Torque Calculator
Calculate torque using τ = r × F × sin(θ). Free torque calculator with interactive charts, step-by-step breakdowns for physics and engineering applications.
About This Calculator
The Torque Calculator computes the rotational force (torque) produced when a force is applied at a distance from a pivot point. Using the standard physics formula τ = r × F × sin(θ), it calculates torque in newton-meters (Nm) from the applied force (N), lever arm distance (m), and angle between force and lever arm (°). Perfect for physics students, engineers, mechanics, and anyone working with rotational motion.
Torque quantifies the twisting force that causes an object to rotate around an axis. Unlike linear force which causes straight-line motion, torque depends on three factors: the magnitude of the force, the length of the lever arm (distance from pivot), and the angle at which the force is applied. Maximum torque occurs when the force is perpendicular to the lever arm (θ = 90°). This calculator handles all angles from 0° to 180°.
The torque formula is a fundamental concept in physics and engineering appearing in Newton's second law for rotation (τ = Iα), mechanical advantage calculations, engine power (horsepower = torque × RPM / 5252), bolt tightening specifications, and structural analysis. Engineers use torque calculations daily for designing wrenches, engines, gearboxes, robotic arms, turbines, and countless mechanical systems.
How to Use
Enter the force in newtons (N), the lever arm distance in meters (m), and the angle in degrees (°). The default angle of 90° assumes perpendicular force application. Click Calculate to see the torque value, a detailed breakdown, and interactive charts showing the relationship between the input values and computed torque.
Frequently Asked Questions
What is torque and how is it calculated?
Torque is the rotational equivalent of linear force. It is calculated using the formula τ = r × F × sin(θ), where r is the lever arm distance, F is the applied force, and θ is the angle between the force vector and the lever arm. The result is expressed in newton-meters (Nm).
What is the difference between torque and force?
Force is a push or pull that causes linear acceleration, measured in newtons (N). Torque is the rotational equivalent that causes angular acceleration, measured in newton-meters (Nm). Torque depends not only on the force applied but also on the distance from the pivot point (lever arm) and the angle of application.
Why does the angle matter in torque calculations?
The angle θ determines how much of the applied force contributes to rotation. When force is applied perpendicular to the lever arm (θ = 90°), sin(90°) = 1, producing maximum torque. When force is applied parallel to the arm (θ = 0° or 180°), sin(0°) = 0, producing zero torque. Any angle between 0° and 90° produces a proportional fraction of the maximum torque.
What units does this torque calculator use?
This calculator uses SI units: force in newtons (N), distance in meters (m), and angle in degrees (°). Torque is displayed in newton-meters (Nm). These are the standard scientific and engineering units for torque calculations worldwide.
How do I calculate torque if I know the force and distance?
Enter the force in newtons and the lever arm distance in meters. If the force is applied perpendicular to the lever arm, leave the angle at the default 90°. For example, a 120 N force applied at 0.5 m from the pivot produces 60 Nm of torque (120 × 0.5 × sin(90°) = 60 Nm).
What are real-world applications of torque?
Torque is essential in countless applications: tightening bolts with a wrench, opening doors, engine crankshaft rotation in vehicles, bicycle pedals, wind turbine blades, robotic arm movements, and any situation involving rotational motion. Engineers use torque calculations to design mechanical systems from simple tools to complex machinery.
Can I calculate torque in imperial units?
This calculator uses SI units (N, m, Nm). To convert results to imperial units: 1 Nm = 0.73756 lbf·ft. So 60 Nm is approximately 44.25 lbf·ft. For force, 1 N = 0.224809 lbf. For distance, 1 m = 3.28084 ft.
Is this torque calculator suitable for engineering use?
Yes, this calculator uses the standard physics formula τ = r × F × sin(θ) with precise floating-point computation. It is suitable for educational purposes, physics homework, engineering prototyping, and general mechanical calculations. For critical engineering applications, always verify results with additional methods.