Use the calculator tabs to estimate required servo/motor torque from a load (mass, lever arm radius, move angle/time, gravity orientation, friction, gear ratio, efficiency, and safety factor), check whether a servo meets torque/speed requirements, or convert torque units and force at a given radius.

Servo Torque Calculator

Start with the fast torque estimate, then compare a servo or use advanced sizing.
Required Torque
Servo Check
Advanced Sizing

Estimate the minimum torque needed to hold or lift a load at a given arm length. This is the fastest answer most people want.

Mass at Arm
Force at Arm
The recommended rating equals load torque multiplied by your safety factor. Angle defaults to 90° if left blank.
Required Servo Torque
Load Torque
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Recommended Minimum
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Recommended in oz·in
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Recommended in lb·ft
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Force at Load Point
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Compare your required torque and move speed against a servo’s published specs.

Mass at Arm
Force at Arm
Servo Check Results
Required Torque
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Required Speed
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Servo Speed
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Torque Margin
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Speed Margin
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Verdict
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Voltage Note
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Use this tab when you need more complete motion sizing with inertia, friction, gearing, efficiency, and RMS torque.

Advanced Sizing Results
Peak Motor Torque
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Peak Motor Torque in kg·cm
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Peak Motor Speed
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Peak Motor Speed
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Approx. RMS Torque
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Approx. RMS in kg·cm
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Estimated Load Peak Torque Before Gearing
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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).

T_{servo}=I\alpha + m g r \sin(\phi)
  • 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)