Calculate servo torque from load, arm length, angle, safety factor, and linkage ratio, or reverse-solve maximum load and arm with common servo units.

Choose a solve target, then complete the visible required fields marked with *.

Use 1 for direct drive; enter the measured linkage torque ratio otherwise.

Servo Torque Formula

The following formula is a simplified way to estimate required servo torque from rotational inertia and gravity (worst-case gravity occurs when the lever arm is perpendicular to gravity).

Tₛₑᵣᵥₒ = Iα + m g r sin(φ)
  • Where Tservo is the Servo Torque (N·m)
  • I  is the moment of inertia about the servo axis (kg·m²) 
  • α is the angular acceleration (rad/s²) 
  • m is the mass (kg) 
  • g is the acceleration due to gravity (9.81 m/s²)
  • r is the lever arm radius (m)
  • φ is the angle from vertical (gravity direction): φ = 0° gives zero gravity torque; φ = 90° gives maximum gravity torque

How to Calculate Servo Torque?

The following example problems outline how to calculate Servo Torque.

Example Problem #1

  1. First, determine the moment of inertia (kg·m²). In this example, the moment of inertia (kg·m²) is determined to be 5.
  2. Next, determine the angular acceleration (rad/s²). For this problem, the angular acceleration (rad/s²) is measured to be 12.
  3. Next, determine the mass (kg). In this case, the mass (kg) is found to be 4.
  4. Next, determine the radius. For this problem, this is 5 m, and assume the arm is horizontal so φ = 90° (maximum gravity torque).
  5. Finally, calculate the Servo Torque using the formula above: 

Tservo = I*α + m * g * r * sin(φ)

Inserting the values from above and solving yields: 

Tservo = 5*12 + 4 * 9.81 * 5 * sin(90°) = 256.2 (N·m)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

moment of inertia (kg·m²) = 89

angular acceleration (rad/s²) = 4

mass (kg) = 58

radius (m) = 2.5

Assume the arm is horizontal so φ = 90° (maximum gravity torque). Entering these given values yields: 

Tservo = 89*4 + 58 * 9.81 * 2.5 * sin(90°) = 1778.45 (N·m)