Enter the total force (N), the radius (m), and the direction of force (degrees) into the calculator to determine the Magnitude of Torque.

## Magnitude of Torque Formula

The following formula is used to calculate the Magnitude of Torque.

Tm = F*r*sin(a)

- Where Tm is the Magnitude of Torque (N-m)
- F is the total force (N)
- r is the radius (m)
- a is the direction of force (degrees)

To calculate the magnitude of the torque, multiply the force, radius, and sine of the angle of the force.

## How to Calculate Magnitude of Torque?

The following example problems outline how to calculate Magnitude of Torque.

**Example Problem #1**

- First, determine the total force (N). In this example, the total force (N) is determined to be 400 .
- Next, determine the radius (m). For this problem, the radius (m) is measured to be 50 .
- Next, determine the direction of force (degrees). In this case, the direction of force (degrees) is found to be 3.
- Finally, calculate the Magnitude of Torque using the formula above:

Tm = F*r*sin(a)

Inserting the values from above and solving yields:

Tm = 400*50*sin(3deg) = 1046.71 (N-m)

**Example Problem #2**

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

total force (N) = 78

radius (m) = 40

direction of force (degrees) = 12

Enter these given values into the calculator or above yields:

Tm = 78*40*sin(12deg) = 648.68** **(N-m)

## FAQ

**What is torque and why is it important in mechanical systems?**

Torque is a measure of the force that can cause an object to rotate about an axis. It is crucial in mechanical systems because it determines the rotational effect of a force applied to a mechanical component. Understanding torque is essential for designing and analyzing the performance of engines, gears, and other rotating machinery.

**How does the angle of force affect the magnitude of torque?**

The angle of the force directly affects the magnitude of torque through the sine function in the torque calculation formula (Tm = F*r*sin(a)). As the angle changes, the sine of the angle also changes, which in turn affects the magnitude of torque. A force applied at a 90-degree angle to the lever arm (radius) generates the maximum possible torque.

**Can torque be negative, and what does it signify?**

Yes, torque can be negative. The sign of torque (positive or negative) indicates the direction of rotation. Positive torque causes a clockwise rotation, while negative torque results in a counterclockwise rotation. The direction is determined by the right-hand rule, where the thumb points along the axis of rotation and the fingers curl in the direction of the applied force.