BLDC Motor Sizing: How to Calculate Kv, Torque, and Efficiency

Why BLDC Motors Are Everywhere

Brushless DC motors have taken over. Drones, electric vehicles, CNC spindles, industrial robots, disk drives, HVAC fans — anywhere you need high efficiency, long life, and controllable speed, there's probably a BLDC motor doing the work. No brushes means no brush wear, no arcing, no dust, and dramatically longer service life.

But picking the right motor for your application requires understanding a few key parameters that interact in ways that trip up even experienced engineers. The Kv rating, torque constant, back-EMF, and efficiency all connect mathematically, and getting any one of them wrong means your motor either can't produce enough torque, overheats, or wastes power.

The BLDC Motor calculator lets you plug in your motor parameters and operating conditions to predict performance before you commit to a purchase. Let's build the understanding behind those numbers.

---

The Kv Rating: What It Actually Means

Every BLDC motor comes with a Kv rating, expressed in RPM per volt. A motor rated at 1000 Kv spins at 1000 RPM for every volt applied to it, under no-load conditions. So on a 12V supply, it'll hit 12,000 RPM with no load on the shaft.

Formally:

But here's what the hobbyist forums often miss: Kv isn't just a speed constant. It's the inverse of the back-EMF constant $K_e$ (after unit conversion), and it directly determines your torque constant $K_t$. These three parameters are all manifestations of the same physical property — the magnetic flux linkage between the permanent magnets and the stator windings.

Kv vs Kt: The Fundamental Relationship

In consistent SI units:

where $K_t$ is in Nm/A and $K_v$ is in rad/s per volt. Since motor specs typically give Kv in RPM/V, the conversion is:

So a 1000 Kv motor has $K_t = 9.549/1000 = 0.00955$ Nm/A (9.55 mNm/A). For every amp you push through it, you get about 9.55 mNm of torque. Low Kv motors (high torque per amp) are used for direct-drive applications. High Kv motors (low torque but high speed) need gearing for torque-demanding applications.

---

Back-EMF: The Speed Limit

As the motor spins, the permanent magnets moving past the stator coils generate a voltage — the back-EMF (electromotive force). This voltage opposes the applied voltage, and it's proportional to speed:

where $K_e$ is the back-EMF constant. In consistent units, $K_e = K_t$. The motor can only accelerate until back-EMF equals the supply voltage (minus resistive losses), at which point current drops to zero and no more torque is produced.

The no-load speed is:

Under load, speed drops because some voltage is consumed by the winding resistance:

This is why motors slow down under load — the current draw increases the $IR$ drop, leaving less voltage to generate back-EMF, which means lower speed.

---

Torque and Current

Torque is directly proportional to current:

Stall torque (maximum torque at zero speed) occurs when back-EMF is zero and current is limited only by winding resistance:

This is also the maximum current your motor controller needs to handle. For a 1000 Kv motor with $R = 0.05\,\Omega$ on a 24V supply:

That's enormous — and it's why BLDC controllers always include current limiting. Without it, you'd destroy the windings in seconds. Most controllers limit current to the motor's rated continuous value, allowing brief peaks for acceleration.

---

Efficiency

BLDC motor efficiency depends on the operating point. The three main loss mechanisms are:

Copper losses (resistive losses in the windings): Iron losses (eddy currents and hysteresis in the stator laminations):

where $f$ is the electrical frequency, $B$ is flux density, and $k_e$, $k_h$, $n$ are material constants. Iron losses increase with speed.

Mechanical losses (bearing friction, windage):

Overall efficiency:

Efficiency is highest at moderate loads — typically 70-90% of rated speed with 50-80% of rated torque. At very low speeds, copper losses dominate because current is high relative to power output. At very high speeds, iron and friction losses climb.

Peak efficiency for a well-designed BLDC motor is typically 85-95%, compared to 70-85% for a similar-size brushed DC motor. The difference comes from eliminating brush contact losses and the ability to optimize commutation timing electronically.

---

Worked Example: Sizing a Motor for a Quadcopter

You're building a quadcopter with an all-up weight of 2 kg. Each motor needs to produce enough thrust for stable hover, plus margin for maneuverability.

Step 1: Required thrust per motor.

Total weight force: $W = 2 \times 9.81 = 19.6$ N. With four motors: $F_{hover} = 19.6 / 4 = 4.9$ N per motor. For agile flight, you want a thrust-to-weight ratio of at least 2:1, so target: $F_{max} = 2 \times 4.9 = 9.8$ N per motor.

Step 2: Propeller selection constrains Kv.

For a 10-inch propeller (common for this size quad), the motor needs to spin around 6000-8000 RPM at hover and up to 12,000 RPM at full throttle. On a 4S LiPo (14.8V nominal):

So you're looking at an 800-900 Kv motor. Typical choices in this range: 2212 or 2213 size (22mm stator diameter, 12-13mm stator height).

Step 3: Current and power at hover.

Using propeller efficiency data (approximately 8 g/W for a 10" prop at hover), the hover power per motor is:

At 14.8V: $I_{hover} = 61 / 14.8 \approx 4.1$ A per motor.

Step 4: Verify thermal limits.

For a typical 2212-900Kv motor with $R = 0.095\,\Omega$:

That's about 2.6% of input power — very manageable thermally. At full throttle with 15A:

This is significant and limits continuous full-throttle operation. Most flight controllers manage this by limiting maximum current duration.

Step 5: Verify torque at hover.

Run these numbers through the BLDC Motor calculator to verify and explore what happens with different battery voltages or propeller sizes.

---

Motor Sizing for Other Applications

Robot Wheels

For wheeled robots, start with required wheel torque: $T = F \times r_{wheel}$, where $F$ includes rolling resistance, incline force, and acceleration force. Low Kv motors (100-300 RPM/V) with gearboxes are typical. The gearbox multiplies torque by the gear ratio while dividing speed, so:

where $\eta_{gear}$ is gearbox efficiency (typically 85-95% for planetary gears). Compare with DC Motor Speed for the brushed alternative.

Electric Vehicle Hub Motors

Hub motors are direct-drive (no gearbox), so they need very low Kv — typically 10-30 RPM/V — to produce enough torque at wheel speed. A 26-inch bicycle wheel at 30 km/h needs about 200 RPM. On a 48V battery: Kv = 200/48 = 4.2 RPM/V. These motors are large diameter to fit in the wheel hub and produce the required torque.

CNC Spindles

Spindles need high speed (10,000-60,000 RPM) and moderate torque. High Kv motors (1000-5000 RPM/V) on 24-48V supplies are typical. The cutting force determines minimum torque: $T = F_{cut} \times r_{tool}$.

---

Kv Selection Guidelines

The rule of thumb: lower Kv = higher torque per amp = lower speed. If your application needs high torque at low speed, pick a low Kv motor or add a gearbox. If you need high speed with moderate torque, pick a high Kv motor.

For stepper motor applications where precise positioning matters more than continuous rotation, see the Stepper Motor calculator.

---

Summary

BLDC motor sizing comes down to understanding three linked parameters:

1. Kv determines speed capability — RPM = Kv $\times$ V_supply under no load
2. Kt determines torque capability — Kt = 9.549 / Kv (in Nm/A with Kv in RPM/V), and T = Kt $\times$ I
3. Efficiency varies with operating point — peak efficiency at moderate load; copper losses dominate at low speed, iron losses at high speed

Start by calculating required torque and speed for your application, then find a motor whose Kv, voltage rating, and continuous current match. Always check thermal limits at your expected operating current using $P_{copper} = I^2 R$. The BLDC Motor calculator makes this iteration fast.