🔩 Torque Calculator
τ = F × r × sin(θ) — Calculate torque or find force / lever arm.
Result
How to Use This Calculator
Choose whether you want to find torque (N·m), force (N), or lever arm length (m), then fill in the remaining three values. The angle field defaults to 90° because that gives maximum torque, but you can change it for any direction of applied force.
Select what you want to solve for: Torque, Force, or Lever Arm from the dropdown menu.
Enter the force in newtons. If you only know the force in kilogram-force, multiply by 9.81 (e.g., 10 kgf = 98.1 N).
Enter the lever arm in metres. This is the distance from the pivot point to where the force is applied.
Set the angle between the force direction and the lever arm. Perpendicular (90°) gives the maximum torque for a given force and distance.
Torque Formula
The sin(θ) factor means only the component of force perpendicular to the lever arm contributes to rotation. Push a door directly toward the hinge and θ = 0°, so sin(0°) = 0: no rotation. Push perpendicular to the door (θ = 90°) and you get the full torque. This is why door handles are placed as far from the hinge as possible.
Worked Examples
Where This Comes Up in Real Life
A car mechanic tightening a bolt needs a specific torque to avoid stripping threads or causing a fatigue failure. A typical car wheel bolt needs about 120 N·m of torque. With a 0.3 m wrench applying force at 90°, the required force is 120 / (0.3 × 1) = 400 N, roughly 40 kgf. Go to 0.4 m with a breaker bar and the required force drops to 300 N, which is why long-handled tools feel so much easier to use.
Electric motors are rated partly by their torque output. A motor producing 50 N·m and spinning at 3000 RPM delivers a power of τ × ω = 50 × 314 = 15,700 W, about 15.7 kW. Engineers balance torque and angular velocity when selecting motors, gears, and drive shafts for machines. In robotics, every joint has a torque limit that determines how much load the arm can handle at a given reach.
Frequently Asked Questions
What is torque?
Torque (τ) is the rotational equivalent of force. It measures how much a force causes an object to rotate about an axis. τ = r × F × sin(θ).
What is the lever arm?
The lever arm (r) is the perpendicular distance from the pivot point to the line of action of the force. Maximum torque occurs when force is perpendicular (θ = 90°).
What are the units of torque?
Newton-meters (N·m) in SI. In imperial: foot-pounds (ft·lb) or inch-pounds (in·lb).
What is the right-hand rule for torque?
Curl the fingers of your right hand from r to F; your thumb points in the direction of the torque vector.
How does torque relate to angular acceleration?
τ = I × α, where I is the moment of inertia and α is angular acceleration — the rotational analog of F = ma.