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Motor

Servo Motor Torque & Speed

Calculate servo motor torque, speed, efficiency, and back-EMF from electrical and load parameters.

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Formula

P_out = T × ω, η = P_out/P_in × 100%

T— Load torque (N·m)
ω— Angular speed (rad/s)

How It Works

A servo motor is a closed-loop rotary actuator that combines a DC or brushless motor with a position encoder and feedback controller. The controller compares the commanded position (via PWM signal pulse width) to the actual shaft angle and drives the motor to minimize the error. Torque output is determined by the motor's stall torque rating and the applied voltage, while speed is governed by the no-load RPM and the control signal duty cycle. The standard PWM control signal uses a 50 Hz frame with pulse widths between 1 ms (0°) and 2 ms (180°).

Worked Example

A hobby servo is rated at 6 V, 3 kg·cm stall torque, and 0.10 sec/60° no-load speed. Step 1 — Convert stall torque to N·m: 3 kg·cm × 0.0981 N·m/(kg·cm) = 0.294 N·m Step 2 — Determine angular velocity at no-load: 60° in 0.10 s → 600 °/s → 600/360 × 2π = 10.47 rad/s Step 3 — Estimate peak mechanical power: P = T × ω/2 (peak power occurs at half stall torque) P = (0.294/2) × (10.47/2) = 0.770 W Step 4 — Check control pulse: For 90° position: pulse = 1 ms + (90/180) × 1 ms = 1.5 ms at 50 Hz Result: The servo delivers up to 0.77 W of mechanical power. Size the supply to provide at least 1.5× stall current to avoid brownout during rapid moves.

Practical Tips

  • ✓Add 100–470 µF bulk capacitance close to the servo power pins to absorb inrush spikes and prevent MCU resets
  • ✓For precise positioning, use digital servos with metal gears; analog servos with plastic gears exhibit noticeable backlash and compliance
  • ✓Measure actual no-load current at operating voltage before finalising your power budget — datasheet values are often measured at a different voltage

Common Mistakes

  • ✗Powering the servo from the microcontroller 5 V rail — stall currents (up to 1.5 A) will crash the MCU supply
  • ✗Ignoring the PWM frame rate: most analog servos require exactly 50 Hz; digital servos tolerate up to 333 Hz
  • ✗Assuming stall torque is continuous — servo gears and windings overheat if stall torque is applied for more than a few seconds

Frequently Asked Questions

Analog servos update their internal PID loop at ~50 Hz (the PWM frame rate). Digital servos sample the PWM input and update the motor drive at 300–400 Hz, giving faster response, higher holding torque, and better resolution — at the cost of higher idle current.
Multiply the load mass (kg) by gravitational acceleration (9.81 m/s²) by the moment arm length (m) to get the required torque in N·m. Apply a safety factor of at least 2× for dynamic loads and position-holding under vibration.
Most servos accept a PWM signal as low as 3.3 V logic levels while running on a separate 4.8–6 V power supply. Connect signal ground, keep the power rail separate, and never source servo power from the MCU pin itself.

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