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What is Torque (Moment of Force)?

Torque or moment of force is a physical quantity that measures the ability of a force to cause an object to rotate about an axis or pivot point. In everyday life, we often use the concept of torque without realizing it: when opening a door, using a wrench, turning a bicycle wheel, or lifting a load with a lever. Kalkulab's Torque Calculator is designed to help high school students, engineering students, and mechanical practitioners calculate torque quickly and accurately. Using the basic formula τ = F × r × sin(θ), this calculator can compute moment of force, required force, lever arm length, and torque equilibrium. The tool supports multiple calculation modes including finding a missing variable and checking torque balance conditions.

Torque Formula

τ = F × r × sin(θ)Formula: F = τ / (r × sin(θ)); r = τ / (F × sin(θ)); Στ = 0 (equilibrium)

Variables:

  • τTorque/Moment of Force
    Ability of a force to cause rotation about a specific axis(e.g.: 50 N·m)
  • FForce
    Magnitude of the force applied to the object(e.g.: 100 N)
  • rLever Arm/Distance
    Perpendicular distance from the axis to the line of action of the force(e.g.: 0.5 m)
  • θAngle
    Angle between the force vector and the lever arm(e.g.: 90°)
  • sin(θ)Sine Function
    Determines the component of force contributing to rotation, maximum at 90°(e.g.: 1 (at θ=90°))

Categories:

Fixed Axis Rotationτ = F × r × sin(θ)
EquilibriumΣτ = 0 (Clockwise torque = Counter-clockwise torque)

How to Use the KalkuLab Torque Calculator

Using the torque calculator is straightforward. Follow these steps based on your calculation needs:

  1. 1

    Select Calculation Mode

    Choose from 4 modes: Calculate Torque, Calculate Force, Calculate Lever Arm, or Torque Equilibrium.

  2. 2

    Enter Known Values

    Input known values for the selected mode (force, distance, angle, or torque).

  3. 3

    Set Angle (Optional)

    Enter the angle between force and lever arm. Default 90° gives maximum torque. For force parallel to lever (θ=0°), torque = 0.

  4. 4

    Click Calculate

    Press calculate for results with step-by-step solution.

  5. 5

    Analyze Equilibrium (Equilibrium Mode)

    For equilibrium mode, enter two force-lever pairs and see if the system is balanced (Στ = 0).

💡 Tip:

  • •Maximum torque occurs at θ = 90° (sin 90° = 1), force perpendicular to lever arm
  • •Torque is zero if force is parallel to lever (θ = 0° or 180°)
  • •Use right-hand rule to determine rotation direction (CW/CCW)
  • •In torque equilibrium, total clockwise torque = total counterclockwise torque
  • •Torque unit is N·m (Newton meter), not Joule despite same dimensions

Examples

Example 1: Torque on a Door

Problem:

Someone pushes a door with 50 N at 0.8 m from the hinge, perpendicular (θ=90°). What torque?

Solution:
  1. 1.τ = F × r × sin(θ)
  2. 2.τ = 50 × 0.8 × sin(90°) = 40 N·m
Result:40 N·m

Torque is 40 N·m. This is why door handles are placed far from hinges — greater torque with same force.

Example 2: Force to Tighten a Bolt

Problem:

Wrench lever arm 0.3 m. Need 60 N·m torque. Force perpendicular (θ=90°)?

Solution:
  1. 1.F = τ / (r × sin(θ))
  2. 2.F = 60 / (0.3 × 1) = 200 N
Result:200 N

200 N force needed with 0.3 m wrench. Longer wrench requires less force.

Example 3: Torque at an Angle

Problem:

1.5 m lever pushed with 80 N at 30° to lever. Torque? (sin 30° = 0.5)

Solution:
  1. 1.τ = 80 × 1.5 × sin(30°) = 60 N·m
Result:60 N·m

Torque is 60 N·m, less than if force were perpendicular (90°), since only the perpendicular component contributes.

Example 4: Seesaw Equilibrium

Problem:

Child A (300 N) sits 2 m left of pivot. Child B (400 N) on right. Where must B sit for balance?

Solution:
  1. 1.τ_left = τ_right
  2. 2.300 × 2 = 400 × r_B
  3. 3.r_B = 600/400 = 1.5 m
Result:1.5 m

Child B must sit 1.5 m from pivot. Heavier person sits closer to pivot.

Example 5: Lever Arm for Required Torque

Problem:

Machine needs 250 N·m torque. Available force 500 N at 90°. Required lever arm?

Solution:
  1. 1.r = τ / (F × sin(θ))
  2. 2.r = 250 / (500 × 1) = 0.5 m
Result:0.5 m

0.5 m lever arm needed. Longer arm allows greater torque with same force.

Frequently Asked Questions

What is torque and why is it important in physics?
Torque (moment of force) measures a force's ability to cause rotation about an axis. Essential in mechanics for understanding how objects rotate — wheels turning, doors opening, machines running. Without torque, we cannot understand rotational dynamics.
Why does 90° give maximum torque?
Because sin(90°) = 1, the maximum value of the sine function. At 90°, force acts perpendicular to the lever arm, so the entire force contributes to rotation. At other angles, only the perpendicular component produces torque.
What is the difference between torque and linear force?
Linear force causes translational motion (sliding). Torque causes rotational motion (spinning). Torque is force multiplied by perpendicular distance from the rotation axis. Pulling a bike chain is linear force; pedaling creates torque.
What is torque equilibrium and what are its conditions?
Torque equilibrium occurs when total torque on an object equals zero (Στ = 0). Clockwise torque equals counterclockwise torque. The object has no rotational acceleration (stays still or rotates at constant angular velocity).
Why is a longer wrench easier to use?
A longer wrench has a greater lever arm (r). Since τ = F × r, the same torque requires less force (F) with a longer arm. This is why long wrenches loosen tight bolts more easily.
Does torque have direction? How do I determine it?
Yes, torque is a vector. Use the right-hand rule: curl fingers in rotation direction, thumb points along the torque vector (out of plane for counterclockwise, into plane for clockwise).
What is the difference between N·m and Joule?
Despite same physical dimensions, torque uses N·m and energy uses Joule. Torque relates to rotation (force × perpendicular distance); energy relates to work (force × parallel distance). Convention avoids confusing the two.
Who should use this calculator?
Ideal for high school students learning rotational dynamics, engineering students, professionals working with rotating machinery, vehicle mechanics, and anyone studying rotational mechanics.

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References