Enter the moment of inertia (kg-m^2), the angular acceleration (rad/s^2), radius (m), and the mass (kg) into the calculator to determine the Servo Torque.

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## Servo Torque Formula

The following formula is used to calculate the Servo Torque.

**Tservo = I*α + m * g * r/2**

- Where Tservo is the Servo Torque (N-m)
- I is the moment of inertia (kg-m^2)
- α is the angular acceleration (rad/s^2)
- m is the mass (kg)
- g is the acceleration due to gravity (9.81 m/s^2)
- r is the radius (m)

## How to Calculate Servo Torque?

The following example problems outline how to calculate Servo Torque.

**Example Problem #1**

- First, determine the moment of inertia (kg-m^2). In this example, the moment of inertia (kg-m^2) is determined to be 5 .
- Next, determine the angular acceleration (rad/s^2). For this problem, the angular acceleration (rad/s^2) is measured to be 12 .
- Next, determine the mass (kg). In this case, the mass (kg) is found to be 4.
- Next, determine the radius. For this problem, this is 5m.
- Finally, calculate the Servo Torque using the formula above:

Tservo = I*α + m * g * r/2

Inserting the values from above and solving yields:

Tservo = 5*12 + 4 * 9.81 * 5/2 = 158.1 (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-m^2) = 89

angular acceleration (rad/s^2) = 4

mass (kg) = 58

radius (m) = 2.5

Enter these given values yields:

Tservo = 89*2.5 + 58 * 9.81 * 2.5/2 = 933.725** **(N-m)