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Servo Motor Torque & Speed

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

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Formula

T=Pout/ω,η=Pout/Pin×100T = P_out / ω, η = P_out/P_in × 100%
T— Mechanical torque (N·m)
ω— Angular speed (= 2π × RPM / 60) (rad/s)

How It Works

This calculator determines servo motor torque, speed, and power requirements from mechanical load parameters and PWM control specifications. Robotics engineers, RC hobbyists, and automation designers use it to select servos that meet position accuracy and response time requirements. Proper servo sizing prevents stalling under load and ensures adequate speed for dynamic applications.

Per IEC 61800-9-2 servo motor standards, a servo system combines a motor, position encoder, and closed-loop controller. Hobby servos use RC PWM control: 50 Hz frame rate with 1-2 ms pulse width mapping to 0-180° position per the 'Futaba standard' established in 1970s RC equipment. Industrial servos use digital protocols (CANopen, EtherCAT) with position resolution of 16-23 bits (65,536-8,388,608 counts/rev).

Torque requirements follow the equation: T_required = T_static + T_dynamic, where T_static = m×g×L (gravitational load) and T_dynamic = J×α (acceleration torque). Per servo manufacturer datasheets, stall torque ratings assume the motor can sustain this load for only 2-5 seconds before thermal shutdown. Continuous torque is typically 30-50% of stall torque. A servo rated at 20 kg·cm stall torque provides approximately 7 kg·cm continuous holding torque.

Worked Example

Select a servo for a 6-DOF robot arm joint. The joint must support a 500g payload at 150mm moment arm and accelerate 90° in 0.3 seconds.

Step 1 — Calculate static torque (gravitational): T_static = m × g × L = 0.5 kg × 9.81 m/s² × 0.15 m = 0.736 N·m Converting: 0.736 N·m × 10.197 = 7.5 kgf·cm

Step 2 — Calculate dynamic torque (acceleration): Angular displacement: θ = 90° = π/2 rad Acceleration (trapezoidal profile): α = 4θ/t² = 4×(π/2)/0.3² = 69.8 rad/s² Payload inertia: J = m×L² = 0.5 × 0.15² = 0.01125 kg·m² T_dynamic = J × α = 0.01125 × 69.8 = 0.785 N·m = 8.0 kgf·cm

Step 3 — Determine required servo rating: Total peak torque: 7.5 + 8.0 = 15.5 kgf·cm With 2× safety factor: 31 kgf·cm stall torque minimum

Step 4 — Verify speed rating: Peak velocity: ω_max = α × (t/2) = 69.8 × 0.15 = 10.5 rad/s = 100 RPM Required servo speed: 0.3 sec/90° → 0.067 sec/60° (meets most digital servo specs)

Result: Select a digital servo with ≥35 kgf·cm stall torque and ≤0.08 sec/60° speed. Budget 3A peak current at 6V supply for the acceleration phase. Total power: 35 kgf·cm × 100 RPM × 0.00105 = 3.7W mechanical output.

Practical Tips

  • ✓Per Futaba and Hitec specs, digital servos update at 300-400 Hz internally vs. 50 Hz for analog, providing 6-8× faster response and 20-30% higher holding torque at the cost of 2× idle current
  • ✓Add 100-470 µF bulk capacitance within 50mm of servo power pins—per RC design guidelines, this absorbs 10-20A inrush spikes that otherwise cause MCU brownout resets
  • ✓Measure actual no-load current before finalizing power budget: datasheet values assume 6V but many systems run at 5V or 7.4V, changing current draw by ±20%

Common Mistakes

  • ✗Using stall torque as continuous rating: Per manufacturer thermal limits, continuous torque is only 30-50% of stall torque; exceeding this for >5 seconds causes thermal shutdown and gear damage
  • ✗Powering servos from MCU 5V rail: Hobby servos draw 1-3A at stall (6V × 3A = 18W peak), exceeding typical USB or LDO current limits by 6-10×; use a dedicated BEC or battery
  • ✗Ignoring gear backlash in positioning: Plastic gears exhibit 1-3° backlash per Hitec specifications; metal gears reduce this to 0.1-0.5° but add 30-50% to servo cost and weight

Frequently Asked Questions

Per Hitec technical documentation: Analog servos sample the PWM input and update motor drive at 50 Hz (the frame rate). Digital servos sample at 300-400 Hz, providing 8× faster error correction, 30% higher holding torque, and reduced deadband (±1° vs. ±3°). Tradeoff: digital servos draw 2-3× higher idle current (30-50 mA vs. 10-20 mA).
Per 'Robotics: Modelling, Planning and Control' (Siciliano, 2009): T_total = m×g×L×cos(θ) + J×α + T_friction. For a 500g load at 150mm arm: T_static = 0.5×9.81×0.15 = 0.736 N·m = 7.5 kgf·cm. Apply 2× safety factor for dynamic loads and 3× for high-duty-cycle applications per industrial servo sizing guidelines.
Yes—per Hitec and Futaba specifications, servos accept 3.0-5.0V logic levels on the signal pin. The signal pin draws <1 mA. However, the power rail must be 4.8-7.4V from a separate supply capable of 2-3A peak current. Never source motor power from the MCU—a stalling servo draws 2-3A, which would destroy most microcontroller voltage regulators rated for 100-500 mA.

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