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Torque Calculator

Calculate torque (moment of force) about a pivot: τ = rF sin θ

Parameters

Nⓘ
mⓘ
°ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Torque:
20.00;N⋅m20.00;N·m
Perpendicular Lever Arm:
0.40;m0.40;m
sin(θ):
1.00;1.00;

Examples

Wrench

50 N at 0.4 m, 90°.

  • Torque: 20.0020.00

Visualization

Torque and Rotational Effect of Force

Torque (moment of force) measures how effectively a force rotates an object about a pivot. Vector form: τ = r × F. Magnitude: τ = rF sin θ.

Here r is the lever arm (distance from pivot to point of application) and θ is the angle between r and F. Maximum torque when θ = 90° (force perpendicular to arm).

Zero torque when the line of action passes through the pivot (θ = 0°) or when F = 0. Use r_perp = r sin θ as the perpendicular distance to the force line.

Net torque Στ = Iα produces angular acceleration (rotational analog of F = ma). Clockwise vs counterclockwise torques are assigned opposite signs by convention.

Static equilibrium requires Στ = 0 and ΣF = 0. Levers, wrenches, and seesaws are classic torque problems.

Key Concepts

  • τ = rF sin θ = r_perp × F
  • τ = Iα — rotational Newton’s second law
  • Maximum τ at θ = 90°; zero through pivot
  • Sign: clockwise vs counterclockwise
  • N·m is torque unit (not joules)
  • Equilibrium: Στ = 0 and ΣF = 0

Real-World Applications

  • Wrenches, bolts, and mechanical advantage
  • Seesaws, doors, and lever systems
  • Engine crankshafts and flywheels
  • Bridge and crane stability (torque balance)
  • Class 11–12 rotational mechanics

Explore Further

More mechanics tools

Physics Equations

Torque:
τ=rFsin⁡θ\tau = rF \sin\theta
Angular Acceleration:
τ=Iα\tau = I\alpha

Step-by-Step Solution

See how the main results are calculated.

1

Find Perpendicular Lever Arm

Only the component of the lever arm perpendicular to the force line contributes to torque:

Equation:

r⊥=rsin⁡θr_\perp = r \sin\theta

Calculation:

r⊥=(0.4)sin⁡(90°)=0.4×1.0000=0.400 mr_\perp = (0.4) \sin(90°) = 0.4 \times 1.0000 = 0.400 \text{ m}

Result:

r⊥=0.400 mr_\perp = 0.400 \text{ m}

Explanation:

θ is the angle between the lever arm vector and the force vector. At 90°, sin θ = 1 (maximum torque for fixed F and r).

2

Calculate Torque Magnitude

Torque magnitude about the pivot:

Equation:

τ=rFsin⁡θ=r⊥F\tau = r F \sin\theta = r_\perp F

Calculation:

τ=(0.4)(50)sin⁡(90°)\tau = (0.4)(50)\sin(90°)
τ=20.00 N\cdotpm\tau = 20.00 \text{ N·m}

Result:

τ=20.00 N\cdotpm\tau = 20.00 \text{ N·m}

Explanation:

Torque is the rotational analog of force. Sign (clockwise vs counterclockwise) depends on convention; magnitude uses |τ|.

3

Link to Rotational Dynamics

Net torque produces angular acceleration (extended bodies):

Equation:

τnet=Iα\tau_{net} = I\alpha

Calculation:

With I known: α=τ/I\text{With } I \text{ known: } \alpha = \tau / I

Result:

τ=20.00 N\cdotpm\tau = 20.00 \text{ N·m}

Explanation:

N·m is the SI unit of torque (not joules—energy and torque differ). Larger τ or smaller I → greater angular acceleration.

Frequently Asked Questions (FAQ)

What is the SI unit of torque?

Newton-meter (N·m). It has the same dimensions as energy but is not joules—context distinguishes torque from work.

Why use sin θ in τ = rF sin θ?

Only the perpendicular component of force (F sin θ) tends to rotate the body about the pivot.

Can torque be zero with nonzero force?

Yes—when the line of action passes through the pivot (θ = 0°) or when F = 0.

How is torque related to angular acceleration?

Net torque τ_net = Iα, the rotational form of Newton’s second law.

Practice MCQs

  1. At θ = 0°, torque is:
  2. Maximum torque for fixed r and F occurs at:
  3. Doubling lever arm (same F, θ) changes torque by:

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