Rotational force tool

Torque Calculator

Solve torque, force, or lever-arm distance using τ = Fr.

Enter two known values

Solve a torque problem

Free tool
N·m

This is the value being calculated.

N

Positive perpendicular force applied to the lever.

m

Perpendicular distance from the pivot to the force.

Use newton-meters for torque, newtons for force, and meters for the lever arm.

Try an example:

Your torque result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Torque Calculator determines the rotational force produced when a force acts on an object around a pivot point. It helps physics students, engineers, and laboratory users analyze motors, tools, machines, robotics, and mechanical systems using force, lever arm distance, and angle relationships.

Formula explanation

Torque measures rotational force and depends on applied force and perpendicular distance.

Formula

Torque = Force × Lever Arm Distance × sin(Angle)

Worked example

Example: Increasing lever arm distance increases rotational effect.

Assumptions

  • Force and distance measurements are accurate.
  • The angle between force and lever arm is correctly measured.
  • Input values use compatible units.
  • The system follows ideal rotational mechanics conditions.

Examples

  • Example: Calculate torque when force, distance, and angle are known.
  • Example: Engineers analyze motors, tools, gears, and mechanical systems using torque calculations.

Common mistakes

  • Using incorrect angle values.
  • Confusing force and torque.
  • Ignoring rotational direction.

Variables

  • Applied force
  • Lever arm distance
  • Angle between force and lever arm
  • Torque
  • Rotational conditions
  • Measurement units

Limitations

  • Results assume ideal rotational conditions.
  • Complex mechanical systems with multiple forces may require advanced torque analysis methods.

Scientific references

  • OpenStax University Physics: Rotational Dynamics
  • NIST SI Units and Measurement References
  • Engineering mechanics references

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Rotational mechanics analysis
  • Engineering machine design
  • Motor and engine analysis
  • Robotics and mechanical systems
  • Laboratory force and motion experiments

Frequently asked questions

How is torque calculated?

Torque is calculated by multiplying force, lever arm distance, and the sine of the angle between them using τ = rFsin(θ).

What is torque?

Torque is the rotational effect of a force that causes an object to rotate around an axis or pivot point.

What factors affect torque?

Torque depends on the applied force, distance from the rotation axis, and the angle at which the force is applied.

What is the difference between torque and force?

Force causes linear acceleration, while torque describes the rotational effect of a force around an axis.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Physics overview

What is torque?

Torque measures the turning effect of a force around a pivot or axis. Greater force or a longer lever arm produces greater torque.

Formula

Torque formula

Torqueτ = Fr

  • τ is torque in newton-meters.
  • F is perpendicular force in newtons.
  • r is lever-arm distance in meters.

Worked example

An 80 N force acts 0.5 m from a pivot

  1. Write the formula: τ = Fr.
  2. Substitute the values: τ = 80 × 0.5.
  3. Calculate the torque: τ = 40 N·m.

Force direction

Perpendicular force assumption

This calculator uses τ = Fr, which assumes the force acts perpendicular to the lever arm. For a force at an angle, the general formula is τ = Fr sin θ.

Rearranged equations

Solve for force or lever arm

Force

F = τ ÷ r

Divide torque by lever-arm distance.

Lever Arm

r = τ ÷ F

Divide torque by force.

Units

Standard SI units

Use newton-meters for torque, newtons for force, and meters for the lever arm.

Real-world applications

Where torque calculations are used

  • Wrenches, spanners, and fasteners.
  • Doors, levers, and rotating handles.
  • Motors, shafts, and mechanical systems.
  • Laboratory rotational-equilibrium experiments.

Calculation limits

Important assumptions

  • Torque, force, and lever arm must be greater than zero.
  • Force is assumed to act perpendicular to the lever arm.
  • Lever arm means perpendicular distance from the pivot.
  • The calculator uses magnitudes and does not represent rotation direction.
  • Units are not converted automatically.

Related tools

Use the Force Calculator to solve force, mass, or acceleration.

Use the Work Calculator to calculate work, force, or distance.

Questions and answers

Calculator FAQ

How is torque calculated?

Torque is calculated by multiplying force, lever arm distance, and the sine of the angle between them using τ = rFsin(θ).

What is torque?

Torque is the rotational effect of a force that causes an object to rotate around an axis or pivot point.

What factors affect torque?

Torque depends on the applied force, distance from the rotation axis, and the angle at which the force is applied.

What is the difference between torque and force?

Force causes linear acceleration, while torque describes the rotational effect of a force around an axis.