPM per volt of back-EMF. The absolute maximum safe speed is determined by mechanical limits like bearings and rotor balance, as well as thermal and driver constraints.
Q4: Can two motors with the same Kv have different torque capability?
Yes. Under consistent measurement conventions, two motors can have the same Kv and therefore a similar Kt, while still having very different continuous torque and power capabilities. Kv is a conversion ratio, not a measure of a motor's thermal or mechanical limits.
Q5: Why can Kt or Kv values differ between motor manufacturers?
The numerical values of Kt and Kv on a datasheet can depend on the manufacturer's specific electrical and measurement conventions, including phase vs. line current definitions, phase vs. line-to-line voltage definitions, peak vs. RMS values, and the commutation convention used. This is why directly comparing constants between brands requires careful review of the datasheet notes.
Novanta / Celera Motion, “What Motor Torque Constant to Use for Drive Type – Theory and Application.” Explains how torque-constant values depend on current and commutation conventions, including peak, RMS, DC, per-phase, phase-to-phase, sinusoidal, and trapezoidal definitions. It also notes that motor and drive manufacturers may specify these quantities differently. ↩
“Motor constants,” Wikipedia. Gives the relationship Kt = 60 / (2πKv) when Kt is expressed in N·m/A and Kv in rpm/V, which yields Kt ≈ 9.549 / Kv. The conversion assumes consistent electrical and mechanical definitions for the two constants. ↩
V. Prakash, “Achieving Energy Efficiency in Three Phase Induction Motors: Non-Destructive Winding Quality Assurance Approach.” Discusses conductor size, number of turns, winding resistance, and available winding space as related winding variables. It states that larger wire size reduces winding resistance and that reducing the number of turns also reduces winding resistance, although it does not explicitly state that fewer turns are what permit the larger conductor size. ↩
“Motor constants,” Wikipedia. Distinguishes winding-dependent constants such as Kv from the motor constant Km, and gives an example in which changing the winding doubles Kv while Km remains unchanged. This illustrates that changing the winding alters the voltage-current and speed-torque conversion relationship without independently increasing the underlying capability of the same motor structure. ↩
University of Utah, “Lumped Parameter Characterization of a Permanent Magnet DC Motor.” Defines motor torque as T = KtI, so the current required for a given electromagnetic torque can be estimated by rearranging the relationship to I = T/Kt. ↩
OpenStax, “Electric Generators and Back Emf,” hosted by the University of Central Florida. Shows that the applied motor voltage must cover both the opposing back-EMF and the resistive I×R voltage drop in the winding. Additional voltage loss or control headroom in the electronic driver is a separate system-level consideration not covered by this source. ↩
MicroMo Electronics, “How to Select a DC Micromotor.” Presents a practical first-pass motor-selection method using available voltage, required speed and torque, torque constant, winding resistance, current, I²R loss, thermal resistance, ambient temperature, and calculated temperature rise to judge whether a candidate motor is suitable for the required operating point. ↩
