⚙️ Torque Calculator
Calculate torque
90° for perpendicular force (maximum torque)
How to Use This Calculator
Enter Force
Input the force (F) in newtons (N). This is the magnitude of the force applied to the object. For example, a 100 N force might be applied by a person pushing on a door or a weight pulling on a lever. Force can be positive or negative, but magnitude is what matters for torque.
Enter Distance from Pivot
Input the distance (r) in meters (m) from the pivot point to the point where the force is applied. This is the lever arm length. For example, if you push a door 0.5 m from the hinge, enter 0.5. The distance must be measured perpendicular to the axis of rotation.
Enter Angle
Input the angle (θ) in degrees between the force vector and the lever arm (distance vector). Default is 90° (perpendicular), which gives maximum torque. At 0° or 180°, torque is zero (force parallel to lever arm). At 90°, sin(90°) = 1, giving maximum torque τ = rF.
Calculate and Review
Click the "Calculate Torque" button to compute the torque in newton-meters (N·m). Torque is a measure of the rotational force - how effectively a force causes rotation. Positive torque causes counterclockwise rotation, negative torque causes clockwise rotation.
Formula
τ = r × F × sin(θ)
Where:
• τ = Torque (N·m)
• r = Distance from pivot (m)
• F = Force (N)
• θ = Angle between force and lever arm (degrees)
For perpendicular force (θ = 90°): τ = rF
For parallel force (θ = 0° or 180°): τ = 0
Example 1: Perpendicular Force
A force of 50 N is applied perpendicular to a lever at a distance of 0.8 m from the pivot. Calculate the torque.
Given:
• Force (F) = 50 N
• Distance (r) = 0.8 m
• Angle (θ) = 90°
Solution:
τ = r × F × sin(θ)
τ = 0.8 × 50 × sin(90°)
τ = 0.8 × 50 × 1
τ = 40 N·m
Example 2: Force at an Angle
A 100 N force is applied at 30° to a lever arm 0.5 m from the pivot. What is the torque?
Given:
• Force (F) = 100 N
• Distance (r) = 0.5 m
• Angle (θ) = 30°
Solution:
τ = 0.5 × 100 × sin(30°)
τ = 0.5 × 100 × 0.5
τ = 25 N·m
Note: At 30°, the effective force is reduced, so torque is half of what it would be at 90°.
Frequently Asked Questions
What is torque?
Torque (τ) is a measure of the rotational force - how effectively a force causes an object to rotate about an axis. It's the rotational equivalent of linear force. Torque depends on three factors: the magnitude of force, the distance from the pivot point (lever arm), and the angle between the force and lever arm. The formula is τ = rF sin(θ).
Why is torque maximum at 90 degrees?
Torque is maximum when the force is perpendicular to the lever arm (θ = 90°) because sin(90°) = 1. At this angle, all of the force contributes to rotation. When the force is parallel to the lever arm (θ = 0° or 180°), sin(θ) = 0, so torque is zero - the force pushes or pulls along the lever but doesn't cause rotation.
What's the difference between torque and force?
Force causes linear acceleration (F = ma), while torque causes angular acceleration (τ = Iα). Force is measured in newtons (N), torque in newton-meters (N·m). A force can push or pull an object in a straight line, while torque twists or rotates an object. The same force can produce different torques depending on where and at what angle it's applied.
How does distance affect torque?
Torque is directly proportional to distance: τ ∝ r. Doubling the distance from the pivot doubles the torque for the same force. This is why longer wrenches make it easier to turn bolts, and why door handles are placed far from hinges - the greater distance multiplies the effect of your force, making rotation easier.
Can torque be negative?
Yes, torque can be negative. The sign indicates the direction of rotation: positive torque causes counterclockwise rotation, negative torque causes clockwise rotation (or vice versa, depending on convention). The magnitude tells you how strong the rotational effect is. When multiple torques act on an object, they add algebraically.
Where is torque used in real-world applications?
Torque is fundamental in: engines and motors (rotational power output), wrenches and tools (applying rotational force), steering systems (turning wheels), propellers and turbines (generating rotation), balance and equilibrium (understanding rotational stability), and any mechanical system involving rotation or turning motion.
About Torque Calculator
The torque calculator computes torque using τ = rF sin(θ) where r is distance from pivot, F is force, and θ is the angle between force and lever arm. Torque is the rotational equivalent of force, measuring how effectively a force causes rotation.
This calculator is essential for engineers designing mechanical systems, students studying rotational dynamics, and anyone analyzing forces that cause rotation. Understanding torque helps explain why longer wrenches make work easier, how engines produce rotational power, and how forces cause objects to turn rather than just move in straight lines.