The Core Formula of Torque of a Motor (and Why HP Isn't Enough)

The fundamental formula of torque of a motor defines the rotational force it can exert on a load. In the imperial system, the relationship between horsepower (HP), speed (RPM), and torque (T in lb-ft) is:

T = (HP × 5252) / RPM

In the metric system, which is standard for most modern embedded and industrial drives, the formula uses kilowatts (kW) and Newton-meters (Nm):

T = (P × 9550) / RPM

Where P is mechanical power in kilowatts and RPM is the rotational speed. A common mistake on the bench is converting HP to kW and assuming the motor is sized correctly. Power conversions are useless without load context. A 1 kW motor spinning at 3000 RPM produces only 3.18 Nm of torque, while a 1 kW motor geared down to 100 RPM produces 95.5 Nm. According to NEMA MG-1 standards, you must always size the motor based on the torque required at the operational speed, not just the peak power rating.

Bench Rule: Never size a motor by its continuous power rating alone. Always calculate the peak stall torque your mechanical load demands, then verify the motor's thermal mass can handle the RMS current required to produce that torque without melting the windings.

Motor Type Comparison: Torque Curves, Control, and Cost

Steppers and servos are not interchangeable. A stepper delivers massive holding torque at zero RPM but suffers a severe torque cliff as speed increases. A Brushless DC (BLDC) motor offers flat torque through its mid-range but requires complex commutation. Here is how the primary motor types stack up for physical automation loads in 2026.

Motor Type Torque Curve Profile Control Needs Typical Cost (2026) Best Load Profile
NEMA 23/34 Stepper High at 0 RPM, drops sharply after 800 RPM Open-loop step/dir pulses or closed-loop FOC $25 - $80 Low-speed, high-precision positioning (CNC, 3D printers)
3-Phase BLDC (Outrunner) Flat torque from 0 to base speed, constant power above Closed-loop FOC with hall sensors or encoders $60 - $150 Dynamic loads, robotics, continuous mid-speed torque
AC Induction (3-Phase) Low starting torque, peaks near synchronous speed VFD (Volts per Hertz) or Vector Control $150 - $400 High-inertia, constant-speed conveyors, pumps, fans
AC Servo (Synchronous) Flat, extreme peak torque (300% continuous) to high RPM Proprietary high-bandwidth servo drive $400 - $1,500+ Pick-and-place, high-speed packaging, extreme precision

Sizing Rule of Thumb and Worked Load Example

The golden rule of motor sizing is to calculate the worst-case mechanical torque, apply a 1.5x safety factor for friction and inertia, and select a motor whose continuous torque rating meets or exceeds that number. Let's walk through a real-world sizing calculation for a vertical hoist.

Worked Example: 20kg Vertical Hoist

The Load: Lifting a 20 kg mass vertically using a cable wrapped around a pulley with a 0.05-meter (50mm) radius.

  1. Calculate Force (F): F = mass × gravity. F = 20 kg × 9.81 m/s² = 196.2 Newtons.
  2. Calculate Required Torque (T): T = F × radius. T = 196.2 N × 0.05 m = 9.81 Nm.
  3. Apply Safety Factor: 9.81 Nm × 1.5 (for pulley friction and startup inertia) = 14.71 Nm.
  4. Calculate Speed: If we need to lift the load at 0.5 meters per second, the pulley circumference is 2πr (0.314m). Speed = 0.5 / 0.314 = 1.59 revolutions per second, or 95.4 RPM.

The Sizing Decision: We need a motor that can deliver at least 14.71 Nm of continuous torque at roughly 100 RPM. A standard NEMA 23 stepper might produce 2 Nm at 100 RPM—far too low. A 3-phase BLDC outrunner rated for 20 Nm continuous at 150 RPM is the correct physical fit, likely paired with a 10:1 planetary gearbox to multiply torque and lower the electrical RPM demand.

Wiring, Terminals, and Driver Demands

For the BLDC motor selected in our hoist example, proper wiring to a Field Oriented Control (FOC) driver is critical. Unlike steppers that use simple A+/A-/B+/B- coils, a 3-phase BLDC requires precise phase sequencing and rotor position feedback. For a comprehensive hardware guide, refer to the ODrive Robotics hardware documentation.

Terminal / Pin Function Wiring Notes & Gauge
U, V, W 3-Phase Motor Power Use 14 AWG silicone wire for >20A. Phase order dictates rotation direction; swap any two to reverse.
Hall A, B, C Rotor Position Feedback Use 22 AWG shielded twisted pair. Keep away from U/V/W lines to prevent EMI commutation faults.
VCC (Hall) Hall Sensor Power Usually 5V. Never connect to 12V or 24V, or you will instantly fry the internal hall ICs.
GND (Hall) Sensor Ground Must share a common ground reference with the FOC driver's logic ground.
Driver Demand: A BLDC producing 15 Nm requires an FOC driver capable of handling the corresponding phase current. If the motor's torque constant (Kt) is 0.2 Nm/A, you need 75A of peak phase current. Ensure your driver's MOSFETs and shunt resistors are rated for at least 80A peak and 50A continuous RMS.

Failure Signatures: Hum, Overheat, and Stall

When a motor drive system fails, it rarely does so silently. Recognizing these acoustic and thermal signatures on the bench will save you from burning out expensive drivers.

  • The 'Hum' or 'Scream' (Commutation Failure): If your BLDC vibrates violently and hums without spinning, your hall sensor sequence is wrong, or two phase wires are swapped. The FOC driver is energizing the stator poles in direct opposition to the rotor magnets. Fix: Power down immediately. Verify hall pinout with a multimeter and oscilloscope, or use the driver's automatic calibration routine.
  • Overheat (RMS vs. Peak Confusion): The motor casing is too hot to touch (>80°C) after 5 minutes of operation, but it hasn't stalled. This happens when you size for peak torque but the load demands that torque continuously. The copper windings are exceeding their thermal dissipation limit. Fix: You must either add forced air cooling, increase the gear reduction ratio to lower the motor's torque demand, or move to a physically larger motor frame.
  • Hard Stall (Mechanical or Current Limit): The motor stops abruptly under load and the driver throws an overcurrent fault. This means the load torque exceeded the motor's peak breakdown torque, or the mechanical axis is bound. Fix: Disconnect the load and spin by hand. If smooth, your motor is undersized for the peak inertia of the load. If bound, fix the mechanical alignment.

The Decision Tree: Picking Your Exact Motor and Drive

Stop guessing. Use this decision matrix to lock in your exact hardware based on your load profile. There is no 'it depends' here—follow the logic to the concrete part number.

If Your Load Profile Is... And Your Speed Is... Then Choose This Motor Type Concrete 2026 Hardware Pick
High precision positioning, low inertia, low budget Low (< 600 RPM) Closed-Loop Stepper BIGTREETECH S42B v2.0 (NEMA 17/23 integrated driver)
Constant speed, high inertia, high duty cycle, mains power available Fixed (1750 RPM base) 3-Phase AC Induction Baldor-Reliance EM3546 (paired with an Allen-Bradley PowerFlex 4M VFD)
High continuous torque, dynamic acceleration, battery or DC bus powered Medium (1000 - 3000 RPM) 3-Phase BLDC Outrunner ODrive D6374 BLDC (paired with ODrive S1 FOC Controller)
Extreme speed, sub-millimeter precision, high shock loads High (> 3000 RPM) AC Synchronous Servo Teknic ClearPath-SDSK (Integrated servo/drive)

The Default Recommendation

If you are building a general-purpose automation rig, robotic arm, or motorized winch (like the 20kg hoist example above) and you are stuck between a heavy stepper and an industrial servo, buy the ODrive D6374 BLDC motor paired with the ODrive S1 controller. It bridges the gap perfectly: it delivers the high continuous torque of an industrial servo at a fraction of the cost, runs natively on a 24V-48V DC bus, and its FOC algorithm eliminates the mid-speed torque cliff that plagues stepper motors. Size your planetary gearbox to keep the motor's operational RPM between 1000 and 2500, and you will have a bulletproof, high-torque drive system.