Torque Calculator
Torque (τ) = Force (F) × Distance (d) × sin(θ)
How to Use the Torque Calculator
- Choose What to Calculate: Select the value you want to calculate from the dropdown menu at the top: Torque, Distance, or Force. The calculator will show only the fields required for your selection.
- Enter the Required Inputs
– If calculating Torque, input the force, distance, and angle values.
– If calculating Distance, input the torque, force, and angle values.
– If calculating Force, input the torque, distance, and angle values.
Use the unit selectors next to each input field to set your preferred measurement units. - Set the Angle: Enter the angle (in degrees or radians) between the applied force and the lever arm.
- Click “Calculate”: Once all the required fields are filled in, click the “Calculate” button. The result will appear below the calculator along with a detailed breakdown of the calculation steps.
- Review and Share Results: The calculator provides a shareable link that includes your inputs and results, making it easy to save or share your work. Simply copy the link from the result section.
What is Torque?
Torque is a measure of the rotational force applied to an object. Think of it as the twist or turn that causes something to rotate around an axis. Whether you’re tightening a bolt with a wrench or turning the steering wheel of a car, torque is at work.
The basic formula for torque is:
τ=F×d×sin(θ)
- F (Force): The push or pull applied.
- d (Distance): How far from the pivot point the force is applied.
- θ (Angle): The angle between the force and the lever arm.
Understanding torque helps in designing tools, vehicles, and machinery to ensure they operate efficiently and safely.
Examples
Here are a few scenarios where the Torque Calculator can come in handy:
Example 1: Calculating Torque with Given Force and Distance
- Force: 100 N
- Distance: 2 m
- Angle: 90°
- Desired Output Unit: Newton meters (Nm)
Torque Calculation: τ=F×d×sin(θ)=100 N×2 m×sin(90°)=200 Nm
- Convert Angle to Radians: θ=90°=π2 rad
- Calculate Sine of Angle: sin(π2)=1
- Compute Torque: τ=100 N×2 m×1=200 Nm
Final Result: τ=200 Nm
Example 2: Calculating Torque with Different Units
- Force: 50 lbf
- Distance: 1 ft
- Angle: 45°
- Desired Output Unit: Pound-force feet (lbf·ft)
Torque Calculation: τ=F×d×sin(θ)=50 lbf×1 ft×sin(45°)≈50 lbf×1 ft×0.7071≈35.355 lbf
- Convert Angle to Radians: θ=45°=π4 rad
- Calculate Sine of Angle: sin(π4)≈0.7071
- Compute Torque: τ=50 lbf×1 ft×0.7071≈35.355 lbf
Final Result: τ≈35.36 lbf
(Rounded to two decimal places)
Example 3: Using Radians for Angle
- Force: 20 kgf
- Distance: 50 cm
- Angle: 1 rad
- Desired Output Unit: Kilogram-force centimeters (kgf·cm)
Torque Calculation:τ=F×d×sin(θ)=20 kgf×50 cm×sin(1 rad)≈20 kgf×50 cm×0.8415≈841.5 kgf
- Compute Sine of Angle: sin(1 rad)≈0.8415
- Compute Torque: τ=20 kgf×50 cm×0.8415≈841.5 kgf
Final Result: τ≈841.5 kgf
(Rounded to one decimal place)
Notes on Units and Conversions
Newton meters (Nm): SI unit for torque.
Kilogram-force centimeters (kgf·cm): Commonly used in certain engineering contexts.
Joules per radian (J/rad): Equivalent to Nm since 1 J = 1 Nm.
Pound-force feet (lbf·ft) & Pound-force inches (lbf·in): Imperial units for torque.
Newton centimeters (N·cm) & Newton millimeters (N·mm): Smaller SI units derived from Nm.