Force to Torque Calculator

Calculate:

Torque (τ):

Force (F):

Lever Arm Length (r):

Angle (θ) in Degrees:

1. What is a Force to Torque Calculator?

Definition: This calculator determines the torque, force, or lever arm length using the relationship between these variables, based on the formula τ = r × F × sin(θ).

Purpose: It is used in physics, engineering, and mechanical design to analyze rotational forces in systems like motors, bolts, and levers.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \tau = r \times F \times \sin(\theta) \] Where:

\(\tau\): Torque (N·m, lbf·ft)
\(r\): Lever arm length (m, cm, ft, in)
\(F\): Force (N, lbf)
\(\theta\): Angle between force and lever arm (degrees)

Unit Conversions:

Torque Units: N·m, lbf·ft (1 lbf·ft = 1.355818 N·m)
Force Units: N, lbf (1 lbf = 4.44822 N)
Length Units: m, cm, ft, in (1 m = 100 cm, 1 m = 0.3048 ft, 1 m = 39.3701 in)

Steps:

Select the variable to calculate: Torque (τ), Force (F), or Lever Arm Length (r)
Enter the known values, selecting units for torque, force, and length
Enter the angle in degrees (default is 90°)
Convert all inputs to SI units for calculation
Calculate the unknown variable using the formula
Select the desired unit for the result and view the converted value

3. Importance of Force to Torque Calculation

Calculating torque is essential for:

Mechanical Design: Designing systems like engines, gears, and levers where rotational force is critical.
Engineering Applications: Ensuring proper torque for bolts, motors, and other components.
Performance Analysis: Optimizing the efficiency of rotating machinery.

4. Using the Calculator

Examples:

Example 1 (Calculate τ): For a force \(F = 100 \, \text{N}\), lever arm \(r = 50 \, \text{cm}\), and angle \(\theta = 90^\circ\):
- Lever arm in m = \(50 \times 0.01 = 0.5 \, \text{m}\)
- Torque = \(r \times F \times \sin(\theta) = 0.5 \times 100 \times \sin(90^\circ) = 50.000 \, \text{N·m}\)
- In lbf·ft = \(50 \times 0.737562 = 36.878 \, \text{lbf·ft}\)
Example 2 (Calculate F): For a torque \(\tau = 30 \, \text{N·m}\), lever arm \(r = 12 \, \text{in}\), and angle \(\theta = 90^\circ\):
- Lever arm in m = \(12 \times 0.0254 = 0.3048 \, \text{m}\)
- Force = \(\frac{\tau}{r \times \sin(\theta)} = \frac{30}{0.3048 \times \sin(90^\circ)} = 98.425 \, \text{N}\)
- In lbf = \(98.425 \times 0.224809 = 22.116 \, \text{lbf}\)
Example 3 (Calculate r): For a torque \(\tau = 20 \, \text{lbf·ft}\), force \(F = 50 \, \text{lbf}\), and angle \(\theta = 60^\circ\):
- Torque in N·m = \(20 \times 1.355818 = 27.1164 \, \text{N·m}\)
- Force in N = \(50 \times 4.44822 = 222.411 \, \text{N}\)
- Lever arm = \(\frac{\tau}{F \times \sin(\theta)} = \frac{27.1164}{222.411 \times \sin(60^\circ)} = 0.141 \, \text{m}\)
- In cm = \(0.141 \times 100 = 14.100 \, \text{cm}\)
- In in = \(0.141 \times 39.3701 = 5.551 \, \text{in}\)

5. Frequently Asked Questions (FAQ)

Q: What is torque?
A: Torque is the rotational force that causes an object to rotate around an axis, calculated as \(\tau = r \times F \times \sin(\theta)\).

Q: Why is the angle important?
A: The angle determines the effectiveness of the force in producing torque. At 90°, the force is fully effective (\(\sin(90^\circ) = 1\)); at 0° or 180°, no torque is produced (\(\sin(0^\circ) = 0\)).

Q: What is the lever arm length?
A: The lever arm length is the perpendicular distance from the axis of rotation to the point where the force is applied.